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A SYSTEM  OE  LOGIC, 

BATIOCINATIYE  AND  INDUCTIVE: 

BEING  A 

CONNECTED  YIEW  OF  THE  PRINCIPLES  OF  EYIDENCE 

AND  THE 

METHODS  OF  SCIENTIFIC  INVESTIGATION. 


JOHN  STUART  MILL. 


EIGHTH  EDITION. 


NEW  YORK: 

HARPER  & BROTHERS,  PUBLISHERS, 

FRANKLIN  SQUARE. 

1 8 9 O0 


/ & 0 

c ' 2-  PREFACE  TO  THE  FIRST  EDITION. 


This  book  makes  no  pretense  of  giving  to  the  world  a new  theory  of  the 
intellectual  operations.  Its  claim  to  attention,  if  it  possess  any,  is  ground- 
ed on  the  fact  that  it  is  an  attempt,  not  to  supersede,  but  to  embody  and 
systematize,  the  best  ideas  which  have  been  either  promulgated  on  its  sub- 
ject by  speculative  writers,  or  conformed  to  by  accurate  thinkers  in  their 
scientific  inquiries. 

To  cement  together  the  detached  fragments  of  a subject,  never  yet  treat- 
ed as  a whole ; to  harmonize  the  true  portions  of  discordant  theories,  by 
supplying  the  links  of  thought  necessary  to  connect  them,  and  by  disentan- 
gling them  from  the  errors  with  which  they  are  always  more  or  less  inter- 
woven, must  necessarily  require  a considerable  amount  of  original  specula- 
tion. To  other  originality  than  this,  the  present  work  lays  no  claim.  In 
the  existing  state  of  the  cultivation  of  the  sciences,  there  would  be  a very 
strong  presumption  against  any  one  who  should  imagine  that  he  had  effect- 
ed a revolution  in  the  theory  of  the  investigation  of  truth,  or  added  any 
fundamentally  new  process  to  the  practice  of  it.  The  improvement  which 
remains  to  be  effected  in  the  methods  of  philosophizing  (and  the  author  be- 
lieves that  they  have  much  need  of  improvement)  can  only  consist  in  per- 
forming more  systematically  and  accurately  operations  with  which,  at  least 
in  their  elementary  form,  the  human  intellect,  in  some  one  or  other  of  its 
employments,  is  already  familiar. 

In  the  portion  of  the  work  which  treats  of  Ratiocination,  the  author  has 
not  deemed  it  necessary  to  enter  into  technical  details  which  may  be  ob- 
tained in  so  perfect  a shape  from  the  existing  treatises  on  what  is  termed 
the  Logic  of  the  Schools.  In  the  contempt  entertained  by  many  modern 
philosophers  for  the  syllogistic  art,  it  will  be  seen  that  he  by  no  means  par- 
ticipates ; though  the  scientific  theory  on  which  its  defense  is  usually  rest- 
ed appears  to  him  erroneous:  and  the  view  which  he  has  suggested  of  the 
nature  and  functions  of  the  Syllogism  may,  perhaps,  afford  the  means  of 
conciliating  the  principles  of  the  art  with  as  much  as  is  well  grounded  in 
the  doctrines  and  objections  of  its  assailants. 

The  same  abstinence  from  details  could  not  be  observed  in  the  First 
Book,  on  Names  and  Propositions  ; because  many  useful  principles  and  dis- 


IV 


PREFACE. 


tinetions  which  were  contained  in  the  old  Logic  have  been  gradually  omit- 
ted from  the  writings  of  its  later  teachers;  and  it  appeared  desirable  both 
to  revive  these,  and  to  reform  and  rationalize  the  philosophical  foundation 
on  which  they  stood.  The  earlier  chapters  of  this  preliminary  Book  will 
consequently  appear,  to  some  readers,  needlessly  elementary  and  scholastic. 
But  those  who  know  in  what  darkness  the  nature  of  our  knowledge,  and 
of  the  processes  by  which  it  is  obtained,  is  often  involved  by  a confused 
apprehension  of  the  import  of  the  different  classes  of  Words  and  Asser- 
tions, will  not  regard  these  discussions  as  either  frivolous,  or  irrelevant  to 
the  topics  considered  in  the  later  Books. 

On  the  subject  of  Induction,  the  task  to  be  performed  was  that  of  gener- 
alizing the  modes  of  investigating  truth  and  estimating  evidence,  by  which 
so  many  important  and  recondite  laws  of  nature  have,  in  the  various  sci- 
ences, been  aggregated  to  the  stock  of  human,  knowledge.  That  this  is  not 
a task  free  from  difficulty  may  be  presumed  from  the  fact  that  even  at  a 
very  recent  period,  eminent  writers  (among  whom  it  is  sufficient  to  name 
Archbishop  Whately,  and  the  author  of  a celebrated  article  on  Bacon  in  the 
Edinburgh  lleview)  have  not  scrupled  to  pronounce  it  impossible.*  The 
author  has  endeavored  to  combat  their  theory  in  the  manner  in  which  Di- 
ogenes confuted  the  skeptical  reasonings  against  the  possibility  of  motion  ; 
remembering  that  Diogenes’s  argument  would  have  been  equally  conclu- 
sive, though  his  individual  perambulations  might  not  have  extended  be- 
yond the  circuit  of  his  own  tub. 

Whatever  may  be  the  value  of  what  the  author  has  succeeded  in  effect- 
ing on  this  branch  of  his  subject,  it  is  a duty  to  acknowledge  that  for  much 
of  it  he  has  been  indebted  to  several  important  treatises,  partly  historical 
and  partly  philosophical,  on  the  generalities  and  processes  of  physical  sci- 
ence, which  have  been  published  within  the  last  few  years.  To  these  trea- 
tises, and  to  their  authors,  he  has  endeavored  to  do  justice  in  the  body  of 
the  work.  But  as  with  one  of  these  writers,  Dr.  Whewell,  he  has  occasion 
frequently  to  express  differences  of  opinion,  it  is  more  particularly  incum- 
bent  on  him  in  this  place  to  declare,  that  without  the  aid  derived  from  the 

* In  the  later  editions  of  Archbishop  Whately’s  “Logic,”  he  states  his  meaning  to  be,  not 
that  “rules”  for  the  ascertainment  of  truths  by  inductive  investigation  can  not  be  laid  down, 
or  that  they  may  not  be  “of  eminent  service,”  but  that  they  “must  always  be  comparatively 
vague  and  general,  and  incapable  of  being  built  up  into  a regular  demonstrative  theory  like 
that  of  the  Syllogism.”  (Book  iv.,  ch.  iv.,  § 3.)  And  he  observes,  that  to  devise  a system 
for  this  purpose,  capable  of  being  “brought  into  a scientific  form,”  would  be  an  achievement 
which  “he  must  be  more  sanguine  than  scientific  who  expects.”  (Book  iv.,  ch.  ii.,  § 4.)  To 
effect  this,  however,  being  the  express  object  of  the  portion  of  the  present  work  which  treats 
of  Induction,  the  words  in  the  text  are  no  overstatement  of  the  difference  of  opinion  between 
Archbishop  Whately  and  me  on  the  subject. 


PREFACE. 


V 


facts  and  ideas  contained  in  that  gentleman’s  “ History  of  the  Inductive 
Sciences,”  the  corresponding  portion  of  this  work  would  probably  not  have 
been  written. 

The  concluding  Book  is  an  attempt  to  contribute  toward  the  solution  of 
a question  which  the  decay  of  old  opinions,  and  the  agitation  that  disturbs 
European  society  to  its  inmost  depths,  render  as  important  in  the  present 
day  to  the  practical  interests  of  human  life,  as  it  must  at  all  times  be  to  the 
completeness  of  our  speculative  knowledge — viz. : Whether  moral  and  so- 
cial phenomena  are  really  exceptions  to  the  general  certainty  and  uniformi- 
ty of  the  course  of  nature ; and  how  far  the  methods  by  which  so  many  of 
the  laws  of  the  physical  world  have  been  numbered  among  truths  irrevo- 
cably acquired  and  universally  assented  to,  can  be  made  instrumental  to 
the  formation  of  a similar  body  of  received  doctrine  in  moral  and  political 


science. 


PREFACE  TO  THE  THIRD  AND  FOURTH  EDITIONS. 


Several  criticisms,  of  a more  or  less  controversial  character,  on  this 
work,  have  appeared  since  the  publication  of  the  second  edition ; and  Dr. 
Whewell  has  lately  published  a reply  to  those  parts  of  it  in  which  some  of 
his  opinions  were  controverted.* 

I have  carefully  reconsidered  all  the  points  on  which  my  conclusions 
have  been  assailed.  But  I have  not  to  announce  a change  of  opinion  on 
any  matter  of  importance.  Such  minor  oversights  as  have  been  detected, 
either  by  myself  or  by  my  critics,  I have,  in  general  silently,  corrected  : but 
it  is  not  to  be  inferred  that  I agree  with  the  objections  which  have  been 
made  to  a passage,  in  every  instance  in  which  I have  altered  or  canceled  it. 
I have  often  done  so,  merely  that  it  might  not  remain  a stumbling-block, 
when  the  amount  of  discussion  necessary  to  place  the  matter  in  its  true 
light  would  have  exceeded  what  was  suitable  to  the  occasion. 

To  several  of  the  arguments  which  have  been  urged  against  me,  I have 
thought  it  useful  to  reply  with  some  degree  of  minuteness ; not  from  any 
taste  for  controversy,  but  because  the  opportunity  was  favorable  for  pla- 
cing my  own  conclusions,  and  the  grounds  of  them,  more  clearly  and  com- 
pletely before  the  reader.  Truth  on  these  subjects  is  militant,  and  can 
only  establish  itself  by  means  of  conflict.  The  most  opposite  opinions  can 
make  a plausible  show  of  evidence  while  each  has  the  statement  of  its  own 
case ; and  it  is  only  possible  to  ascertain  v'hich  of  them  is  in  the  right,  af- 
ter hearing  and  comparing  what  each  can  say  against  the  other,  and  what 
the  other  can  urge  in  its  defense. 

Even  the  criticisms  from  which  I most  dissent  have  been  of  great  serv- 
ice to  me,  by  show'ing  in  what  places  the  exposition  most  needed  to  be 
improved,  or  the  argument  strengthened.  And  I should  have  been  -well 
pleased  if  the  book  had  undergone  a much  greater  amount  of  attack ; as  in 
that  case  I should  probably  have  been  enabled  to  improve  it  still  more  than 
I believe  I have  now  done. 

In  the  subsequent  editions,  the  attempt  to  improve  the  work  by  addi- 
tions and  corrections,  suggested  by  criticism  or  by  thought,  has  been  con- 
* Now  forming  a chapter  in  his  volume  on  “The  Philosophy  of  Discovery.” 


PREFACE. 


viii 

turned.  The  additions  and  corrections  in  the  present  (eighth)  edition, 
which  are  not  very  considerable,  are  chiefly  such  as  have  been  suggested 
by  Professor  Bain’s  “ Logic,”  a book  of  great  merit  and  value.  Mr.  Bain’s 
view  of  the  science  is  essentially  the  same  with  that  taken  in  the  present 
treatise,  the  differences  of  opinion  being  few  and  unimportant  compared 
with  the  agreements ; and  he  has  not  only  enriched  the  exposition  by  many 
applications  and  illustrative  details,  but  has  appended  to  it  a minute  and 
very  valuable  discussion  of  the  logical  principles  specially  applicable  to 
each  of  the  sciences — a task  for  which  the  encyclopedical  character  of  his 
knowledge  peculiarly  qualified  him.  I have  in  several  instances  made  use 
of  his  exposition  to  improve  my  own,  by  adopting,  and  occasionally  by 
controverting,  matter  contained  in  his  treatise. 

The  longest  of  the  additions  belongs  to  the  chapter  on  Causation,  and  is 
a discussion  of  the  question  how  far,  if  at  all,  the  ordinary  mode  of  stating 
the  law  of  Cause  and  Effect  requires  modification  to  adapt  it  to  the  new 
doctrine  of  the  Conservation  of  Force — a point  still  more  fully  and  elabo- 
rately treated  in  Mr.  Bain’s  work. 


CONTENTS 


INTRODUCTION. 

PAGE 


§ 1.  A definition  at  the  commencement  of  a sub- 
ject must  be  provisional 17 

2.  Is  logic  the  art  and  science  of  reasoning  ?.  17 

3.  Or  the  art  and  science  of  the  pursuit  of 

truth? 18 

4.  Logic  is  concerned  with  inferences,  not 

with  intuitive  truths 19 

5.  Relation  of  logic  to  the  other  sciences 21 

6.  Its  utility,  how  shown 22 

7.  Definition  of  logic  stated  and  illustrated..  23 


BOOK  I. 

OF  NAMES  AND  PROPOSITIONS. 

Chapter  1.  Of  the  Necessity  of  commencing  with  an 
Analysis  of  Language. 

§ 1.  Theory  of  names,  why  a necessary  part  of 


logic 26 

2.  First  step  in  the  analysis  of  Propositions..  27 

3.  Names  must  be  studied  before  Things 28 


Chapter  II.  Of  Names. 

§1.  Names  are  names  of  things,  not  of  onrideas  29 
2.  Words  which  are  not  names,  but  parts  of 


names 30 

3.  General  and  Singular  names 32 

4.  Concrete  and  Abstract 33 

5.  Connotative  and  Non-conuotative 34 

6.  Positive  and  Negative 41 

7.  Relative  and  Absolute 42 

8.  Univocal  and  ASquivocal 44 

Chapter  III.  Of  the  Things  denoted  by  Names. 
51.  Necessity  of  an  enumeration  of  Namable 

Things.  The  Categories  of  Aristotle 45 

2.  Ambiguity  of  the  most  general  names 46 

3.  Peelings,  or  states  of  consciousness 48 

4.  Feelings  must  be  distinguished  from  their 

physical  antecedents.  Perceptions,  what.  49 

5.  Volitions,  and  Actions,  what 51 

6.  Substance  and  Attribute 51 

7.  Body 52 

8.  Mind 56 

9.  Qualities 57 

10.  Relations 59 

11.  Resemblance 60 

12.  Quantity 62 

13.  All  attributes  of  bodies  are  grounded  on 

states  of  consciousness 63 

14.  So  also  all  attributes  of  mind 64 

15.  Recapitulation 64 


PAGE 


Chapter  IV.  Of  Propositions. 

§1.  Nature  and  office  of  the  copula 66 

2.  Affirmative  and  Negative  propositions 67 

3.  Simple  and  Complex 69 

4.  Universal,  Particular,  and  Singular 71 

Chapter  V.  Of  the  Import  of  Propositions. 

§ 1.  Doctrine  that  a proposition  is  the  expres- 
sion of  a relation  between  two  ideas 73 

2.  — that  it  is  the  expression  of  a relation  be- 

tween the  meanings  of  two  names 75 

3.  — that  it  consists  in  referring  something 

to,  or  excluding  something  from,  a class.  71 

4.  What  it  really  is 80 

5.  It  asserts  (or  denies)  a sequence,  a co-exist- 

ence, a simple  existence,  a causation SI 

6.  — or  a resemblance 83 

7.  Propositions  of  which  the  terms  are  ab- 

stract  86 

Chapter  VI.  Of  Propositions  merely  Verbal. 

5 1.  Essential  and  Accidental  propositions 8S 

2.  All  essential  propositions  are  identical 

propositions S9 

3.  Individuals  have  no  essences 91 

4.  Real  propositions,  how  distinguished  from 

verbal 92 

5.  Two  modes  of  representing  the  import  of 

a Real  proposition 93 


Chapter  VII.  Of  the  Nature  of  Classification,  and 


the  Five  Predicables. 

§1.  Classification,  how  connected  with  Naming  94 

2.  The  Predicables,  what 95 

3.  Genus  and  Species 95 

4.  Kinds  have  a real  existence  in  nature 97 

5.  Differentia 100 

6.  Differentiae  for  general  purposes,  and  differ- 

entiae for  special  or  technical  purposes. . . 101 

7.  Proprium 103 

8.  Accidens 104 

Chapter  VIII.  Of  Definition. 

§1.  A definition,  what 105 

2.  Every  name  can  be  defined,  whose  meaning 

is  susceptible  of  analysis 106 

3.  Complete,  how  distinguished  from  incom- 

plete definitions 107 

4.  — and  from  descriptions 108 

5.  What  are  called  definitions  of  Things,  are 

definitions  of  Names  with  an  implied  as- 
sumption of  the  existence  of  Things  cor- 
responding to  them Ill 

6.  — • even  when  such  things  do  not  in  reality 

exist 116 


X 


CONTENTS. 


PAGE 

5 7.  Definitions,  though  of  names  only,  must  be 
grounded  on  knowledge  of  the  corre- 
sponding things 117 


BOOK  II. 

OF  REASONING. 

Ch  apter  I.  Of  Inference,  or  Reasoning,  in  general. 


51.  Retrospect  of  the  preceding  book 121 

2.  Inferences  improperly  so  called 122 

3.  /Inferences  proper,  distinguished  into  in- 

ductions and  ratiocinations 125 

Chapter  II.  Of  Ratiocination,  or  Syllogism. 

5 1.  Analysis  of  the  Syllogism 126 

2.  The  dictum  de  (mini  not  the  foundation  of 

reasoning,  but  a mere  identical  proposi- 
tion  132 

3.  What  is  the  really  fundamental  axiom  of 

Ratiocination 135 

4.  The  other  form  of  the  axiom 137 


Chapter  III.  Of  the  Functions,  and  Logical  Value 


of  the  Syllogism. 

51.  Is  the  Syllogism  a petitio principal 139 

2.  Insufficiency  of  the  common  theory 139 

3.  All  inference  is  from  particulars  to  partic- 

ulars   141 

4.  General  propositions  are  a record  of  such 

inferences,  and  the  rules  of  the  syllogism 
are  rules  for  the  interpretation  of  the 
record 146 

5.  The  syllogism  not  the  type  of  reasoning, 


The  true  type,  what 151 

ft.  Relation  between  Induction  and  Deduc- 
I tion 153 

8.  Objections  answered 154 

9.  Of  Formal  Logic,  and  its  relation  to  the 

Logic  of  Truth 156 


Chapter  IV.  Of  Trains  of  Reasoning,  and  Deduct- 


ive Sciences. 

51.  For  what  purpose  trains  of  reasoning  exist.  153 

2.  A train  of  reasoning  is  a series  of  induct- 

ive inferences 158 

3.  — from  particulars  to  particulars  through 

marks  of  marks 160 

4.  W’hy  there  are  deductive  sciences 161 

5.  Why  other  sciences  still  remain  experi- 

mental  164 

6.  Experimental  sciences  may  become  deduct- 

ive by  the  progress  of  experiment 165 

7.  In  what  manner  this  usually  takes  place..  166 


Chapter  V.  Of  Demonstration,  and  Necessary 


Truths. 

51.  The  Theorems  of  geometry  are  necessary 
truths  only  in  the  sense  of  necessarily  fol- 
lowing from  hypotheses 168 

2.  Those  hypotheses  are  real  facts  with  some 

of  their  circumstances  exaggerated  or 
omitted 170 

3.  Some  of  the  first  principles  of  geometry  are 

axioms,  and  these  are  not  hypothetical. . 171 

4.  — but  are  experimental  truths 172 


PAGE 


55.  An  objection  answered 174 

6.  Dr.  Whewell’s  opinions  on  axioms  exam- 
ined  176 

Chapter  VI.  The  same  Subject  continued. 

51.  All  deductive  sciences  are  inductive 187 

2.  The  propositions  of  the  science  of  number 
are  not  verbal,  but  generalizations  from 
experience 188 


4.  The  characteristic  property  of  demonstra/ 

five  science  is  to  be  hypothetical 192 

0.  Definition  of  demonstrative  evidence 193 

| Cuapter  VII.  Examination  of  some  Opinions  op- 
posed to  the  preceding  doctrines. 

51.  Doctrine  of  the  Universal  Postulate 193 

2.  The  test  of  inconceivability  does  not  rep- 

resent the  aggregate  of  past  experience. . 195 

3.  — nor  is  implied  in  every  process  of 

thought 197 

4.  Objections  answered 201 

5.  Sir  W.  Hamilton’s  opinion  on  the  Princi- 

ples of  Contradiction  and  Excluded  Mid- 
dle  204 


BOOK  III. 

OF  INDUCTION. 

Chapter  I.  Preliminary  Observations  on  Induc- 


tion in  general. 

5 1.  Importance  of  an  Inductive  Logic 207 

2.  The  logic  of  science  is  also  that  of  business 
and  life 208 

Chapter  II.  Of  Inductions  improperly  so  called. 

§ 1.  Inductions  distinguished  from  verbal  trans- 
formations  210 

2.  — from  inductions,  falsely  so  called, in  math- 

ematics  212 

3.  — and  from  descriptions 213 

4.  Examination  of  Dr.  Whewell’s  theory  of 

Induction 214 

5.  Further  illustration  of  the  preceding  re- 

marks  221 

Chapter  III.  Of  the  Ground  of  Induction. 

51.  Axiom  of  the  uniformity  of  the  course  of 

nature. 223 

2.  Not  true  in  every  sense.  Induction  per 

enumerationem  simplicem 226 

3.  The  question  of  Inductive  Logic  stated. .. . 227 

Chapter  IV.  Of  Laws  of  Nature. 

51.  The  general  regularity  in  nature  is  a tissue 

of  partial  regularities,  called  laws 229 

2.  Scientific  induction  must  be  grounded  on 

previous  spontaneous  inductions 231 

3.  Are  there  any  inductions  fitted  to  be  a test 

of  all  others  ? 232 

Chapter  V.  Of  the  Law  of  Universal  Causation. 

5 1.  The  universal  law  of  successive  phenomena 

is  the  Law  of  Causation 234 

| 2.  — i.  e.,  the  law  that  every  consequent  has 

an  invariable  antecedent 236 


CONTENTS. 


xi 


PAGE 


! 3.  The  cause  of  a phenomenon  is  the  assem- 
blage of  its  conditions 237 

4.  The  distinction  of  agent  and  patient  illu- 

sory  241 

5.  Case  in  which  the  effect  consists  in  giving 

a property  to  an  object 243 

6.  The  cause  is  not  the  invariable  antecedent, 

but  the  unconditional  invariable  anteced- 
ent  244 

7.  Can  a cause  be  simultaneous  with  its  ef- 

fect?  247 

8.  Idea  of  a Permanent  Cause,  or  original  nat- 

ural agent 248 

9.  Uniformities  of  co-existence  between  ef- 

fects of  different  permanent  causes,  are 
not  laws 251 

10.  Theory  of  the  Conservation  of  Force 251 

11.  Doctrine  that  volition  is  an  efficient  cause, 

examined 255 

Chapter  VI.  Of  the  Composition  of  Causes. 

§ 1.  Two  modes  of  the  conjunct  action  of  causes, 

the  mechanical  and  the  chemical 2G6 

2.  The  composition  of  causes  the  general 

rule ; the  other  case  exceptional 268 

3.  Are  effects  proportional  to  their  causes?. . 270 


Chapter  VII.  Of  Observation  and  Experiment 


§1.  The  first  step  of  inductive  inquiry  is  a men- 
tal analysis  of  complex  phenomena  into 
their  elements 272 

2.  The  next  is  an  actual  separation  of  those 

elements  273 

3.  Advantages  of  experiment  over  observa- 

tion  274 

4.  Advantages  of  observation  over  experi- 

ment  276 

Chapter  VIII.  Of  the  Four  Methods  of  Experi- 
mental Inquiry. 

§1.  Method  of  Agreement 27S 

2.  Method  of  Difference 2S0 

3.  Mutual  relation  of  these  two  methods 281 

4.  Joint  Method  of  Agreement  and  Difference.  283 

5.  Method  of  Residues 2S4 

6.  Method  of  Concomitant  Variations 285 

7.  Limitations  of  this  last  method 289 

CnArTEP.  IX.  Miscellaneous  Examples  of  the  Four 
Methods. 

§ 1.  Liebig’s  theory  of  metallic  poisons 292 

2.  Theory  of  induced  electricity 294 

3.  Dr.  Wells’s  theory  of  dew 296 

4.  Dr.  Brown-Seqnard’s  theory  of  cadaveric 

rigidity 301 

5.  Examples  of  the  Method  of  Residues 305 

6.  Dr.  Whewell’s  objections  to  the  Four 

Methods 307 

Chapter  X.  Of  Plurality  of  Causes;  and  of  the 
Intermixture  of  Effects. 

5 1.  One  effect  may  have  several  causes 311 

2.  — which  is  the  source  of  a characteristic 

imperfection  of  the  Method  of  Agree- 
ment  311 

3.  Plurality  of  Causes,  how  ascertained 314 

4.  Concurrence  of  Causes  which  do  not  com- 

pound their  effects 315 

5.  Difficulties  of  the  investigation,  when 

causes  compound  their  effects. 317 


PAGE 

§ 6.  Three  modes  of  investigating  the  laws  of 


complex  effects 320 

7.  The  method  of  simple  observation  inap- 
plicable..  321 

S.  The  purely  experimental  method  inappli- 
cable  322 


Chapter  XI.  Of  the  Deductive  Method. 

§1.  First  stage;  ascertainment  of  the  laws  of 

the  separate  causes  by  direct  induction. . 325 
2.  Second  stage ; ratiocination  from  the  sim- 


ple laws  of  the  complex  cases 328 

3.  Third  stage  ; verification  by  specific  expe- 
rience   329 

Chapter  XII.  Of  the  Explanation  of  Laws  of  Na- 
ture. 

51.  Explanation  defined 332 

2.  First  mode  of  explanation,  by  resolving  the 

law  of  a complex  effect  into  the  laws  of 
the  concurrent  causes  and  the  fact  of 
their  co-existence 332 

3.  Second  mode ; by  the  detection  of  an  in- 

termediate link  in  the  sequence 332 

4.  Laws  are  always  resolved  into  laws  more 

general  than  themselves 333 

5.  Third  mode  ; the  subsumption  of  less  gen- 

eral laws  under  a more  general  one 335 

6.  What  the  explanation  of  a law  of  nature 

amounts  to 337 

Chapter  XIII.  Miscellaneous  Examples  of  the  Ex- 
planation of  Laws  of  Future.  , 

§ 1.  The  general  theories  of  the  sciences 338 

2.  Examples  from  chemical  speculations 339 

3.  Example  from  Dr.  Brown  - Sequard’s  re- 

searches on  the  nervous  system 340 

4.  Examples  of  following  newly -discovered 

laws  into  their  complex  manifestations. . 341 

5.  Examples  of  empirical  generalizations,  af- 

terward confirmed  and  explained  deduct- 
ively  342 

6.  Example  from  mental  science 343 

7.  Tendency  of  all  the  sciences  to  become  de- 

ductive  344 


Chapter  XIV.  Of  the  Limits  to  the  Explanation 


of  Laws  of  Nature ; and  of  Hypotheses. 

§ 1.  Can  all  the  sequences  in  nature  be  resolva- 
ble into  one  law? 345 

2.  Ultimate  laws  can  not  be  less  numerous 

than  the  distinguishable  feelings  of  our 
nature 346 

3.  In  what  sense  ultimate  facts  can  be  ex- 

plained  34S 

4.  The  proper  use  of  scientific  hypotheses 349 

5.  Their  indispensableness 353 

6.  The  two  degrees  of  legitimacy  in  hypoth- 

eses   355 

7.  Some  inquiries  apparently  hypothetical  are 

really  inductive 359 


Chapter  XV.  Of  Progressive  Effects ; and  of  the 
Continued  Action  of  Causes. 

51.  How  a progressive  effect  results  from  the 
simple  continuance  of  the  cause 361 

2.  — and  from  the  progressiveness  of  the 

cause 363 

3.  Derivative  laws  generated  from  a single 

ultimate  law 365 


CONTENTS. 


xii 


PAGE 

Chapter  XVI.  Of  Empirical  Laws. 

5 1.  Definition  of  an  empirical  law 3GG 

2.  Derivative  laws  commonly  depend  on  col- 

locations   3G7 

3.  The  collocatious  of  the  permanent  causes 

are  not  reducible  to  any  law 3G7 

4.  Hence  empirical  laws  can  not  he  relied  on 

beyond  the  limits  of  actual  experience. . . 3GS 

5.  Generalizations  which  rest  only  on  the 

Method  of  Agreement  can  only  he  re- 
ceived as  empirical  laws 3G9 

6.  Signs  from  which  an  observed  uniformity 

of  sequence  may  be  presumed  to  be  re- 
solvable  3G9 

7.  Two  kinds  of  empirical  laws 371 

Chapter  XVII.  Of  Chance,  and  its  Elimination. 

5 1.  The  proof  of  empirical  laws  depends  on 

the  theory  of  chance 372 

2.  Chance  defined  and  characterized 373 

3.  The  elimination  of  chance 376 

4.  Discovery  of  residual  phenomena  by  elim- 

inating chance 377 

5.  The  doctrine  of  chances 378 

Chapter  XVIII.  Of  the  Calculation  of  Chances. 

§ 1.  Foundation  of  the  doctrine  of  chances,  as 

taught  by  mathematics 379 

2.  The  doctrine  tenable 380 

3.  On  what  foundation  it  really  rests 3S1 

4.  Its  ultimate  dependence  on  causation 383 

5.  Theorem  of  the  doctrine  of  chances  which 

relates  to  the  cause  of  a given  event 3S5 

G.  How  applicable  to  the  elimination  of 
chance 3SG 

Chapter  XIX.  Of  the  Extension  of  Derivative  Laws 
to  Adjacent  Cases. 

51.  Derivative  laws,  when  not  casual,  are  al- 
most always  contingent  on  collocations..  3SS 

2.  On  what  grounds  they  can  be  extended  to 
cases  beyond  the  bounds  of  actual  expe- 


rience  389 

3.  Those  cases  must  be  adjacent  cases 390 

Chapter  XX.  Of  Analogy. 

51.  Various  senses  of  the  word  analogy 393 

2.  Nature  of  analogical  evidence 393 


3.  On  what  circumstances  its  value  depends..  39G 

Chapter  XXI.  Of  the  Evidence  of  the  Law  of  Uni- 
versal Carnation. 

51.  The  law  of  causality  does  not  rest  on  an 

instinct 397 

2.  — but  on  an  induction  by  simple  enumera- 

tion  : 400 

3.  In  what  cases  such  induction  is  allowable.  402 

4.  The  universal  prevalence  of  the  law  of  cau- 

sality, on  what  grouuds  admissible 403 

Chapter  XXII.  Of  Uniformities  of  Co-existence 


not  dependent  on  Causation. 

§1.  Uniformities  of  co-existence  which  result 
from  laws  of  sequence 406 

2.  The  properties  of  Kinds  are  uniformities 

of  co-existence 408 

3.  Some  are  derivative,  others  ultimate 409 

4.  No  universal  axiom  of  co-existence 410 

5.  The  evidence  of  uniformities  of  co-exist- 

ence, how  measured 411 


PAGE 

5 G.  When  derivative,  their  evidence  is  that  of 


empirical  laws 412 

7.  So  also  when  ultimate 413 

8.  The  evidence  stronger  in  proportion  as  the 

law  is  more  general 413 

9.  Every  distinct  Kind  must  be  examined 414 


Chapter  XXIII.  Of  Approximate  Generalizations, 


and  Probable  Evidence. 

5 1.  The  inferences  called  probable,  rest  on  ap- 
proximate generalizations 41G 

2.  Approximate  generalizations  less  useful 

in  science  than  in  life 416 

3.  In  what  cases  they  may  be  resorted  to 417 

4.  In  what  manner  proved 41S 

5.  With  what  precautions  employed 420 

6.  The  two  modes  of  combining  probabilities.  421 

7.  How  approximate  generalizations  may  be 

converted  into  accurate  generalizations 
equivalent  to  them 423 


Chapter  XXIV.  Of  the  Remaining  Laws  of  Na- 


ture. 

§1.  Propositions  which  assert  mere  existence.  425 

2.  Resemblance,  considered  as  a subject  of 

science 426 

3.  The  axioms  and  theorems  of  mathematics 

comprise  the  principal  laws  of  resem- 
blance  427 

4.  — and  those  of  order  in  place,  and  rest  on 

induction  by  simple  enumeration 428 

5.  The  propositions  of  arithmetic  affirm  the 

modes  of  formation  of  some  given  num- 
ber  429 

G.  Those  of  algebra  affirm  the  equivalence 
of  different  modes  of  formation  of  num- 
bers generally 432 

7.  The  propositions  of  geometry  are  laws  of 

outward  nature 433 

8.  Why  geometry  is  almost  entirely  deduct- 

ive   435 

9.  Function  of  mathematical  truths  in  the 

other  sciences,  and  limits  of  that  function.  436 

Cn apter  XXV.  Of  the  Grounds  of  Disbelief. 

51.  Improbability  and  impossibility 438 

2.  Examination  of  Hume’s  doctrine  of  mir- 

acles   438 

3.  The  degrees  of  improbability  correspond 

to  differences  in  the  nature  of  the  gener- 
alization with  which  an  assertion  con- 
flicts   441 

4.  A fact  is  not  incredible  because  the  chances 

are  against  it 443 

5.  Are  coincidences  less  credible  than  other 

facts? 444 

6.  An  opinion  of  Laplace  examined 44G 


BOOK  IY. 

OF  OPERATIONS  SUBSIDIARY  TO  IN- 
DUCTION. 

Chapter  I.  Of  Observation  and  Description. 


§1.  Observation,  how  far  a subject  of  logic 449 

2.  A great  part  of  what  seems  observation  is 
really  inference 450 


CONTENTS. 


xm 


PAGE 

§3.  The  description  of  an  observation  affirms 
more  than  is  contained  in  the  observa- 


tion  452 

4.  — namely,  an  agreement  among  phenom- 
ena ; and  the  comparison  of  phenomena 
to  ascertain  such  agreements  is  a prelim- 
inary to  induction 453 


Chapter  II.  Of  A bstraction,  or  the  Formation  of 
Conceptions. 

§ 1.  The  comparison  which  is  a preliminary  to 


induction  implies  general  conceptions...  455 

2.  — but  these  need  not  be  pre-existent 456 

3.  A general  conception,  originally  the  result 

of  a comparison,  becomes  itself  the  type 
of  comparison 45S 

4.  What  is  meant  by  appropriate  conceptions.  459 

5.  — and  by  clear  conceptions 461 

6.  Farther  illustration  of  the  subject 462 


Chapter  III.  Of  Famine/  as  Subsidiary  to  Induc- 


tion. 

§ 1.  The  fundamental  property  of  names  as  an 

instrument  of  thought 464 

2.  Names  are  not  indispensable  to  induc- 

tion  465 

3.  In  what  manner  subservient  to  it 465 

4.  General  names  not  a mere  contrivance  to 

economize  the  use  of  language 466 


Chapter  IV.  Of  the  Requisites  of  a Philosophical 


Language,  and  the  Principles  of  Definition. 

§ 1.  First  requisite  of  philosophical  language, 
a steady  and  determinate  meaning  for  ev- 
ery general  name. 46T 

■ 2.  Names  in  common  use  have  often  a loose 

connotation 467 

3.  — which  the  logician  should  fix,  with  as 

tittle  alteration  as  possible 469 

4.  Why  definition  is  often  a question  not  of 

words  but  of  things 470 

5.  How  the  logician  should  deal  with  the 

transitive  applications  of  words 472 

6.  Evil  consequences  of  casting  off  any  por- 

tion of  the  customary  connotation  of 
words 476 


Chapter  V.  On  the  Natural  History  of  the  Varia- 
tions in  the  Meaning  of  Terms. 

§1.  How  circumstances  originally  accidental 
become  incorporated  into  the  meaning  of 


words 4S0 

2.  — and  sometimes  become  the  whole  mean- 

ing  481 

3.  Tendency  of  words  to  become  generalized.  4S2 

4.  — and  to  become  specialized 486 


Chapter  VI.  The  Principles  of  Philosophical  Lan- 


guage farther  considered. 

§ 1.  Second  requisite  of  philosophical  language, 

a name  for  every  important  meaning 4S7 

2.  — viz.,  first,  an  accurate  descriptive  ter- 

minology  487 

3.  — secondly,  a name  for  each  of  the  more 

important  results  of  scientific  abstrac- 
tion   490 

4.  — thirdly,  a nomenclature,  or  system  of 

the  names  of  Kinds 491 


5.  Peculiar  nature  of  the  connotation  of 
names  which  belong  to  a nomenclature..  493 


PAGE 

§ 6.  In  what  cases  language  may,  and  may  not, 

be  used  mechanically 494 

Chapter  VII.  Of  Classification,  as  Subsidiary  to 
Induction. 

§ 1.  Classification  as  here  treated  of,  wherein 


different  from  the  classification  implied 
in  naming 497 

2.  Theory  of  natural  groups 493 

3.  Are  natural  groups  given  by  type,  or  by 

definition  ? 501 

4.  Kinds  are  natural  groups 502 

5.  How  the  names  of  Kinds  should  be  con- 

structed  505 

Chapter  VIII.  Of  Classification  by  Series. 

51.  Natural  groups  should  be  arranged  in  a 
natural  series 507 

2.  The  arrangement  should  follow  the  de- 

grees of  the  main  phenomenon 50S 

3.  — which  implies  the  assumption  of  a type 

species 509 

4.  How  the  divisions  of  the  series  should  be 

determined 510 

5.  Zoology  affords  the  completest  type  of  sci- 

entific classification 511 


BOOK  Y. 

ON  FALLACIES. 


Chapter  I.  Of  Fallacies  in  General. 

51.  Theory  of  fallacies  a necessary  part  of 

logic 512 

2.  Casual  mistakes  are  not  fallacies 513 

3.  The  moral  sources  of  erroneous  opinion, 

how  related  to  the  intellectual 513 

Chapter  II.  Classification  of  Fallacies. 

§ 1.  On  what  criteria  a classification  of  fallacies 

should  be  grounded 515 

2.  The  five  classes  of  fallacies 516 

3.  The  reference  of  a fallacy  to  one  or  an- 

other class  is  sometimes  arbitrary 51S 

Chapter  III.  Fallacies  of  Simple  Inspection,  or 
A Priori  Fallacies. 

5 1.  Character  of  this  class  of  fallacies 520 

2.  Natural  prejudice  of  mistaking  subjective 

laws  for  objective,  exemplified  in  popular 
superstitions 521 

3.  — that  things  which  we  think  of  together 

must  exist  together,  and  that  what  is  in- 
conceivable must  be  false 523 

4.  — of  ascribing  objective  existence  to  ab- 

abstractions 527 

5.  Fallacy  of  the  Sufficient  Reason 52S 

6.  Natural  prejudice,  that  the  differences  in 

nature  correspond  to  the  distinctions  in 
language 529 

7.  Prejudice,  that  a phenomenon  can  not  have 

more  than  one  cause 532 

S.  — that  the  conditions  of  a phenomenon 
must  resemble  the  phenomenon 533 

Chapter  IV.  Fallacies  of  Observation. 

51.  Non-observation,  and  Mal-observation 53S 


xiv 


CONTENTS. 


PAGE 


5 2.  Non -observation  of  instances,  and  non- 

observation  of  circumstances B3S 

3.  Examples  of  the  former 539 

4.  — and  of  the  latter 542 

5.  Mal-observation  characterized  and  exem- 

plified  545 

Chapter  V.  Fallacies  of  Generalization. 

5 1.  Character  of  the  class 547 

2.  Certain  kinds  of  generalization  must  al- 

ways be  groundless 547 

3.  Attempts  to  resolve  phenomena  radically 

different  into  the  same 548 

4.  Fallacy  of  mistaking  empirical  for  casual 

laws 549 

5.  Post  hoc,  ergo  propter  hoc;  and  the  deduct- 

ive fallacy  corresponding  to  it 551 

C.  Fallacy  of  False  Analogies 553 

7.  Function  of  metaphors  in  reasoning 557 

8.  How  fallacies  of  generalization  grow  out 

of  bad  classification 558 

Chapter  VI.  Fallacies  of  Ratiocination. 

{ 1.  Introductory  Remarks 559 

2.  Fallacies  in  the  conversion  and  tequipol- 

lency  of  propositions 559 

3.  — in  the  syllogistic  process 5G0 

4.  Fallacy  of  changing  the  premises 561 

Chapter  VII.  Fallacies  of  Confusion. 

51.  Fallacy  of  Ambiguous  Terms 563 

2.  — ofPetitio  Priucipii 570 

3.  — of  Ignoratio  Elenchi 576 


BOOK  VI. 

ON  THE  LOGIC  OF  THE  MORAL  SCI- 
ENCES. 


Chapter  I.  Introductory  Remarks. 

51.  The  backward  state  of  the  Moral  Sciences 
can  only  be  remedied  by  applying  to  them 
the  methods  of  Physical  Science,  duly  ex- 
tended and  generalized 579 

2.  How  far  this  can  be  attempted  in  the  pres- 
ent work 5S0 

Chapter  II.  Of  Liberty  and  Necessity. 

5 1.  Are  human  actions  subject  to  the  law  of 

causality? 581 

2.  The  doctrine  commonly  called  Philosoph- 

ical Necessity,  in  what  sense  true 5S1 

3.  Inappropriateness  and  pernicious  effect  of 

the  term  Necessity 583 

4.  A motive  not  always  the  anticipation  of  a 

pleasure  or  a pain 585 


Chapter  III.  That  there  is,  or  may  he,  a Science  of 


Human  Nature. 

5 1.  There  may  be  sciences  which  are  not  exact 

sciences 586 

2.  To  what  scientific  type  the  Science  of  Hu- 
man Nature  corresponds 583 

Chapter  IV.  Of  the  Laws  of  Mind. 

51.  What  is  meant  by  Laws  of  Mind 589 

2.  Is  there  a Science  of  Psychology  ? 599 


page 


§3.  The  pru-Cipai  Investigations  of  Psychology 

characterized 591 

4.  Relation  of  mental  facto  to  physical  con- 
ditions   594 

Cuapter  V.  Of  lithology,  nr  the  Science  of  the  For 
mation  of  Character. 

51.  The  Empirical  Laws  of  Human  Nature 59C 

2.  — are  merely  approximate  generalizations. 

The  universal  laws  are  those  of  the  for- 
mation of  character 597 

3.  The  laws  of  the  formation  of  character  can 

not  he  ascertained  by  observation  and 
experiment 599 

4.  — but  must  be  studied  deductively.. .' 601 

5.  The  principles  of  Ethology  are  the  axio- 

mata  media  of  mental  science 003 

C.  Ethology  characterized 604 


Cuapter  VI.  General  Considerations  on  the  Social 
Science. 

§1.  Are  Social  Phenomena  a subject  of  Sci- 
ence ? 606 

2.  Of  what  nature  the  Social  Science  must 
he 607 

Chapter  VII.  Of  the  Chemical  or  Experimental 


Method  in  the  Social  Science. 

51.  Characters  of  the  mode  of  thinking  which 
deduces  political  doctrines  from  specific 
experience 608 

2.  In  the  Social  Science  experiments  are  im- 

possible  610 

3.  — the  Method  of  Difference  inapplicable. . 610 

4.  — and  the  Methods  of  Agreement,  nud  of 

Concomitant  Variations,  inconclusive ....  611 

5.  The  Method  of  Residues  also  inconclusive, 

and  presupposes  Deduction 612 

Chapter  VIII.  Of  the  Geometrical,  or  Abstract 
Method. 

§ 1.  Characters  of  this  mode  of  thinking 614 

2.  Examples  of  the  Geometrical  Method 615 

3.  The  interest-philosophy  of  the  Bentham 

school 616 

Chapter  IX.  Of  the  Physical,  or  Concrete  Deductive 
Method. 

§ 1.  The  Direct  aud  Inverse  Deductive  Meth- 
ods  619 

2.  Difficulties  of  the  Direct  Deductive  Meth- 
od in  the  Social  Science 621 


3.  To  what  extent  the  different  branches  of 

sociological  speculation  can  be  studied 
apart.  Political  Economy  characterized.  G23 

4.  Political  Ethology,  or  the  science  of  nation- 


al character 626 

5.  The  Empirical  Laws  of  the  Social  Sci- 

ence  628 

6.  The  Verification  of  the  Social  Science 629 


Chapter  X.  Of  the  Inverse.  Deductive,  or  Historical 
Method. 

51.  Dbtinction  between  the  general  Science  of 


Society,  and  special  sociological  inquiries.  030 

2.  What  is  meant  by  a State  ofSociety? 631 

3.  The  Progressiveuess  of  Man  aud  Society. . 631 

4.  The  laws  of  the  succession  of  states  of  so- 

ciety can  only  he  ascertained  by  the  In- 
verse Deductive  Method 633 


CONTENTS. 


xv 


PAGE 


5 5.  Social  Statics,  or  the  science  of  the  Co-ex- 
istences of  Social  Phenomena G35 

6.  Social  Dynamics,  or  the  science  of  the  Suc- 

cessions of  Social  Phenomena 639 

7.  Outlines  of  the  Historical  Method 640 

8.  Future  prospects  of  Sociological  Inquiry. . 642 


Chapter  XI.  Additional  Elucidations  of  the  Sci- 
ence of  History. 

5 1.  The  subjection  of  historical  facts  to  uni-  - 


form  laws  is  verified  by  statistics 644 

2.  — does  not  imply  the  insignificance  of 

moral  causes 646 

3.  — nor  the  inefficacy  of  the  characters  of 

individuals  and  of  the  acts  of  govern- 
ments  647 

4.  The  historical  importance  of  eminent  men 


PAGE 

and  of  the  policy  of  governments  illus- 
trated  G50 

Chapter  XII.  Of  the  Logic  of  Practice,  or  Art ; in- 
cluding Morality  and  Policy. 

§1.  Morality  not  a Science,  hut  an  Art 652 

2.  Relation  between  rules  of  art  and  the  the- 

orems of  the  corresponding  science 653 

3.  What  is  the  proper  function  of  rules  of  art  ? 654 

4.  Art  can  not  be  deductive 655 

5.  Every  Art  consists  of  truths  of  Science,  ar- 

ranged in  the  order  suitable  for  some  prac- 
• tical  use 655 

6.  Teleology,  or  the  Doctrine  of  Ends G5G 

7.  Necessity  of  an  ultimate  standard,  or  first 

principle  of  Teleology 657 

8.  Conclusion 659 


INTRODUCTION 


§ 1.  There  is  as  great  diversity  among  authors  in  the  modes  which  they 
have  adopted  of  defining  logic,  as  in  their  treatment  of  the  details  of  it. 
This  is  what  might  naturally  be  expected  on  any  subject  on  which  writers 
have  availed  themselves  of  the  same  language  as  a means  of  delivering 
different  ideas.  Ethics  and  jurisprudence  are  liable  to  the  remark  in  com- 
mon with  logic.  Almost  every  writer  having  taken  a different  view  of 
some  of  the  particulars  which  these  branches  of  knowledge  are  usually 
understood  to  include ; each  has  so  framed  his  definition  as  to  indicate 
beforehand  his  own  peculiar  tenets,  and  sometimes  to  beg  the  question  in 
their  favor. 

This  diversity  is  not  so  much  an  evil  to  be  complained  of,  as  an  inevita- 
ble and  in  some  degree  a proper  result  of  the  imperfect  state  of  those 
sciences.  It  is  not  to  be  expected  that  there  should  be  agreement  about 
the  definition  of  any  thing,  until  there  is  agreement  about  the  thing  itself. 
To  define,  is  to  select  from  among  all  the  properties  of  a thing,  those  which 
shall  be  understood  to  be  designated  and  declared  by  its  name;  and  the 
properties  must  be  well  known  to  us  before  we  can  be  competent  to  deter- 
mine which  of  them  are  fittest  to  be  chosen  for  this  purpose.  According- 
ly, in  the  case  of  so  complex  an  aggregation  of  particulars  as  are  compre- 
hended in  any  thing  which  can  be  called  a science,  the  definition  we  set 
out  with  is  seldom  that  which  a more  extensive  knowledge  of  the  subject 
shows  to  be  the  most  appropriate.  Until  we  know  the  particulars  them- 
selves, we  can  not  fix  upon  the  most  correct  and  compact  mode  of  circum- 
scribing them  by  a general  description.  It  was  not  until  after  an  extensive 
and  accurate  acquaintance  with  the  details  of  chemical  phenomena,  that  it 
was  found  possible  to  frame  a rational  definition  of  chemistry;  and  the 
definition  of  the  science  of  life  and  organization  is  still  a matter  of  dispute. 
So  long  as  the  sciences  are  imperfect,  the  definitions  must  partake  of  their 
imperfection ; and  if  the  former  are  progressive,  the  latter  ought  to  be  so 
too.  As  much,  therefore,  as  is  to  be  expected  from  a definition  placed  at 
the  commencement  of  a subject,  is  that  it  should  define  the  scope  of  our 
inquiries : and  the  definition  which  I am  about  to  offer  of  the  science  of 
logic,  pretends  to  nothing  more  than  to  be  a statement  of  the  question 
which  I have  put  to  myself,  and  which  this  book  is  an  attempt  to  resolve. 
The  reader  is  at  liberty  to  object  to  it  as  a definition  of  logic;  but  it  is  at 
all  events  a correct  definition  of  the  subject  of  this  volume. 

§ 2.  Logic  has  often  been  called  the  Art  of  Reasoning.  A writer*  who 
has  done  more  than  any  other  person  to  restore  this  study  to  the  rank  from 
which  it  had  fallen  in  the  estimation  of  the  cultivated  class  in  our  own 
country,  has  adopted  the  above  definition  with  an  amendment ; he  has  de- 


Archbishop  Whately. 


18 


INTRODUCTION. 


fined  Logie  to  be  the  Science,  as  well  as  the  Art,  of  reasoning;  meaning 
by  the  former  term,  the  analysis  of  the  mental  process  which  takes  place 
whenever  we  reason,  and  by  the  latter,  the  rules,  grounded  on  that  analy- 
sis, for  conducting  the  process  correctly.  There  can  be  no  doubt  as  to  the 
propriety  of  the  emendation.  A right  understanding  of  the  mental  process 
itself,  of  the  conditions  it  depends  on,  and  the  steps  of  which  it  consists, 
is  the  only  basis  on  which  a system  of  rules,  fitted  for  the  direction  of  the 
process,  can  possibly  be  founded.  Art  necessarily  presupposes  knowledge; 
art,  in  any  but  its  infant  state,  presupposes  scientific  knowledge : and  if  ev- 
ery art  does  not  bear  the  name  of  a science,  it  is  only  because  several  sci- 
ences are  often  necessary  to  form  the  groundwork  of  a single  art.  So  com- 
plicated are  the  conditions  which  govern  our  practical  agency,  that  to  ena- 
ble one  thing  to  be  done,  it  is  often  requisite  to  know  the  nature  and  prop- 
erties of  many  things. 

Logic,  then,  comprises  the  science  of  reasoning,  as  well  as  an  art,  found- 
ed on  that  science.  But  the  word  Reasoning,  again,  like  most  other  scien- 
tific terms  in  popular  use,  abounds  in  ambiguities.  In  one  of  its  accepta- 
tions, it  means  syllogizing;  or  the  mode  of  inference  which  may  be  called 
(with  sufficient  accuracy  for  the  present  purpose)  concluding  from  generals 
to  particulars.  In  another  of  its  senses,  to  reason  is  simply  to  infer  any 
assertion,  from  assertions  already  admitted : and  in  this  sense  induction  is 
as  much  entitled  to  be  called  reasoning  as  the  demonstrations  of  geometry. 

W l iters  on  logic  have  generally  preferred  the  former  acceptation  of  the 
term  : the  latter,  and  more  extensive  signification  is  that  in  which  I mean 
to  use  it.  I do  this  by  virtue  of  the  right  I claim  for  every  author,  to  give 
whatever  provisional  definition  he  pleases  of  his  own  subject.  But  suffi- 
cient reasons  will,  I believe,  unfold  themselves  as  we  advance,  why  this 
should  be  not  only  the  provisional  but  the  final  definition.  It  involves,  at 
all  events,  no  arbitrary  change  in  the  meaning  of  the  word ; for,  with  the 
general  usage  of  the  English  language,  the  wider  signification,  I believe, 
accords  better  than  the  more  restricted  one. 

§ 3.  But  reasoning,  even  in  the  widest  sense  of  which  the  word  is  sus- 
ceptible, does  not  seem  to  comprehend  all  that  is  included,  either  in  the 
best,  or  even  in  the  most  current,  conception  of  the  scope  and  province  of 
our  science.  The  employment  of  the  word  Logic  to  denote  the  theory  of 
Argumentation,  is  derived  from  the  Aristotelian,  or,  as  they  are  commonly 
termed,  the  scholastic,  logicians.  Yet  even  with  them,  in  their  systematic 
treatises,  Argumentation  was  the  subject  only  of  the  third  part:  the  two 
former  treated  of  Terms,  and  of  Propositions ; under  one  or  other  of  which 
heads  were  also  included  Definition  and  Division.  By  some,  indeed,  these 
previous  topics  were  professedly  introduced  only  on  account  of  their  con- 
nection with  reasoning,  and  as  a preparation  for  the  doctrine  and  rules  of 
the  syllogism.  Yet  they  were  treated  with  greater  minuteness,  and  dwelt 
on  at  greater  length,  than  was  required  for  that  purpose  alone.  More  re- 
cent writers  on  logic  have  generally  understood  the  term  as  it  was  employ- 
ed by  the  able  author  of  the  Port  Royal  Logic ; viz.,  as  equivalent  to  the 
Art  of  Thinking.  Nor  is  this  acceptation  confined  to  books,  and  scientific 
inquiries.  Even  in  ordinary  conversation,  the  ideas  connected  with  the 
word  Logic  include  at  least  precision  of  language,  and  accuracy  of  classifi- 
cation : and  we  perhaps  oftener  hear  persons  speak  of  a logical  arrange- 
ment, or  of  expressions  logically  defined,  than  of  conclusions  logically  de 
(luced  from  premises.  Again,  a man  is  often  called  a great  logician,  or  a 


DEFINITION  AND  PROVINCE  OE  LOGIC. 


19 


man  of  powerful  logic,  not  for  the  accuracy  of  his  deductions,  but  for  the 
extent  of  his  command  over  premises  ; because  the  general  propositions 
required  for  explaining  a difficulty  or  refuting  a sophism,  copiously  and 
promptly  occur  to  him : because,  in  short,  his  knowledge,  besides  being- 
ample,  is  well  under  his  command  for  argumentative  use.  Whether,  there- 
fore, we  conform  to  the  practice  of  those  who  have  made  the  subject  their 
particular  study,  or  to  that  of  popular  writers  and  common  discourse,  the 
province  of  logic  will  include  several  operations  of  the  intellect  not  usually 
considered  to  fall  within  the  meaning  of  the  terms  Reasoning  and  Argu- 
mentation. 

These  various  operations  might  be  brought  within  the  compass  of  the 
science,  and  the  additional  advantage  be  obtained  of  a very  simple  defini- 
tion, if,  by  an  extension  of  the  term,  sanctioned  by  high  authorities,  we 
were  to  define  logic  as  the  science  which  treats  of  the  operations  of  the  hu- 
man understanding  in  the  pursuit  of  truth.  For  to  this  ultimate  end,  nam- 
ing, classification,  definition,  and  all  other  operations  over  which  logic  has 
ever  claimed  jurisdiction,  are  essentially  subsidiary.  They  may  all  be  re- 
garded as  contrivances  for  enabling  a person  to  know  the  truths  which  are 
needful  to  him,  and  to  know  them  at  the  precise  moment  at  which  they  are 
needful.  Other  purposes,  indeed,  are  also  served  by  these  operations ; for 
instance,  that  of  imparting  our  knowledge  to  others.  But,  viewed  with  re- 
gard to  this  purpose,  they  have  never  been  considered  as  within  the  prov- 
ince of  the  logician.  The  sole  object  of  Logic  is  the  guidance  of  one’s  own 
thoughts : the  communication  of  those  thoughts  to  others  falls  under  the 
consideration  of  Rhetoric,  in  the  large  sense  in  which  that  art  was  con- 
ceived by  the  ancients ; or  of  the  still  more  extensive  art  of  Education. 
Logic  takes  cognizance  of  our  intellectual  operations  only  as  they  conduce 
to  our  own  knowledge,  and  to  our  command  over  that  knowledge  for  our 
own  uses.  If  there  were  but  one  rational  being  in  the  universe,  that  being 
might  be  a perfect  logician ; and  the  science  and  art  of  logic  would  be  the 
same  for  that  one  person  as  for  the  whole  human  race. 

§ 4.  But,  if  the  definition  which  we  formerly  examined  included  too  lit- 
tle, that  which  is  now  suggested  has  the  opposite  fault  of  including  too 
much. 

Truths  are  known  to  us  in  two  ways : some  are  known  directly,  and  of 
themselves ; some  through  the  medium  of  other  truths.  The  former  are 
the  subject  of  Intuition,  or  Consciousness  ;*  the  latter,  of  Inference.  The 
truths  known  by  intuition  are  the  original  premises  from  which  all  others 
are  inferred.  Our  assent  to  the  conclusion  being  grounded  on  the  truth  of 
the  premises,  we  never  could  arrive  at  any  knowledge  by  reasoning,  unless 
something  could  be  known  antecedently  to  all  reasoning. 

Examples  of  truths  known  to  us  by  immediate  consciousness,  are  our 
own  bodily  sensations  and  mental  feelings.  I know  directly,  and  of  my 
own  knowledge,  that  I was  vexed  yesterday,  or  that  I am  hungry  to-day. 
Examples  of  truths  which  we  know  only  by  way  of  inference,  are  occur- 
rences which  took  place  while  we  were  absent,  the  events  recorded  in  his- 
tory, or  the  theorems  of  mathematics.  The  two  former  we  infer  from  the 
testimony  adduced,  or  from  the  traces  of  those  past  occurrences  which  still 

* I use  these  terms  indiscriminately,  because,  for  the  purpose  in  view,  there  is  no  need  for 
making  any  distinction  between  them.  But  metaphysicians  usually  restrict  the  name  Intui- 
tion to  the  direct  knowledge  we  are  supposed  to  have  of  things  external  to  our  minds,  and 
Consciousness  to  our  knowledge  of  our  own  mental  phenomena. 


•JO 


INTRODUCTION. 


exist  : the  latter,  from  the  premises  laid  down  in  books  of  geometry,  under 
the  title  of  definitions  and  axioms.  Whatever  we  are  capable  of  knowing 
must  belong  to  the  one  class  or  to  the  other;  must  be  in  the  number  of  the 
primitive  data,  or  of  the  conclusions  which  can  be  drawn  from  these. 

With  the  original  data,  or  ultimate  premises  of  our  knowledge;  with 
their  number  or  nature,  the  mode  in  which  they  are  obtained,  or  the  tests 
by  which  they  may  be  distinguished;  logic,  in  a direct  way  at  least,  has, 
in  the  sense  in  which  I conceive  the  science,  nothing  to  do.  These  ques- 
tions are  partly  not  a subject  of  science  at  all,  partly  that  of  a very  differ- 
ent science. 

W hatever  is  known  to  us  by  consciousness  is  known  beyond  possibility 
,.f  question.  What  one  sees  or  feels,  whether  bodily  or  mentally,  one  can 
not  but  be  sure  that  one  sees  or  feels.  No  science  is  required  for  the  pur- 
pose of  establishing  such  truths;  no  rules  of  art  can  render  our  knowledge 
of  them  more  certain  than  it  is  in  itself.  There  is  no  logic  for  this  jjortion 
of  our  knowledge. 

But  we  may  fancy  that  we  see  or  feel  what  we  in  reality  infer.  A truth, 
or  supposed  truth,  which  is  really  the  result  of  a very  rapid  inference,  may 
seem  to  be  apprehended  intuitively.  It  has  long  been  agreed  by  thinkers  of 
the  most  opposite  schools,  that  this  mistake  is  actually  made  in  so  familiar 
an  instance  as  that  of  the  eyesight.  There  is  nothing  of.  which  we  appear 
to  ourselves  to  be  more  directly  conscious  than  the  distance  of  an  object 
from  us.  Yet  it  has  long  been  ascertained,  that  what  is  perceived  by  the 
eye,  is  at  most  nothing  more  than  a variously  colored  surface ; that  when 
we  fancy  we  see  distance,  all  we  really  see  is  certain  variations  of  apparent 
size,  and  degrees  of  faintness  of  color;  that  our  estimate  of  the  object’s 
distance  from  us  is  the  result  partly  of  a rapid  inference  from  the  muscular 
sensations  accompanying  the  adjustment  of  the  focal  distance  of  the  eye  to 
objects  unequally  remote  from  us,  and  partly  of  a comparison  (made  with 
so  much  rapidity  that  we  are  unconscious  of  making  it)  between  the  size 
and  color  of  the  object  as  they  appear  at  the  time,  and  the  size  and  color 
of  the  same  or  of  similar  objects  as  they  appeared  when  close  at  hand,  or 
when  their  degree  of  remoteness  was  known  by  other  evidence.  The  per- 
ception of  distance  by  the  eye.  which  seems  so  like  intuition,  is  thus,  in  re- 
ality, an  inference  grounded  on  experience ; an  inference,  too,  which  we 
learn  to  make ; and  which  we  make  with  more  and  more  correctness  as  our 
experience  increases;  though  in  familiar  cases  it  takes  place  so  rapidly  as 
lo  appear  exactly  on  a par  with  those  perceptions  of  sight  which  are  really 
intuitive,  our  perceptions  of  color.* 

Of  the  science,  therefore,  which  expounds  the  operations  of  the  human 
understanding  in  the  pursuit  of  truth,  one  essential  part  is  the  inquiry : 
What  are  the  facts  which  are  the  objects  of  intuition  or  consciousness,  and 
what  are  those  which  we  merely  infer?  But  this  inquiry  has  never  been 
considered  a portion  of  logic.  Its  place  is  in  another  and  a perfectly  dis- 
tinct department  of  science,  to  which  the  name  metaphysics  more  particu- 
larly belongs : that  portion  of  mental  philosophy  which  attempts  to  deter- 
mine what  part  of  the  furniture  of  the  mind  belongs  to  it  originally,  and 


* This  important  theory  has  of  late  been  called  in  question  by  a writer  of  deserved  reputa- 
tion, Mr.  Samuel  Bailey;  but  I do  not  conceive  that  the  grounds  on  which  it  has  been  ad- 
mitted as  an  established  doctrine  for  a century  past,  have  been  at  all  shaken  by  that  gentle- 
man’s objections.  I have  elsewhere  said  what  appeared  to  me  necessary  in  reply  to  his  argu- 
ments. ( Westminster  Revieiv  for  October.  1842;  reprinted  in  “Dissertations  and  Discus- 
sions,” vol.  ii.) 


DEFINITION  AND  PROVINCE  OF  LOGIC. 


21 


what  part  is  constructed  out  of  materials  furnished  to  it  from  without.  To 
this  science  appertain  the  great  and  much  debated  questions  of  the  exist- 
ence of  matter ; the  existence  of  spirit,  and  of  a distinction  between  it  and 
matter ; the  reality  of  time  and  space,  as  things  without  the  mind,  and 
distinguishable  from  the  objects  which  are  said  to  exist  in  them.  For 
in  the  present  state  of  the  discussion  on  these  topics,  it  is  almost  uni- 
versally allowed  that  the  existence  of  matter  or  of  spirit,  of  space  or  of 
time,  is  in  its  nature  unsusceptible  of  being  proved ; and  that  if  any  thing 
is  known  of  them,  it  must  be  by  immediate  intuition.  To  the  same  science 
belong  the  inquiries  into  the  nature  of  Conception,  Perception,  Memory, 
and  Belief ; all  of  which  are  operations  of  the  understanding  in  the  pursuit 
of  truth ; but  with  which,  as  phenomena  of  the  mind,  or  with  the  possibili- 
ty which  may  or  may  not  exist  of  analyzing  any  of  them  into  simpler  phe- 
nomena, the  logician  as  such  has  no  concern.  To  this  science  must  also  be 
referred  the  following,  and  all  analogous  questions : To  what  extent  our  in- 
tellectual faculties  and  our  emotions  are  innate — to  what  extent  the  result 
of  association : Whether  God  and  duty  are  realities,  the  existence  of  which 
is  manifest  to  us  a •priori  by  the  constitution  of  our  rational  faculty ; or 
whether  our  ideas  of  them  are  acquired  notions,  the  origin  of  which  we 
are  able  to  trace  and  explain;  and  the  reality  of  the  objects  themselves  a 
question  not  of  consciousness  or  intuition,  but  of  evidence  and  reasoning. 

The  province  of  logic  must  be  restricted  to  that  portion  of  our  knowl- 
edge which  consists  of  inferences  from  truths  previously  known ; whether 
those  antecedent  data  be  general  propositions,  or  particular  observations 
and  perceptions.  Logic  is  not  the  science  of  Belief,  but  the  science  of 
Proof,  or  Evidence.  In  so  far  as  belief  professes  to  be  founded  on  proof, 
the  office  of  logic  is  to  supply  a test  for  ascertaining  whether  or  not  the  be- 
lief is  well  grounded.  With  the  claims  which  any  proposition  has  to  be- 
lief on  the  evidence  of  consciousness  — that  is,  without  evidence  in  the 
proper  sense  of  the  word — logic  has  nothing  to  do. 

§ 5.  By  far  the  greatest  portion  of  our  knowledge,  whether  of  general 
truths  or  of  particular  facts,  being  avowedly  matter  of  inference,  nearly  the 
whole,  not  only  of  science,  but  of  human  conduct,  is  amenable  to  the  au- 
thority of  logic.  To  draw  inferences  has  been  said  to  be  the  great  business 
of  life.  Every  one  has  daily,  hourly,  and  momentary  need  of  ascertaining 
facts  which  he  has  not  directly  observed ; not  from  any  general  purpose  of 
adding  to  his  stock  of  knowledge,  but  because  the  facts  themselves  are  of 
importance  to  his  interests  or  to  his  occupations.  The  business  of  the 
magistrate,  of  the  military  commander,  of  the  navigator,  of  the  physician, 
of  the  agriculturist,  is  merely  to  judge  of  evidence,  and  to  act  accordingly. 
They  all  have  to  ascertain  certain  facts,  in  order  that  they  may  afterward 
apply  certain  rules,  either  devised  by  themselves  or  prescribed  for  their 
guidance  by  others ; and  as  they  do  this  well  or  ill,  so  they  discharge  well 
or  ill  the  duties  of  their  several  callings.  It  is  the  only  occupation  in  which 
the  mind  never  ceases  to  be  engaged;  and  is  the  subject,  not  of  logic,  but 
of  knowledge  in  general. 

Logic,  however,  is  not  the  same  thing  with  knowledge,  though  the  field 
of  logic  is  co-extensive  with  the  field  of  knowledge.  Logic  is  the  com- 
mon judge  and  arbiter  of  all  particular  investigations.  It  does  not  under- 
take to  find  evidence,  but  to  determine  whether  it  has  been  found.  Logic 
neitheV  observes,  nor  invents,  nor  discovers;  but  judges.  It  is  no  part  of 
the  business  of  logic  to  inform  the  surgeon  what  appearances  are  found  to 


oo 


INTRODUCTION. 


accompany  a violent  death.  This  he  must  learn  from  his  own  experience 
and  observation,  or  from  that  of  others,  his  predecessors  in  his  peculiar 
pursuit.  But  logic  sits  in  judgment  on  the  sufficiency  of  that  observation 
and  experience  to  justify  his  rules,  and  on  the  sufficiency  of  his  rules  to 
justify  his  conduct.  It  does  not  give  him  proofs,  but  teaches  him  what 
makes  them  proofs,  and  how  he  is  to  judge  of  them.  It  does  not  teach 
that  any  particular  fact  proves  any  other,  but  points  out  to  what  conditions 
all  facts  must  conform,  in  order  that  they  may  prove  other  facts.  To  de- 
cide whether  any  given  fact  fulfills  these  conditions,  or  whether  facts  can 
be  found  which  fulfill  them  in  a given  case,  belongs  exclusively  to  the  par- 
ticular art  or  science,  or  to  our  knowledge  of  the  particular  subject. 

It  is  in  this  sense  that  logic  is,  what  it  was  so  expressively  called  by  the 
schoolmen  and  by  Bacon,  ars  artium  ; the  science  of  science  itself.  All 
science  consists  of  data  and  conclusions  from  those  data,  of  proofs  and  what 
they  prove : now  logic  points  out  what  relations  must  subsist  between  data 
and  whatever  can  be  concluded  from  them,  between  proof  and  every  thing 
which  it  can  prove.  If  there  be  any  such  indispensable  relations,  and  if 
these  can  be  precisely  determined,  every  particular  branch  of  science,  as 
well  as  every  individual  in  the  guidance  of  his  conduct,  is  bound  to  con- 
form to  those  relations,  under  the  penalty  of  making  false  inferences — of 
drawing  conclusions  which  are  not  grounded  in  the  realities  of  things. 
Whatever  has  at  any  time  been  concluded  justly,  whatever  knowledge  has 
been  acquired  otherwise  than  by  immediate  intuition,  depended  on  the  ob- 
servance of  the  laws  which  it  is  the  province  of  logic  to  investigate.  If 
the  conclusions  are  just,  and  the  knowledge  real,  those  laws,  whether  known 
or  not,  have  been  observed. 

§ 6.  We  need  not,  therefore,  seek  any  further  for  a solution  of  the  ques- 
tion, so  often  agitated,  respecting  the  utility  of  logic.  If  a science  of  logic 
exists,  or  is  capable  of  existing,  it  must  be  useful.  If  there  be  rules  to 
which  every  mind  consciously  or  unconsciously  conforms  in  every  instance 
in  which  it  infers  rightly,  there  seems  little  necessity  for  discussing  whether 
a person  is  more  likely  to  observe  those  rules,  when  he  knows  the  rules,  than 
when  he  is  unacquainted  with  them. 

A science  may  undoubtedly  be  brought  to  a certain,  not  inconsiderable, 
stage  of  advancement,  without  the  application  of  any  other  logic  to  it  than 
what  all  persons,  who  are  said  to  have  a sound  understanding,  acquire  em- 
pirically in  the  course  of  their  studies.  Mankind  judged  of  evidence,  and 
often  correctly,  before  logic  was  a science,  or  they  never  could  have  made 
it  one.  And  they  executed  great  mechanical  works  before  they  understood 
the  laws  of  mechanics.  But  there  are  limits  both  to  what  mechanicians  can 
do  without  principles  of  mechanics,  and  to  what  thinkers  can  do  without 
principles  of  logic.  A few  individuals,  by  extraordinary  genius,  or  by  the 
accidental  acquisition  of  a good  set  of  intellectual  habits,  may  work  with- 
out principles  in  the  same  way,  or  nearly  the  same  way,  in  which  they 
would  have  worked  if  they  had  been  in  possession  of  principles.  But  the 
bulk  of  mankind  require  either  to  understand  the  theory  of  what  they  are 
doing,  or  to  have  rules  laid  down  for  them  by  those  who  have  understood 
the  theory.  In  the  progress  of  science  from  its  easiest  to  its  more  difficult 
problems,  each  great  step  in  advance  has  usually  had  either  as  its  precur- 
sor, or  as  its  accompaniment  and  necessary  condition,  a corresponding  im- 
provement in  the  notions  and  principles  of  logic  received  among  the  most 
advanced  thinkers.  And  if  several  of  the  more  difficult  sciences  are  still 


DEFINITION  AND  PROVINCE  OF  LOGIC. 


23 


in  so  defective  a state ; if  not  only  so  little  is  proved,  but  disputation  has 
not  terminated  even  about  the  little  which  seemed  to  be  so ; the  reason 
perhaps  is,  that  men’s  logical  notions  have  not  yet  acquired  the  degree  of 
extension,  or  of  accuracy,  requisite  for  the  estimation  of  the  evidence  prop- 
er to  those  particular  departments  of  knowledge. 

§ 7.  Logic,  then,  is  the  science  of  the  operations  of  the  understanding 
which  are  subservient  to  the  estimation  of  evidence : both  the  process  it- 
self of  advancing  from  known  truths  to  unknown,  and  all  other  intellectual 
operations  in  so  far  as  auxiliary  to  this.  It  includes,  therefore,  the  opera- 
tion of  Naming ; for  language  is  an  instrument  of  thought,  as  well  as  a 
means  of  communicating  our  thoughts.  It  includes,  also,  Definition,  and 
Classification.  For,  the  use  of  these  operations  (putting  all  other  minds 
than  one’s  own  out  of  consideration)  is  to  serve  not  only  for  keeping  our 
evidences  and  the  conclusions  from  them  permanent  and  readily  accessible 
in  the  memory,  but  for  so  marshaling  the  facts  which  we  may  at  any  time 
be  engaged  in  investigating,  as  to  enable  us  to  perceive  more  clearly  what 
evidence  there  is,  and  to  judge  with  fewer  chances  of  error  whether  it  be 
sufficient.  These,  therefore,  are  operations  specially  instrumental  to  the 
estimation  of  evidence,  and,  as  such,  are  within  the  province  of  Logic. 
There  are  other  more  elementary  processes,  concerned  in  all  thinking,  such 
as  Conception,  Memory,  and  the  like ; but  of  these  it  is  not  necessary  that 
Logic  should  take  any  peculiar  cognizance,  since  they  have  no  special 
connection  with  the  problem  of  Evidence,  further  than  that,  like  all  other 
problems  addressed  to  the  understanding,  it  presupposes  them. 

Our  object,  then,  will  be,  to  attempt  a correct  analysis  of  the  intellectual 
process  called  Reasoning  or  Inference,  and  of  such  other  mental  operations 
as  are  intended  to  facilitate  this : as  well  as,  on  the  foundation  of  this  anal- 
ysis, and  pari  passu  with  it,  to  bring  together  or  frame  a set  of  rules  or 
canons  for  testing  the  sufficiency  of  any  given  evidence  to  prove  any  given 
proposition. 

With  respect  to  the  first  part  of  this  undertaking,  I do  not  attempt  to 
decompose  the  mental  operations  in  question  into  their  ultimate  elements. 
It  is  enough  if  the  analysis  as  far  as  it  goes  is  correct,  and  if  it  goes  far 
enough  for  the  practical  purposes  of  logic  considered  as  an  art.  The  sep- 
aration of  a complicated  phenomenon  into  its  component  parts  is  not  like 
a connected  and  interdependent  chain  of  proof.  If  one  link  of  an  argu- 
ment breaks,  the  whole  drops  to  the  ground ; but  one  step  toward  an  anal- 
ysis holds  good  and  has  an  independent  value,  though  we  should  never  be 
able  to  make  a second.  The  results  which  have  been  obtained  by  analytical 
chemistry  are  not  the  less  valuable,  though  it  should  be  discovered  that 
all  which  we  now  call  simple  substances  are  really  compounds.  All  other 
things  are  at  any  rate  compounded  of  those  elements : whether  the  ele- 
ments themselves  admit  of  decomposition,  is  an  important  inquiry,  but 
does  not  affect  the  certainty  of  the  science  up  to  that  point. 

I shall,  accordingly,  attempt  to  analyze  the  process  of  inference,  and  the  • 
processes  subordinate  to  inference,  so  far  only  as  may  be  requisite  for  as- 
certaining the  difference  between  a correct  and  an  incorrect  performance 
of  those  processes.  The  reason  for  thus  limiting  our  design,  is  evident. 
It  has  been  said  by  objectors  to  logic,  that  we  do  not  learn  to  use  our 
muscles  by  studying  their  anatomy.  The  fact  is  not  quite  fairly  stated; 
for  if  the  action  of  any  of  our  muscles  were  vitiated  by  local  weakness,  or 
other  physical  defect,  a knowledge  of  their  anatomy  might  be  very  neces- 


INTRODUCTION. 


•24 

saw  for  effecting  a cure.  But  we  should  be  justly  liable  to  the  criticism 
involved  in  this  objection,  were  we,  in  a treatise  on  logic,  to  carry  the  anal- 
ysis of  the  reasoning  process  beyond  the  point  at  which  any  inaccuracy 
which  may  have  crept  into  it  must  become  visible.  In  learning  bodily 
exercises  (to  carry  on  the  same  illustration)  we  do,  and  must,  analyze  the 
bodily  motions  so  far  as  is  necessary  for  distinguishing  those  which  ought 
to  be  performed  from  those  which  ought  not.  To  a similar  extent,  and  no 
further,  it  is  necessary  that  the  logician  should  analyze  the  mental  processes 
with  which  Logic  is  concerned.  Logic  has  no  interest  in  carrying  the  anal- 
ysis beyond  the  point  at  which  it  becomes  apparent  whether  the  operations 
have  in  any  individual  case  been  rightly  or  wrongly  performed : in  the 
same  manner  as  the  science  of  music  teaches  us  to  discriminate  between 
musical  notes,  and  to  know  the  combinations  of  which  they  are  susceptible, 
but  not  what  number  of  vibrations  in  a second  correspond  to  each;  which, 
though  useful  to  be  known,  is  useful  for  totally  different  purposes.  The 
extension  of  Logic  as  a Science  is  determined  by  its  necessities  as  an  Art : 
whatever  it  does  not  need  for  its  practical  ends,  it  leaves  to  the  larger 
science  which  may  be  said  to  correspond,  not  to  any  particular  art,  but  to 
art  in  general ; the  science  which  deals  with  the  constitution  of  the  human 
faculties;  and  to  which,  in  the  part  of  our  mental  nature  which  concerns 
Logic,  as  well  as  in  all  other  parts,  it  belongs  to  decide  what  are  ultimate 
facts,  and  what  are  resolvable  into  other  facts.  And  I believe  it  will  be 
found  that  most  of  the  conclusions  arrived  at  in  this  work  have  no  neces- 
sary connection  with  any  particular  views  respecting  the  ulterior  analysis. 
Logic  is  common  ground  on  which  the  partisans  of  Hartley  and  of  Reid, 
of  Locke  and  of  Kant,  may  meet  and  join  hands.  Particular  and  detached 
opinions  of  all  these  thinkers  will  no  doubt  occasionally  be  controverted, 
since  all  of  them  were  logicians  as  well  as  metaphysicians ; but  the  field  on 
which  their  principal  battles  have  been  fought,  lies  beyond  the  boundaries 
of  our  science. 

It  can  not,  indeed,  be  pretended  that  logical  principles  can  be  altogether 
irrelevant  to  those  more  abstruse  discussions;  nor  is  it  possible  but  that 
the  view  we  are  led  to  take  of  the  problem  which  logic  proposes,  must 
have  a tendency  favorable  to  the  adoption  of  some  one  opinion,  on  these 
controverted  subjects,  rather  than  another."  For  metaphysics,  in  endeavor- 
ing to  solve  its  own  peculiar  problem,  must  employ  means,  the  validity  of 
which  falls  under  the  cognizance  of  logic.  It  proceeds,  no  doubt,  as  far  as 
possible,  merely  by  a closer  and  more  attentive  interrogation  of  our  con- 
sciousness, or  more  properly  speaking,  of  our  memory;  and  so  far  is  not 
amenable  to  logic.  But  wherever  this  method  is  insufficient  to  attain  the 
end  of  its  inquiries,  it  must  proceed,  like  other  sciences,  by  means  of  evi- 
dence. Now,  the  moment  this  science  begins  to  draw  inferences  from  evi- 
dence, logic  becomes  the  sovereign  judge  whether  its  inferences  are  well 
grounded,  or  what  other  inferences  would  be  so. 

This,  however,  constitutes  no  nearer  or  other  relation  between  logic  and 
metaphysics,  than  that  which  exists  between  logic  and  every  other  science. 
And  I can  conscientiously  affirm  that  no  one  proposiuon  laid  down  in  this 
work  has  been  adopted  for  the  sake  of  establishing,  or  with  any  reference 
to  its  fitness  for  being  employed  in  establishing,  preconceived  opinions  in 
any  department  of  knowledge  or  of  inquiry  on  which  the  speculative  world 
is  still  undecided.* 

* The  view  taken  in  the  text,  of  the  definition  and  pui'pose  of  Logic,  stands  in  marked  op- 
position to  that  of  the  school  of  philosophy  which,  in  this  country,  is  represented  by  the  writ- 


DEFINITION  AND  PROVINCE  OF  LOGIC. 


25 


ings  of  Sir  William  Hamilton  and  of  his  numerous  pupils.  Logic,  as  this  school  conceives  it, 
is  “the  Science  of  the  Formal  Laws  of  Thought;”  a definition  framed  for  the  express  pur- 
pose of  excluding,  as  irrelevant  to  Logic,  whatever  relates  to  Belief  and  Disbelief,  or  to  the 
pursuit  of  truth  as  such,  and  restricting  the  science  to  that  very  limited  portion  of  its  total 
province,  which  has  reference  to  the  conditions,  not  of  Truth,  but  of  Consistency.  What  I 
have  thought  it  useful  to  say  in  opposition  to  this  limitation  of  the  field  of  Logic,  has  been 
said  at  some  length  in  a separate  work,  first  published  in  1865,  and  entitled  “An  Examina- 
tion of  Sir  William  Hamilton’s  Philosophy,  and  of  the  Principal  Philosophical  Questions  dis- 
cussed in  his  Writings.”  For  the  purposes  of  the  present  Treatise,  I am  content  that  the  jus- 
tification of  the  larger  extension  which  I give  to  the  domain  of  the  science,  should  rest  on  the 
sequel  of  the  Treatise  itself.  Some  remarks  on  the  relation  which  the  Logic  of  Consistency 
bears  to  the  Logic  of  Truth,  and  on  the  place  which  that  particular  part  occupies  in  the  whole 
to  which  it  belongs,  will  be  found  in  the  present  volume  (Book  II.,  chap,  iii.,  § 9). 


BOOK  I. 

OF  NAMES  AND  PROPOSITIONS. 


“La  seolastique,  qui  pvoduisit  dans  la  logique,  comme  dans  la  morale,  et  dans  une  partie 
de  la  metaphysique,  une  subtilite,  une  precision  d'ide'es,  dont  1’habitude  inconnue  aux  anciens, 
a contribue  plus  qu’on  ne  croit  au  progres  de  la  bonne  philosophic.” — Condorcet,  Vie  de 
Turgot. 

“To  the  schoolmen  the  vulgar  languages  are  principally  indebted  for  what  precision  and 
analytic  subtlety  they  possess.” — Sir  W.  Hamilton,  Discussions  in  Philosophy. 


CHAPTER  I. 

OF  TIIE  NECESSITY  OF  COMMENCING  WITH  AN  ANALYSIS  OF  LANGUAGE. 

§ 1.  It  is  so  much  the  established  practice  of  writers  on  logic  to  com- 
mence their  treatises  by  a few  general  observations  (in  most  cases,  it  is 
true,  rather  meagre)  on  Terms  and  their  varieties,  that  it  will,  perhaps, 
scarcely  be  required  from  me,  in  merely  following  the  common  usage,  to  be 
as  particular  in  assigning  my  reasons,  as  it  is  usually  expected  that  those 
should  be  who  deviate  from  it. 

The  practice,  indeed,  is  recommended  by  considerations  far  too  obvious 
to  require  a formal  justification.  Logic  is  a portion  of  the  Art  of  Think- 
ing : Language  is  evidently,  and  by  the  admission  of  all  philosophers,  one 
of  the  principal  instruments  or  helps  of  thought ; and  any  imperfection  in 
the  instrument,  or  in  the  mode  of  employing  it,  is  confessedly  liable,  still 
more  than  in  almost  any  other  art,  to  confuse  and  impede  the  process,  and 
destroy  all  ground  of  confidence  in  the  result.  For  a mind  not  previously 
versed  in  the  meaning  and  right  use  of  the  various  kinds  of  words,  to  at- 
tempt the  study  of  methods  of  philosophizing,  would  be  as  if  some  one 
should  attempt  to  become  an  astronomical  observer,  having  never  learned  to 
adjust  the  focal  distance  of  Ins  optical  instruments  so  as  to  see  distinctly. 

Since  Reasoning,  or  Inference,  the  principal  subject  of  logic,  is  an  opera- 
tion which  usually  takes  place  by  means  of  words,  and  in  complicated  cases 
can  take  place  in  no  other  way ; those  who  have  not  a thorough  insight 
into  the  signification  and  purposes  of  words,  will  be  under  chances,  amount- 
ing almost  to  certainty,  of  reasoning  or  inferring  incorrectly.  And  logi- 
cians have  generally  felt  that  unless,  in  the  very  first  stage,  they  removed 
this  source  of  error;  unless  they  taught  their  pupil  to  put  away  the  glasses 
which  distort  the  object,  and  to  use  those  which  are  adapted  to  his  pur- 
pose in  such  a manner  as  to  assist,  not  perplex,  his  vision;  he  would  not  be 
in  a condition  to  practice  the  remaining  part  of  their  discipline  with  any 
prospect  of  advantage.  Therefore  it  is  that  an  inquiry  into  language,  so 
far  as  is  needful  to  guard  against  the  errors  to  which  it  gives  rise,  has  at 
all  times  been  deemed  a necessary  preliminary  to  the  study  of  logic. 


NECESSITY  OF  AN  ANALYSIS  OF  NAMES. 


27 


But  there  is  another  reason,  of  a still  more  fundamental  nature,  why  the 
import  of  words  should  be  the  earliest  subject  of  the  logician’s  considera- 
tion : because  without  it  he  can  not  examine  into  the  import  of  Proposi- 
tions. Now  this  is  a subject  which  stands  on  the  very  threshold  of  the 
science  of  logic. 

The  object  of  logic,  as  defined  in  the  Introductory  Chapter,  is  to  ascer- 
tain how  we  come  by  that  portion  of  our  knowledge  (much  the  greatest 
portion)  which  is  not  intuitive:  and  by  what  criterion  we  can,  in  matters 
not  self-evident,  distinguish  between  things  proved  and  things  not  proved, 
between  what  is  worthy  and  what  is  unworthy  of  belief.  Of  the  various 
questions  which  present  themselves  to  our  inquiring  faculties,  some  receive 
an  answer  from  direct  consciousness,  others,  if  resolved  at  all,  can  only  be 
resolved  by  means  of  evidence.  Logic  is  concerned  with  these  last.  But 
before  inquiring  into  the  mode  of  resolving  questions,  it  is  necessary  to  in- 
quire what  are  those  which  offer  themselves ; what  questions  are  conceiva- 
ble; what  inquiries  are  there,  to  which  mankind  have  either  obtained,  or 
been  able  to  imagine  it  possible  that  they  should  obtain,  an  answer.  This 
point  is  best  ascertained  by  a survey  and  analysis  of  Propositions. 

§ 2.  The  answer  to  every  question  which  it  is  possible  to  frame,  must 
be  contained  in  a Proposition,  or  Assertion.  Whatever  can  be  an  object 
of  belief,  or  even  of  disbelief,  must,  when  put  into  words,  assume  the  form 
of  a proposition.  All  truth  and  all  error  lie  in  propositions.  What,  by 
a convenient  misapplication  of  an  abstract  term,  we  call  a Truth,  means 
simply  a True  . Proposition ; and  errors  are  false  propositions.  To  know 
the  import  of  all  possible  propositions  would  be  to  know  all  questions 
which  can  be  raised,  all  matters  which  are  susceptible  of  being  either  be- 
lieved or  disbelieved.  How  many  kinds  of  inquiries  can  be  propound- 
ed; how  many  kinds  of  judgments  can  be  made;  and  how  many  kinds 
of  propositions  it  is  possible  to  frame  with  a meaning,  are  but  different 
forms  of  one  and  the  same  question.  Since,  then,  the  objects  of  all  Be- 
lief and  of  all  Inquiry  express  themselves  in  propositions,  a sufficient  scru- 
tiny of  Propositions  and  of  their  varieties  will  apprise  us  what  questions 
mankind  have  actually  asked  of  themselves,  and  what,  in  the  nature  of  an- 
swers to  those  questions,  they  have  actually  thought  they  had  grounds  to 
believe. 

Now  the  first  glance  at  a proposition  shows  that  it  is  formed  by  putting 
together  two  names.  A proposition,  according  to  the  common  simple  defi- 
nition, which  is  sufficient  for  our  purpose  is,  discourse,  in  which  something 
is  affirmed  or  denied  of  something.  Thus,  in  the  proposition,  Gold  is  yel- 
low, the  quality  yellow  is  affirmed  of  the  substance  gold.  In  the  proposi- 
tion, Franklin  was  not  born  in  England,  the  fact  expressed  by  the  words 
born  in  England  is  denied  of  the  man  F ranklin. 

Every  proposition  consists  of  three  parts : the  Subject,  the  Predicate, 
and  the  Copula.  The  predicate  is  the  name  denoting  that  which  is  affirmed 
or  denied.  The  subject  is  the  name  denoting  the  person  or  thing  which 
something  is  affirmed  or  denied  of.  The  copula  is  the  sign  denoting  that 
there  is  an  affirmation  or  denial,  and  thereby  enabling  the  hearer  or  reader 
to  distinguish  a proposition  from  any  other  kind  of  discourse.  Thus,  in  the 
proposition,  The  earth  is  round,  the  Predicate  is  the  word  round,  which  de- 
notes the  quality  affirmed,  or  (as  the  phrase  is)  predicated  : the  earth,  words 
denoting  the  object  which  that  quality  is  affirmed  of,  compose  the  Subject; 
the  word  is,  which  serves  as  the  connecting  mark  between  the  subject  and 


28 


NAMES  AND  PROPOSITIONS. 


predicate,  to  show  that  one  of  them  is  affirmed  of  the  other,  is  called  the 
Copula. 

Dismissing,  for  the  present,  the  copula,  of  which  more  will  be  said  here- 
after, every  proposition,  then,  consists  of  at  least  two  names — brings  to- 
gether two  names,  in  a particular  manner.  This  is  already  a first  step  to- 
ward what  we  are  in  quest  of.  It  appears  from  this,  that  for  an  act  of  be- 
lief, one  object  is  not  sufficient;  the  simplest  act  of  belief  supposes,  and  has 
something  to  do  with, two  objects — two  names, to  say  the  least;  and  (since 
the  names  must  be  names  of  something)  two  namable  things.  A large 
class  of  thinkers  would  cut  the  matter  short  by  saying,  two  ideas.  They 
would  say,  that  the  subject  and  predicate  are  both  of  them  names  of  ideas ; 
the  idea  of  gold,  for  instance,  and  the  idea  of  yellow ; and  that  what  takes 
place  (or  part  of  what  takes  place)  in  the  act  of  belief  consists  in  bring- 
ing (as  it  is  often  expressed)  one  of  these  ideas  under  the  other.  But  this 
we  are  not  yet  in  a condition  to  say : whether  such  be  the  correct  mode 
of  describing  the  phenomenon,  is  an  after  consideration.  The  result  with 
which  for  the  present  we  must  be  contented,  is,  that  in  every  act  of  belief 
two  objects  are  in  some  manner  taken  cognizance  of;  that  there  can  be  no 
belief  claimed,  or  question  propounded,  which  does  not  embrace  two  dis- 
tinct (either  material  or  intellectual)  subjects  of  thought;  each  of  them 
capable,  or  not,  of  being  conceived  by  itself,  but  incapable  of  being  believed 
by  itself. 

I may  say,  for  instance,  “ the  sun.”  The  word  has  a meaning,  and  sug- 
gests that  meaning  to  the  mind  of  any  one  who  is  listening  to  me.  But 
suppose  I ask  him,  Whether  it  is  true : whether  he  believes  it  ? He  can 
give  no  answer.  There  is  as  yet  nothing  to  believe,  or  to  disbelieve.  Now, 
however,  let  me  make,  of  all  possible  assertions  respecting  the  sun,  the  one 
which  involves  the  least  of  reference  to  any  object  besides  itself;  let  me 
say,  “ the  sun  exists.”  Here,  at  once,  is  something  which  a person  can  say 
he  believes.  But  here,  instead  of  only  one,  we  find  two  distinct  objects  of 
conception  : the  sun  is  one  object;  existence  is  another.  Let  it  not  be  said 
that  this  second  conception,  existence,  is  involved  in  the  first ; for  the  sun 
may  be  conceived  as  no  longer  existing.  “The  sun”  does  not  convey  all 
the  meaning  that  is  conveyed  by  “the  sun  exists:”  “my  father”  does  not 
include  all  the  meaning  of  “ my  father  exists,”  for  he  may  be  dead ; “ a 
round  square”  does  not  include  the  meaning  of  “a  round  squai’e  exists,” 
ror  it  does  not  and  can  not  exist.  When  I say  “ the  sun,”  “ my  father,”  or 
a “ round  square,”  I do  not  call  upon  the  hearer  for  any  belief  or  disbelief, 
nor  can  either  the  one  or  the  other  be  afforded  me;  but  if  I say,  “ the  sun 
exists,”  “my  father  exists,”  or  “a  round  square  exists,”  I call  for  belief; 
and  should,  in  the  first  of  the  three  instances,  meet  with  it;  in  the  second, 
with  belief  or  disbelief,  as  the  case  might  be ; in  the  third,  with  disbelief. 

§ 3.  This  first  step  in  the  analysis  of  the  object  of  belief,  which,  though 
so  obvious,  will  be  found  to  be  not  unimportant,  is  the  only  one  which  we 
shall  find  it  practicable  to  make  without  a preliminary  survey  of  language. 
If  we  attempt  to  proceed  further  in  the  same  path,  that  is,  to  analyze  any 
further  the  import  of  Propositions ; we  find  forced  upon  us,  as  a subject  of 
previous  consideration,  the  import  of  Names.  For  every  proposition  con- 
sists of  two  names ; and  every  proposition  affirms  or  denies  one  of  these 
names,  of  the  other.  Now  what  we  do,  what  passes  in  our  mind,  when  we 
affirm  or  deny  two  names  of  one  another,  must  depend  on  what  they  are 
names  of;  since  it  is  with  reference  to  that,  and  not  to  the  mere  names 


NAMES. 


29 


themselves,  that  we  make  the  affirmation  or  denial.  Here,  therefore,  we 
find  a new  reason  why  the  signification  of  names,  and  the  relation  general- 
ly between  names  and  the  things  signified  by  them,  must  occupy  the  pre- 
liminary stage  of  the  inquiry  we  are  engaged  in. 

It  may  be  objected  that  the  meaning  of  names  can  guide  us  at  most  only 
to  the  opinions,  possibly  the  foolish  and  groundless  opinions,  which  man- 
kind have  formed  concerning  things,  and  that  as  the  object  of  philosophy 
is  truth,  not  opinion,  the  philosopher  should  dismiss  words  and  look  into 
things  themselves,  to  ascertain  what  questions  can  be  asked  and  answered 
in  regard  to  them.  This  advice  (which  no  one  has  it  in  his  power  to  fol- 
low) is  in  reality  an  exhortation  to  discard  the  whole  fruits  of  the  labors  of 
his  predecessors,  and  conduct  himself  as  if  he  were  the  first  person  who 
had  ever  turned  an  inquiring  eye  upon  nature.  What  does  any  one’s  per- 
sonal knowledge  of  Things  amount  to,  after  subtracting  all  which  he  has 
acquired  by  means  of  the  words  of  other  people?  Even  after  he  has  learn- 
ed as  much  as  people  usually  do  learn  from  others,  will  the  notions  of 
things  contained  in  his  individual  mind  afford  as  sufficient  a basis  for  a 
catalogue  raisonn'e  as  the  notions  which  are  in  the  minds  of  all  mankind  ? 

In  any  enumeration  and  classification  of  Things,  which  does  not  set  out 
from  their  names,  no  varieties  of  things  will  of  course  be  comprehended 
but  those  recognized  by  the  particular  inquirer;  and  it  will  still  remain  to 
be  established,  by  a subsequent  examination  of  names,  that  the  enumera- 
tion has  omitted  nothing  which  ought  to  have  been  included.  But  if  we 
begin  Avith  names,  and  use  them  as  our  clue  to  the  things,  we  bring  at  once 
before  us  all  the  distinctions  tvhich  have  been  recognized,  not  by  a single 
inquirer,  but  by  all  inquirers  taken  together.  It  doubtless  may,  and  I be- 
lieve it  Avill,  be  found,  that  mankind  have  multiplied  the  varieties  unneces- 
sarily, and  have  imagined  distinctions  among  things,  where  there  were  only 
distinctions  in  the  manner  of  naming  them.  But  we  are  not  entitled  to  as- 
sume this  in  the  commencement.  We  must  begin  by  recognizing  the  dis- 
tinctions made  by  ordinary  language.  If  some  of  these  appear,  on  a close 
examination,  not  to  be  fundamental,  the  enumeration  of  the  different  kinds 
of  realities  may  be  abridged  accordingly.  But  to  impose  upon  the  facts  in 
the  first  instance  the  yoke  of  a theory,  Avhile  the  grounds  of  the  theory  are 
reserved  for  discussion  in  a subsequent  stage,  is  not  a course  which  a logi- 
cian can  reasonably  adopt. 


CHAPTER  II. 

OF  NAMES. 

§ 1.  “A  name,”  says  Hobbes,*  “is  a Avord  taken  at  pleasure  to  serve  for 
a mark  Avhich  may  raise  in  our  mind  a thought  like  to  some  thought  Ave  had 
before,  and  Avhich  being  pronounced  to  others,  may  be  to  them  a sign  of 
what  thought  the  speaker  hadf  before  in  his  mind.”  This  simple  defini- 
tion of  a name,  as  a Avord  (or  set  of  Avords)  serving  the  double  purpose  of 
a mark  to  recall  to  ourselves  the  likeness  of  a former  thought,  and  a sign 

* Computation  or  Logic , chap.  ii. 

t In  the  original  “had,  or  had  not.”  These  last  words,  as  involving  a subtlety  foreign  to 
our  present  purpose,  I have  forborne  to  quote. 


30 


NAMES  AND  PROPOSITIONS. 


to  make  it  known  to  others,  appears  unexceptionable.  Names,  indeed,  do 
much  more  than  this;  but  whatever  else  they  do,  grows  out  of,  and  is  the 
result  of  this:  as  will  appear  in  its  proper  place. 

Are  names  more  properly  said  to  be  the  names  of  things,  or  of  our  ideas 
of  things?  The  tirst  is  the  expression  in  common  use;  the  last  is  that  of 
some  metaphysicians,  who  conceived  that  in  adopting  it  they  were  intro- 
ducing a highly  important  distinction.  The  eminent  thinker,  just  quoted, 
seems  to  countenance  the  latter  opinion.  “But  seeing,”  he  continues, 
“ names  ordered  in  speech  (as  is  defined)  are  signs  of  our  conceptions,  it 
is  manifest  they  are  not  signs  of  the  things  themselves;  for  that  the  sound 
of  this  word  stone  should  be  the  sign  of  a stone,  can  not  be  understood  in 
any  sense  but  this,  that  he  that  hears  it  collects  that  he  that  pronounces  it 
thinks  of  a stone.” 

If  it  be  merely  meant  that  the  conception  alone,  and  not  the  thing  itself, 
is  recalled  by  the  name,  or  imparted  to  the  hearer,  this  of  course  can  not 
be  denied.  Nevertheless,  there  seems  good  reason  for  adhering  to  the 
common  usage,  and  calling  (as  indeed  Hobbes  himself  does  in  other  places) 
the  word  sun  the  name  of  the  sun,  and  not  the  name  of  our  idea  of  the 
sun.  For  names  are  not  intended  only  to  make  the  hearer  conceive  what 
we  conceive,  but  also  to  inform  him  what  we  believe.  Now,  when  I use  a 
name  for  the  purpose  of  expressing  a belief,  it  is  a belief  concerning  the 
thing  itself,  not  concerning  my  idea  of  it.  When  I say,  “the  sun  is  the 
cause  of  day,”  I do  not  mean  that  my  idea  of  the  sun  causes  or  excites  in 
me  the  idea  of  day  ; or  in  other  words,  that  thinking  of  the  sun  makes  me 
think  of  day.  I mean,  that  a certain  physical  fact,  which  is  called  the  sun’s 
presence  (and  which,  in  the  ultimate  analysis,  resolves  itself  into  sensations, 
not  ideas)  causes  another  physical  fact,  which  is  called  day.  It  seems  prop- 
er to  consider  a word  as  the  name  of  that  which  we  intend  to  be  under- 
stood by  it  when  we  use  it;  of  that  which  any  fact  that  we  assert  of  it  is 
to  be  understood  of;  that,  in  short,  concerning  which,  when  we  employ  the 
word,  we  intend  to  give  information.  Names,  therefore,  shall  always  be 
spoken  of  in  this  work  as  the  names  of  things  themselves,  and  not  merely 
of  our  ideas  of  things. 

But  the  question  now  arises,  of  what  things?  and  to  answer  this  it  is 
necessary  to  take  into  consideration  the  different  kinds  of  names. 

§ 2.  It  is  usual,  before  examining  the  various  classes  into  which  names 
are  commonly  divided,  to  begin  by  distinguishing  from  names  of  every 
description,  those  words  which  are  not  names,  but  only  parts  of  names. 
Among  such  are  reckoned  particles,  as  of,  to,  truly,  often ; the  inflected 
cases  of  nouns  substantive,  as  me,  him,  John's  ; and  even  adjectives,  as 
large,  heavy.  These  words  do  not  express  things  of  w'hich  any  thing  can 
be  affirmed  or  denied.  We  can  not  say,  Heavy  fell,  or  A heavy  fell ; Truly, 
or  A truly,  was  asserted;  Of,  or  An  of,  was  in  the  room.  Unless,  indeed, 
we  are  speaking  of  the  mere  words  themselves,  as  when  we  say,  Truly  is 
an  English  word,  or,  Heavy  is  an  adjective.  In  that  case  they  are  complete 
names — viz.,  names  of  those  particular  sounds,  or  of  those'  particular  col- 
lections of  written  characters.  This  employment  of  a word  to  denote  the 
mere  letters  and  syllables  of  which  it  is  composed,  was  termed  by  the 
schoolmen  the  suppositio  materialis  of  the  word.  In  any  other  sense  we 
can  not  introduce  one  of  these  words  into  the  subject  of  a proposition, 
unless  in  combination  with  other  words ; as,  A heavy  body  fell,  A truly 
important  fact  was  asserted,  A member  of  parliament  was  in  the  room. 


NAMES. 


31 


An  adjective,  however,  is  capable  of  standing  by  itself  as  the  predicate 
of  a proposition ; as  when  we  say,  Snow  is  white ; and  occasionally  even 
as  the  subject,  for  we  may  say,  White  is  an  agreeable  color.  The  adjec- 
tive is  often  said  to  be  so  used  by  a grammatical  ellipsis : Snow  is  white, 
instead  of  Snow  is  a white  object;  White  is  an  agreeable  color,  instead  of, 
A white  color,  or,  The  color  white,  is  agreeable.  The  Greeks  and  Romans 
were  allowed,  by  the  rules  of  their  language,  to  employ  this  ellipsis  uni- 
versally in  the  subject  as  well  as  in  the  predicate  of  a proposition.  In 
English  this  can  not,  generally  speaking,  be  done.  We  may  say,  The  earth 
is  round ; but  we  can  not  say,  Round  is  easily  moved ; we  must  say,  A 
round  object.  This  distinction,  however,  is  rather  grammatical  than  log- 
ical. Since  there  is  no  difference  of  meaning  between  round , and  a round 
object,  it  is  only  custom  which  prescribes  that  on  any  given  occasion  one 
shall  be  used,  and  not  the  other.  We  shall,  therefore,  without  scruple, 
speak  of  adjectives  as  names,  whether  in  their  own  right,  or  as  representa- 
tive of  the  more  circuitous  forms  of  expression  above  exemplified.  The 
other  classes  of  subsidiary  words  have  no  title  whatever  to  be  considered 
as  names.  An  adverb,  or  an  accusative  case,  can  not  under  any  circum- 
stances (except  wThen  their  mere  letters  and  syllables  are  spoken  of)  figure 
as  one  of  the  terms  of  a proposition. 

Words  which  are  not  capable  of  being  used  as  names,  but  only  as  parts 
of  names,  were  called  by  some  of  the  schoolmen  Syncategorematic  terms : 
from  avr,  with,  and  Kar^yopew,  to  predicate,  because  it  was  only  with  some 
other  word  that  they  could  be  predicated.  A word  which  could  be  used 
either  as  the  subject  or  predicate  of  a proposition  without  being  accom- 
panied by  any  other  word,  was  termed  by  the  same  authorities  a Cate- 
gorematic  term.  A combination  of  one  or  more  Categorematic,  and  one 
or  more  Syncategorematic  words,  as  A heavy  body,  or  A court  of  justice, 
they  sometimes  called  a mixed  term ; but  this  seems  a needless  multiplica- 
tion of  technical  expressions.  A mixed  term  is,  in  the  only  useful  sense  of 
the  word,  Categorematic.  It  belongs  to  the  class  of  what  have  been  called 
manv-worded  names. 

For,  as  one  word  is  frequently  not  a name,  but  only  part  of  a name,  so 
a number  of  words  often  compose  one  single  name,  and  no  more.  These 
words,  “ The  place  which  the  wisdom  or  policy  of  antiquity  had  destined 
for  the  residence  of  the  Abyssinian  princes,”  form  in  the  estimation  of  the 
logician  only  one  name;  one  Categorematic  term.  A mode  of  determining 
whether  any  set  of  words  makes  only  one  name,  or  more  than  one,  is  by 
predicating  something  of  it,  and  observing  whether,  by  this  predication,  we 
make  only  one  assertion  or  several.  Thus,  when  we  say,  John  Nokes,  who 
was  the  mayor  of  the  town,  died  yesterday — by  this  predication  we  make 
but  one  assertion;  whence  it  appears  that  “John  Nokes,  who  was  the 
mayor  of  the  town,”  is  no  more  than  one  name.  It  is  true  that  in  this 
proposition,  besides  the  assertion  that  John  Nokes  died  yesterday,  there 
is  included  another  assertion,  namely,  that  John  Nokes  was  mayor  of  the 
town.  But  this  last  assertion  was  already  made:  we  did  not  make  it  by 
adding  the  predicate,  “ died  yesterday.”  Suppose,  however,  that  the  words 
had  been,  John  Nokes  and  the  mayor  of  the  town,  they  would  have  formed 
two  names  instead  of  one.  For  when  we  say,  John  Nokes  and  the  mayor 
of  the  town  died  yesterday,  we  make  two  assertions:  one,  that  John  Nokes 
died  yesterday ; the  other,  that  the  mayor  of  the  town  died  yesterday. 

It  being  needless  to  illustrate  at  any  greater  length  the  subject  of  many- 
worded  names,  we  proceed  to  the  distinctions  which  have  been  established 


32 


NAMES  AND  PROPOSITIONS. 


among  names,  not  according  to  the  words  they  are  composed  of,  but  ac- 
cording to  their  signification. 

§ 3.  All  names  are  names  of  something,  real  or  imaginary;  but  all  things 
have  not  names  appropriated  to  them  individually.  For  some  individual 
objects  we  require,  and  consequently  have,  separate  distinguishing  names ; 
there  is  a name  for  every  person,  and  for  every  remarkable  place.  Other 
objects,  of  which  we  have  not  occasion  to  speak  so  frequently,  we  do  not 
designate  by  a name  of  their  own ; but  when  the  necessity  arises  for  nam- 
ing them,  we  do  so  by  putting  together  several  words,  each  of  which,  by 
itself,  might  be  and  is  used  for  an  indefinite  number  of  other  objects;  as 
when  I say,  this  stone:  “this”  and  “stone”  being,  each  of  them,  names 
that  may  be  used  of  many  other  objects  besides  the  particular  one  meant, 
though  the  only  object  of  which  they  can  both  be  used  at  the  given  mo- 
ment, consistently  with  their  signification,  may  be  the  one  of  which  I wish 
to  speak. 

Were  this  the  sole  purpose  for  which  names,  that  are  common  to  more 
things  than  one,  could  be  employed ; if  they  only  served,  by  mutually  lim- 
iting each  other,  to  afford  a designation  for  such  individual  objects  as  have 
no  names  of  their  own : they  could  only  be  ranked  among  contrivances  for 
economizing  the  use  of  language.  But  it  is  evident  that  this  is  not  their 
sole  function.  It  is  by  their  means  that  we  are  enabled  to  assert  general 
propositions ; to  affirm  or  deny  any  predicate  of  an  indefinite  number  of 
things  at  once.  The  distinction,  therefore,  between  general  names,  and  in- 
dividual or  singular  names,  is  fundamental;  and  may  be  considered  as  the 
first  grand  division  of  names. 

A general  name  is  familiarly  defined,  a name  which  is  capable  of  being 
truly  affirmed,  in  the  same  sense,  of  each  of  an  indefinite  number  of  things. 
An  individual  or  singular  name  is  a name  which  is  only  capable  of  being 
truly  affirmed,  in  the  same  sense,  of  one  thing. 

Thus,  man  is  capable  of  being  truly  affirmed  of  John,  George,  Mary,  and 
other  persons  without  assignable  limit ; and  it  is  affirmed  of  all  of  them  in 
the  same  sense ; for  the  word  man  expresses  certain  qualities,  and  when  we 
predicate  it  of  those  persons,  we  assert  that  they  all  possess  those  qualities. 
But  thohn  is  only  capable  of  being  truly  affirmed  of  one  single  person,  at 
least  in  the  same  sense.  For,  though  there  are  many  persons  who  bear 
that  name,  it  is  not  conferred  upon  them  to  indicate  any  qualities,  or  any 
thing  which  belongs  to  them  in  common  ; and  can  not  be  said  to  be  affirm- 
ed of  them  in  any  sense  at  all,  consequently  not  in  the  same  sense.  “ The 
king  who  succeeded  William  the  Conqueror,”  is  also  an  individual  name. 
For,  that  there  can  not  be  more  than  one  person  of  whom  it  can  be  truly 
affirmed,  is  implied  in  the  meaning  of  the  words.  Even  “ the  king,”  when 
the  occasion  or  the  context  defines  the  individual  of  whom  it  is  to  be  un- 
derstood, may  justly  be  regarded  as  an  individual  name. 

It  is  not  unusual,  by  way  of  explaining  what  is  meant  by  a general  name, 
to  say  that  it  is  the  name  of  a class.  But  this,  though  a convenient  mode 
of  expression  for  some  purposes,  is  objectionable  as  a definition,  since  it 
explains  the  clearer  of  two  things  by  the  more  obscure.  It  would  be  more 
logical  to  reverse  the  proposition,  and  turn  it  into  a definition  of  the  word 
class  : “A  class  is  the  indefinite  multitude  of  individuals  denoted  by  a gen- 
eral name.” 

It  is  necessary  to  distinguish  general  from  collective  names.  A general 
name  is  one  which  can  be  predicated  of  each  mdmdual  of  a multitude ; a 


NAMES. 


33 


collective  name  can  not  be  predicated  of  each  separately,  but  only  of  all 
taken  together.  “The  76th  regiment  of  foot  in  the  British  army,”  which 
is  a collective  name,  is  not  a general  but  an  individual  name;  for  though  it 
can  be  predicated  of  a multitude  of  individual  soldiers  taken  jointly,  it  can 
Tint  be  predicated  of  them  severally.  We  may  say,  Jones  is  a soldier,  and 
Thompson  is  a soldier,  and  Smith  is  a soldier,  but  we  can  not  say,  Jones  is 
the  76th  regiment,  and  Thompson  is  the  76th  regiment,  and  Smith  is  the 
76th  regiment.  We  can  only  say,  Jones,  and  Thompson,  and  Smith,  and 
Brown,  and  so  forth  (enumerating  all  the  soldiers),  are  the  76th  regiment. 

“The  76th  regiment”  is  a collective  name,  but  not  a general  one:  “a 
regiment”  is  both  a collective  and  a general  name.  General  with  respect 
to  all  individual  regiments,  of  each  of  which  separately  it  can  be  affirmed : 
collective  with  respect  to  the  individual  soldiers  of  whom  any  regiment  is 
composed. 

§ 4.  The  second  general  division  of  names  is  into  concrete  and  abstract. 
A concrete  name  is  a name  which  stands  for  a thing;  an  abstract  name  is 
a name  which  stands  for  an  attribute  of  a thing.  Thus  John , the  sea , this 
table , are  names  of  things.  White,  also,  is  a name  of  a thing,  or  rather  of 
things.  Whiteness,  again,  is  the  name  of  a quality  or  attribute  of  those 
things.  Man  is  a name  of  many  things;  humanity  is  a name  of  an  attri- 
bute of  those  things.  Old  is  a name  of  things : old  age  is  a name  of  one 
of  their  attributes. 

I have  used  the  words  concrete  and  abstract  in  the  sense  annexed'  to 
them  by  the  schoolmen,  who,  notwithstanding  the  imperfections  of  their 
philosophy,  were  unrivaled  in  the  construction  of  technical  language,  and 
whose  definitions,  in  logic  at  least,  though  they  never  went  more  than  a lit- 
tle way  into  the  subject,  have  seldom,  I think,  been  altered  but  to  be  spoil- 
ed. A practice,  however,  has  grown  up  in  more  modern  times,  which,  if 
not  introduced  by  Locke,  has  gained  currency  chiefly  from  his  example,  of 
applying  the  expression  “abstract  name”  to  all  names  which  are  the  result 
of  abstraction  or  generalization,  and  consequently  to  all  general  names,  in- 
stead of  confining  it  to  the  names  of  attributes.  The  metaphysicians  of  the 
Condillac  school — whose  admiration  of  Locke,  passing  over  the  profound- 
est  speculations  of  that  truly  original  genius,  usually  fastens  with  peculiar 
eagerness  upon  his  weakest  points — have  gone  on  imitating  him  in  this 
abuse  of  language,  until  there  is  now  some  difficulty  in  restoring  the  word 
to  its  original  signification.  A more  wanton  alteration  in  the  meaning  of  a 
word  is  rarely  to  be  met  with ; for  the  expression  general  name,  the  exact 
equivalent  of  which  exists  in  all  languages  I am  acquainted  with,  was  al- 
ready available  for  the  purpose  to  which  abstract  has  been  misappropri- 
ated,  while  the  misappropriation  leaves  that  important  class  of  words,  the 
names  of  attributes,  without  any  compact  distinctive  appellation.  The  old 
acceptation,  however,  has  not  gone  so  completely  out  of  use  as  to  deprive 
those  who  still  adhere  to  it  of  all  chance  of  being  understood.  By  abstract, 
then,  I shall  always,  in  Logic  proper,  mean  the  opposite  of  concrete ; by  an 
abstract  name,  the  name  of  an  attribute ; by  a concrete  name,  the  name  of 
an  object. 

Do  abstract  names  belong  to  the  class  of  general,  or  to  that  of  singular 
names  ? Some  of  them  are  certainly  general.  I mean  those  which  are 
names  not  of  one  single  and  definite  attribute,  but  of  a class  of  attributes. 
Such  is  the  word  color,  which  is  a name  common  to  whiteness,  redness, 
etc.  Such  is  even  the  word  whiteness,  in  respect  of  the  different  shades  of 

3 


NAMES  AND  PROPOSITIONS. 


.>4 

whiteness  to  which  it  is  applied  in  common:  the  word  magnitude,  in  re- 
spect of  the  various  degrees  of  magnitude  and  the  various  dimensions  of 
spare;  tile  word  weight,  in  respect  of  the  various  degrees  of  weight.  Such 
also  is  the  word  attribute  itself,  the  common  name  of  all  particular  attri- 
butes. But  when  only  one  attribute,  neither  variable  in  degree  nor  in 
kind,  is  designated  by  the  name;  as  visibleness;  tangibleness;  equality; 
squareness;  milk-whiteness;  then  the  name  can  hardly  be  considered  gen- 
eral; for  though  it  denotes  an  attribute  of  many  different  objects,  the  at- 
tribute itself  is  always  conceived  as  one,  not  many.*  To  avoid  needless  lo- 
gomachies, the  best  course  would  probably  be  to  consider  these  names  as 
neither  general  nor  individual,  and  to  place  them  in  a class  apart. 

It  may  be  objected  to  our  definition  of  an  abstract  name,  that  not  only 
the  names  which  we  have  called  abstract,  but  adjectives,  which  we  have 
placed  in  the  concrete  class,  are  names  of  attributes;  that  white,  for  exam- 
ple, is  as  much  the  name  of  the  color  as  whiteness  is.  But  (as  before  re- 
marked) a word  ought  to  be  considered  as  the  name  of  that  which  we  intend 
to  be  understood  by  it  when  we  put  it  to  its  principal  use,  that  is,  when  we 
employ  it  in  predication.  When  we  say  snow  is  white,  milk  is  white,  linen 
is  white,  we  do  not  mean  it  to  be  understood  that  snow,  or  linen,  or  milk, 
is  a color.  We  mean  that  they  are  things  having  the  color.  The  reverse 
is  the  case  with  the  word  whiteness;  what  we  affirm  to  be  whiteness  is  not 
snow,  but  the  color  of  snow.  Whiteness,  therefore,  is  the  name  of  the  col- 
or exclusively:  white  is  a name  of  all  things  whatever  having  the  color;  a 
name,  not  of  the  quality  whiteness,  but  of  every  white  object.  It  is  true, 
this  name  was  given  to  all  those  various  objects  on  account  of  the  quality; 
and  we  may  therefore  say,  without  impropriety,  that  the  quality  forms  part 
of  its  signification;  but  a name  can  only  be  said  to  stand  for,  or  to  be  a 
name  of,  the  things  of  which  it  can  be  predicated.  We  shall  presently  see 
that  all  names  which  can  be  said  to  have  any  signification,  all  names  by  ap- 
plying which  to  an  individual  we  give  any  information  respecting  that  in- 
dividual, may  be  said  to  imply  an  attribute  of  some  sort;  but  they  are  not 
names  of  the  attribute ; it  has  its  own  proper  abstract  name. 

§ 5.  This  leads  to  the  consideration  of  a third  great  division  of  names, 
into  connotative  and  non-connotative , the  latter  sometimes,  but  improperly, 
called  absolute.  This  is  one  of  the  most  important  distinctions  which  we 
shall  have  occasion  to  point  out,  and  one  of  those  which  go  deepest  into 
the  nature  of  language. 

A non-connotative  term  is  one  which  signifies  a subject  only,  or  an  attri- 
bute only.  A connotative  term  is  one  which  denotes  a subject,  and  implies 
an  attribute.  By  a subject  is  here  meant  any  thing  which  possesses  attri- 
butes. Thus  John,  or  London,  or  England,  are  names  which  signify  a sub- 
ject only.  Whiteness,  length,  virtue,  signify  an  attribute  only.  None  of 
these  names,  therefore,  are  connotative.  But  white , long,  virtuous,  are  con- 
notative. The  word  white,  denotes  all  white  things,  as  snow,  paper,  the 
foam  of  the  sea,  etc.,  and  implies,  or  in  the  language  of  the  schoolmen,  con- 
notes,,f  the  attribute  vihiteness.  The  word  white  is  not  predicated  of  the 
attribute,  but  of  the  subjects,  snow,  etc.;  but  when  we  predicate  it  of 
them,  we  convey  the  meaning  that  the  attribute  whiteness  belongs  to  them. 
The  same  may  be  said  of  the  other  words  above  cited.  Virtuous,  for  ex- 

* Vide  infra,  note  at  the  end  of  § 3,  book  ii. , chap.  ii. 

t Notaro.,  to  mark  ; corcnotare,  to  mark  along  with ; to  mark  one  thing  with  or  in  addition 
to  another. 


NAMES. 


35 


ample,  is  the  name  of  a class,  which  includes  Socrates,  Howard,  the  Man  of 
Ross,  and  an  undefinable  number  of  other  individuals,  past,  present,  and  to 
come.  These  individuals,  collectively  and  severally,  can  alone  be  said  with 
propriety  to  be  denoted  by  the  word  : of  them  alone  can  it  properly  be  said 
to  be  a name.  But  it  is  a name  applied  to  all  of  them  in  consequence  of 
an  attribute  which  they  are  supposed  to  possess  in  common,  the  attribute 
which  has  received  the  name  of  virtue.  It  is  applied  to  all  beings  that  are 
considered  to  possess  this  attribute ; and  to  none  which  are  not  so  con- 
sidered. 

All  concrete  general  names  are  connotative.  The  word  man , for  exam- 
ple, denotes  Peter,  Jane,  John,  and  an  indefinite  number  of  other  individu- 
als, of  whom,  taken  as  a class,  it  is  the  name.  But  it  is  applied  to  them, 
because  they  possess,  and  to  signify  that  they  possess,  certain  attributes. 
These  seem  to  be,  corporeity,  animal  life,  rationality,  and  a certain  exter- 
nal form,  which  for  distinction  we  call  the  human.  Every  existing  thing, 
which  possessed  all  these  attributes,  would  be  called  a man ; and  any  thing 
which  possessed  none  of  them,  or  only  one,  or  two,  or  even  three  of  them 
without  the  fourth,  would  not  be  so  called.  For  example,  if  in  the  interior 
of  Africa  there  were  to  be  discovered  a race  of  animals  possessing  reason 
equal  to  that  of  human  beings,  but  with  the  form  of  an  elephant,  they 
would  not  be  called  men.  Swift’s  Houyhnhnms  would  not  be  so  called. 
Or  if  such  newly-discovered  beings  possessed  the  form  of  man  without  any 
vestige  of  reason,  it  is  probable  that  some  other  name  than  that  of  man 
would  be  found  for  them.  How  it  happens  that  there  can  be  any  doubt 
about  the  matter,  will  appear  hereafter.  The  word  man , therefore,  signi- 
fies all  these  attributes,  and  all  subjects  which  possess  these  attributes. 
But  it  can  be  predicated  only  of  the  subjects.  What  we  call  men,  are  the 
subjects,  the  individual  Stiles  and  Hokes;  not  the  qualities  by  which  their 
humanity  is  constituted.  The  name,  therefore,  is  said  to  signify  the  sub- 
jects directly , the  attributes  indirectly  ; it  denotes  the  subjects,  and  im- 
plies, or  involves,  or  indicates,  or  as  we  shall  say  henceforth  connotes , the 
attributes.  It  is  a connotative  name. 

Connotative  names  have  hence  been  also  called  denominative , because 
the  subject  which  they  denote  is  denominated  by,  or  receives  a name  from 
the  attribute  which  they  connote.  Snow,  and  other  objects,  receive  the 
name  white,  because  they  possess  the  attribute  which  is  called  whiteness ; 
Peter,  James,  and  others  receive  the  name  man  because  they  possess  the 
attributes  which  are  considered  to  constitute  humanity.  The  attribute,  or 
attributes,  may  therefore  be  said  to  denominate  those  objects,  or  to  give 
them  a common  name.* 

It  has  been  seen  that  all  concrete  general  names  are  connotative.  Even 
abstract  names,  though  the  names  only  of  attributes,  may  in  some  instances 
be  justly  considered  as  connotative;  for  attributes  themselves  may  have 
attributes  ascribed  to  them ; and  a word  which  denotes  attributes  may  con- 
note an  attribute  of  those  attributes.  Of  this  description,  for  example,  is 
such  a word  as  fault;  equivalent  to  bad  or  hurtful  quality.  This  word  is 
a name  common  to  many  attributes,  and  connotes  hurtfulness,  an  attribute 

* Archbishop  Whately,  who,  in  the  later  editions  of  his  Elements  of  Logic,  aided  in  reviving 
the  important  distinction  treated  of  in  the  text,  proposes  the  term  “Attributive”  as  a substi- 
tute for  “Connotative”  (p.  22,  9th  edit.).  The  expression  is,  in  itself,  appropriate:  but  as 
it  has  not  the  advantage  of  being  connected  with  any  verb,  of  so  markedly  distinctive  a char- 
acter as  “to  connote,”  it  is  not,  I think,  fitted  to  supply  the  place  of  the  word  Connotative  in 
scientific  use. 


o6 


NAMES  AND  PROPOSITIONS. 


of  those  various  attributes.  When,  for  example,  we  say  that  slowness,  in 
a horse,  is  a fault,  we  do  not  mean  that  the  slow  movement,  the  actual 
change  of  place  of  the  slow  horse,  is  a bad  thing,  but  that  the  property  or 
peculiarity  of  the  horse,  from  which  it  derives  that  name,  the  quality  of  be- 
ing a slow  mover,  is  an  undesirable  peculiarity. 

In  regard  to  those  concrete  names  which  are  not  general  but  individual, 
a distinction  must  be  made. 

Proper  names  are  not  connotative:  they  denote  the  individuals  who  are 
called  by  them ; but  they  do  not  indicate  or  imply  any  attributes  as  belong- 
ing to  those  individuals.  When  we  name  a child  by  the  name  Paul,  or  a 
dog  by  the  name  Ciesar,  these  names  are  simply  marks  used  to  enable  those 
individuals  to  be  made  subjects  of  discourse.  It  may  be  said,  indeed,  that 
we  must  have  had  some  reason  for  giving  them  those  names  rather  than 
any  others ; and  this  is  true ; but  the  name,  once  given,  is  independent 
of  the  reason.  A man  may  have  been  named  John,  because  that  was  the 
name  of  his  father;  a town  may  have  been  named  Dartmouth,  because  it  is 
situated  at  the  mouth  of  the  Dart.  But  it  is  no  part  of  the  signification  of 
the  word  John,  that  the  father  of  the  person  so  called  bore  the  same  name ; 
nor  even  of  the  word  Dartmouth,  to  be  situated  at  the  mouth  of  the  Dart. 
If  sand  should  choke  up  the  mouth  of  the  river,  or  an  earthquake  change 
its  course,  and  remove  it  to  a distance  from  the  town,  the  name  of  the 
town  would  not  necessarily  be  changed.  That  fact,  therefore,  can  form  no 
part  of  the  signification  of  the  word;  for  otherwise,  when  the  fact  confess- 
edly ceased  to  be  true,  no  one  would  any  longer  think  of  applying  the 
name.  Proper  names  are  attached  to  the  objects  themselves,  and  are  not 
dependent  on  the  continuance  of  any  attribute  of  the  object. 

But  there  is  another  kind  of  names,  which,  although  they  are  individual 
names — that  is,  predicable  only  of  one  object — are  really  connotative.  For, 
though  we  may  give  to  an  individual  a name  utterly  unmeaning,  which  we 
call  a proper  name — a word  which  answers  the  purpose  of  showing  what 
thing  it  is  we  are  talking  about,  but  not  of  telling  any  thing  about  it;  yet 
a name  peculiar  to  an  individual  is  not  necessarily  of  this  description.  It 
may  be  significant  of  some  attribute,  or  some  union  of  attributes,  which, 
being  possessed  by  no  object  but  one,  determines  the  name  exclusively  to 
that  individual.  “The  sun”  is  a name  of  this  description;  “God,”  when 
used  by  a monotheist,  is  another.  These,  however,  are  scarcely  examples 
of  what  we  are  now  attempting  to  illustrate,  being,  in  strictness  of  lan- 
guage, general,  not  individual  names:  for,  however  they  may  be  in  fact 
predicable  only  of  one  object,  there  is  nothing  in  the  meaning  of  the  words 
themselves  which  implies  this:  and,  accordingly,  when  we  are  imagining 
and  not  affirming,  we  may  speak  of  many  suns;  and  the  majority  of  man- 
kind have  believed,  and  still  believe,  that  there  are  many  gods.  But  it  is 
easy  to  produce  words  which  are  real  instances  of  connotative  individual 
names.  It  may  be  part  of  the  meaning  of  the  connotative  name  itself,  that 
there  can  exist  but  one  individual  possessing  the  attribute  which  it  con- 
notes: as,  for  instance,  “the  only  son  of  John  Stiles;”  “the  first  emperor 
of  Rome.”  Or  the  attribute  connoted  may  be  a connection  with  some  de- 
terminate event,  and  the  connection  may  be  of  such  a kind  as  only  one  in- 
dividual could  have;  or  may  at  least  be  such  as  only  one  individual  actually 
had  ; and  this  may  be  implied  in  the  form  of  the  expression.  “ The  father 
of  Socrates  ” is  an  example  of  the  one  kind  (since  Socrates  could  not  have 
had  ttvo  fathers) ; “ the  author  of  the  Iliad,”  “ the  murderer  of  Henri  Qua- 
tre,”  of  the  second.  For,  though  it  is  conceivable  that  more  persons  than 


NAMES. 


37 


one  might  have  participated  in  the  authorship  of  the  Iliad,  or  in  the  mur- 
der of  Henri  Quatre,  the  employment  of  the  article  the  implies  that,  in 
fact,  this  was  not  the  case.  What  is  here  done  by  the  word  the , is  done 
in  other  cases  by  the  context:  thus,  “ Caesar’s  army”  is  an  individual 
name,  if  it  appears  from  the  context  that  the  army  meant  is  that  which 
Ctesar  commanded  in  a particular  battle.  The  still  more  general  expres- 
sions, “the  Roman  army,”  or  “the  Christian  army,”  may  be  individual- 
ized in  a similar  manner.  Another  case  of  frequent  occurrence  has  already 
been  noticed;  it  is  the  following:  The  name,  being  a many-worded  one, 
may  consist,  in  the  first  place,  of  a general  name,  capable  therefore  in  it- 
self of  being  affirmed  of  more  things  than  one,  but  which  is,  in  the  second 
place,  so  limited  by  other  words  joined  with  it,  that  the  entire  expression 
can  only  be  predicated  of  one  object,  consistently  with  the  meaning  of 
the  general  term.  This  is  exemplified  in  such  an  instance  as  the  follow- 
ing: “ the  present  j:>rime  minister  of  England.”  Prime  Minister  of  Eng- 
land is  a general  name;  the  attributes  which  it  connotes  may  be  possessed 
by  an  indefinite  number  of  persons:  in  succession,  however,  not  simulta- 
neously; since  the  meaning  of  the  name  itself  imports  (among  other 
things)  that  there  can  be  only  one  such  person  at  a time.  This  being 
the  case,  and  the  application  of  the  name  being  afterward  limited  by  the 
article  and  the  word  present,  to  such  individuals  as  possess  the  attributes 
at  one  indivisible  point  of  time,  it  becomes  applicable  only  to  one  indi- 
vidual. And  as  this  appears  from  the  meaning  of  the  name,  without  any 
extrinsic  proof,  it  is  strictly  an  individual  name. 

From  the  preceding  observations  it  will  easily  be  collected,  that  when- 
ever the  names  given  to  objects  convey  any  information— that  is,  when- 
ever they  have  properly  any  meaning — the  meaning  resides  not  in  what 
they  denote , but  in  what  they  connote.  The  only  names  of  objects  which 
connote  nothing  are  proper  names ; and  these  have,  strictly  speaking,  no 
signification.* 

If,  like  the  robber  in  the  Arabian  Nights,  we  make  a mark  with  chalk  on 
a house  to  enable  us  to  know  it  again,  the  mark  has  a purpose,  but  it  has 
not  properly  any  meaning.  The  chalk  does  not  declare  any  thing  about 
the  house ; it  does  not  mean,  This  is  such  a person’s  house,  or  This  is  a 
house  which  contains  booty.  The  object  of  making  the  mark  is  merely 
distinction.  I say  to  myself,  All  these  houses  are  so  nearly  alike  that  if  I 
lose  sight  of  them  I shall  not  again  be  able  to  distinguish  that  which  I am 
now  looking  at,  from  any  of  the  others ; I must  therefore  contrive  to  make 
the  appearance  of  this  one  house  unlike  that  of  the  others,  that  I may  here- 
after know  when  I see  the  mark — not  indeed  any  attribute  of  the  house — 
but  simply  that  it  is  the  same  house  which  I am  now  looking  at.  Mor- 
giana  chalked  all  the  other  houses  in  a similar  manner,  and  defeated  the 
scheme : how  ? simply  by  obliterating  the  difference  of  appearance  between 
that  house  and  the  others.  The  chalk  was  still  there,  but  it  no  longer 
served  the  purpose  of  a distinctive  mark. 

* A writer  who  entitles  his  book  Philosophy ; or,  the  Science  of  Truth,  charges  me  in  his 
very  first  page  (referring  at  the  foot  of  it  to  this  passage)  with  asserting  that  general  names 
have  properly  no  signification.  And  he  repeats  this  statement  many  times  in  the  course  of 
his  volume,  with  comments,  not  at  all  flattering,  thereon.  It  is  well  to  be  now  and  then  re- 
minded to  how  great  a length  perverse  misquotation  (for,  strange  as  it  appears,  I do  not  be- 
lieve that  the  writer  is  dishonest)  can  sometimes  go.  It  is  a warning  to  readers  when  they 
see  an  author  accused,  with  volume  and  page  referred  to,  and  the  apparent  guarantee  of  invert- 
ed commas,  of  maintaining  something  more  than  commonly  absurd,  not  to  give  implicit  cre- 
dence to  the  assertion  without  verifying  the  reference. 


38 


NAMES  AND  PROPOSITIONS. 


When  we  impose  a proper  name,  we  perform  an  operation  in  some  de- 
gree analogous  to  what  the  robber  intended  in  chalking  the  house.  We 
put  a mark,  not  indeed  upon  the  object  itself,  but,  so  to  speak,  upon  the 
idea  of  the  object.  A proper  name  is  but  an  unmeaning  mark  which  we 
connect  in  our  minds  with  the  idea  of  the  object,  in  order  that  whenever 
the  mark  meets  our  eyes  or  occurs  to  our  thoughts,  we  may  think  of  that 
individual  object.  Not  being  attached  to  the  thing  itself,  it  does  not,  like 
the  chalk,  enable  us  to  distinguish  the  object  when  we  see  it;  but  it  ena- 
bles us  to  distinguish  it  when  it  is  spoken  of,  either  in  the  records  of  our 
own  experience,  or  in  the  discourse  of  others;  to  know  that  what  we  find 
asserted  in  any  proposition  of  which  it  is  the  subject,  is  asserted  of  the  in- 
dividual thing  with  which  we  were  previously  acquainted. 

When  we  predicate  of  any  thing  its  proper  name;  when  we  say,  point- 
ing to  a man,  this  is  Brown  or  Smith,  or  pointing  to  a city,  that  it  is  York, 
we  do  not,  merely  by  so  doing,  convey  to  the  reader  any  information  about 
them,  except  that  those  are  their  names.  By  enabling  him  to  identify  the 
individuals,  we  may  connect  them  with  information  previously  possessed 
by  him ; by  saying,  This  is  York,  we  may  tell  him  that  it  contains  the  Min- 
ster. But  this  is  in  virtue  of  what  he  has  previously  heard  concerning 
York ; not  by  any  thing  implied  in  the  name.  It  is  otherwise  when  ob- 
jects are  spoken  of  by  connotative  names.  When  we  say,  The  town  is 
built  of  marble,  we  give  the  hearer  what  may  be  entirely  new  information, 
and  this  merely  by  the  signification  of  the  many-worded  connotative  name, 
“ built  of  marble.”  Such  names  are  not  signs  of  the  mere  objects,  invented 
because  we  have  occasion  to  think  and  speak  of  those  objects  individually; 
but  signs  which  accompany  an  attribute;  a kind  of  livery  in  which  the 
attribute  clothes  all  objects  which  are  recognized  as  possessing  it.  They 
are  not  mere  marks,  but  more,  that  is  to  say,  significant  marks ; and  the 
connotation  is  what  constitutes  their  significance. 

As  a proper  name  is  said  to  be  the  name  of  the  one  individual  which  it 
is  predicated  of,  so  (as  well  from  the  importance  of  adhering  to  analogy,  as 
for  the  other  reasons  formerly  assigned)  a connotative  name  ought  to  be 
considered  a name  of  all  the  various  individuals  which  it  is  predicable  of, 
or  in  other  words  denotes , and  not  of  what  it  connotes.  But  by  learning 
what  things  it  is  a name  of,  we  do  not  learn  the  meaning  of  the  name : for 
to  the  same  thing  we  may,  with  equal  propriety,  apply  many  names,  not 
equivalent  in  meaning.  Thus,  I call  a certain  man  by  the  name  Sophronis- 
cus:  I call  him  by  another  name,  The  father  of  Socrates.  Both  these  are 
names  of  the  same  individual,  but  their  meaning  is  altogether  different; 
they  are  applied  to  that  individual  for  two  different  purposes:  the  one, 
merely  to  distinguish  him  from  other  persons  who  are  spoken  of ; the  other 
to  indicate  a fact  relating  to  him,  the  fact  that  Socrates  was  his  son.  I 
further  apply  to  him  these  other  expressions  : a man,  a Greek,  an  Athenian, 
a sculptor,  an  old  man,  an  honest  man,  a brave  man.  All  these  are,  or  may 
be,  names  of  Sophroniscus,  not  indeed  of  him  alone,  but  of  him  and  each 
of  an  indefinite  number  of  other  human  beings.  Each  of  these  names  is 
applied  to  Sophroniscus  for  a different  reason,  and  by  each  whoever  under- 
stands its  meaning  is  apprised  of  a distinct  fact  or  number  of  facts  con- 
cerning him;  but  those  who  knew  nothing  about  the  names  except  that 
they  were  applicable  to  Sophroniscus,  would  be  altogether  ignorant  of  their 
meaning.  It  is  even  possible  that  I might  know  every  single  individual  of 
whom  a given  name  could  be  with  truth  affirmed,  and  yet  could  not  be  said 
to  know  the  meaning  of  the  name.  A child  knows  who  are  its  brothers 


NAMES. 


39 


and  sisters,  long  before  it  has  any  definite  conception  of  the  nature  of  the 
facts  which  are  involved  in  the  signification  of  those  words. 

In  some  cases  it  is  not  easy  to  decide  precisely  how  much  a particular 
word  does  or  does  not  connote;  that  is,  we  do  not  exactly  know  (the  case 
not  having  ai’isen)  what  degree  of  difference  in  the  object  would  occasion 
a difference  in  the  name.  Thus,  it  is  clear  that  the  word  man,  besides 
animal  life  and  rationality,  connotes  also  a certain  external  form ; but  it 
would  be  impossible  to  say  precisely  what  form ; that  is,  to  decide  how 
great  a deviation  from  the  form  ordinarily  found  in  the  beings  whom  we  are 
accustomed  to  call  men,  would  suffice  in  a newly-discovered  race  to  make 
us  refuse  them  the  name  of  man.  Rationality,  also,  being  a quality  which 
admits  of  degrees,  it  has  never  been  settled  what  is  the  lowest  degree  of 
that  quality  which  would  entitle  any  creature  to  be  considered  a human 
being.  In  all  such  cases,  the  meaning  of  the  general  name  is  so  far  un- 
settled and  vague ; mankind  have  not  come  to  any  positive  agreement 
about  the  matter.  When  we  come  to  treat  of  Classification,  we  shall  have 
occasion  to  show  under  what  conditions  this  vagueness  may  exist  without 
practical  inconvenience;  and  cases  will  appear  in  which  the  ends  of  lan- 
guage are  better  promoted  by  it  than  by  complete  precision;  in  order  that, 
in  natural  history  for  instance,  individuals  or  species  of  no  very  marked 
character  may  be  ranged  with  those  more  strongly  characterized  individuals 
or  species  to  which,  in  all  their  properties  taken  together,  they  bear  the 
nearest  resemblance. 

But  this  partial  uncertainty  in  the  connotation  of  names  can  only  be 
free  from  mischief  when  guarded  by  strict  precautions.  One  of  the  chief 
sources,  indeed,  of  lax  habits  of  thought,  is  the  custom  of  using  connotative 
terms  without  a distinctly  ascertained  connotation,  and  with  no  more  pre- 
cise notion  of  their  meaning  than  can  be  loosely  collected  from  observing 
what  objects  they  are  used  to  denote.  It  is  in  this  manner  that  we  all  ac- 
quire, and  inevitably  so,  our  first  knowledge  of  our  vernacular  language. 
A child  learns  the  meaning  of  the  words  man , or  white,  by  hearing  them 
applied  to  a variety  of  individual  objects,  and  finding  out,  by  a process  of 
generalization  and  analysis  which  he  could  not  himself  describe,  what  those 
different  objects  have  in  common.  In  the  case  of  these  two  words  the 
process  is  so  easy  as  to  require  no  assistance  from  culture;  the  objects 
called  human  beings,  and  the  objects  called  white,  differing  from  all  others 
by  qualities  of  a peculiarly  definite  and  obvious  character.  But  in  many 
other  cases,  objects  bear  a general  resemblance  to  one  another,  which  leads 
to  their  being  familiarly  classed  together  under  a common  name,  while, 
without  more  analytic  habits  than  the  generality  of  mankind  jmssess,  it  is 
not  immediately  apparent  what  are  the  particular  attributes,  upon  the  pos- 
session of  which  in  common  by  them  all,  their  general  resemblance  depends. 
When  this  is  the  case,  people  use  the  name  without  any  recognized  con- 
notation, that  is,  without  any  precise  meaning  ; they  talk,  and  consequently 
think,  vaguely,  and  remain  contented  to  attach  only  the  same  degree  of 
significance  to  their  own  words,  which  a child  three  years  old  attaches  to 
the  words  brother  and  sister.  The  child  at  least  is  seldom  puzzled  by  the 
starting  up  of  new  individuals,  on  whom  he  is  ignorant  whether  or  not  to 
confer  the  title ; because  there  is  usually  an  authority  close  at  hand  com- 
petent to  solve  all  doubts.  But  a similar  resource  does  not  exist  in  the 
generality  of  cases ; and  new  objects  are  continually  presenting  themselves 
to  men,  women,  and  children,  which  they  are  called  upon  to  class  proprio 
motu.  They,  accordingly,  do  this  on  no  other  principle  than  that  of  super- 


40 


NAMES  AND  PROPOSITIONS. 


ficial  similarity,  giving  to  each  new  object  the  name  of  that  familiar  object, 
the  idea  of  which  it  most  readily  recalls,  or  which,  on  a cursory  inspection, 
it  seems  to  them  most  to  resemble:  as  an  unknown  substance  found  in  the 
ground  will  be  called,  according  to  its  texture,  earth,  sand,  or  a stone.  In 
this  manner,  names  creep  on  from  subject  to  subject,  until  all  traces  of 
a common  meaning  sometimes  disappear,  and  the  word  comes  to  denote 
a number  of  things  not  only  independently  of  any  common  attribute, 
but  which  have  actually  no  attribute  in  common;  or  none  but  what  is 
shared  by  other  things  to  which  the  name  is  capriciously  refused.*  Even 
scientific  writers  have  aided  in  this  perversion  of  general  language  from 
its  purpose ; sometimes  because,  like  the  vulgar,  they  knew  no  better ; 
and  sometimes  in  deference  to  that  aversion  to  admit  new  words,  which 
induces  mankind,  on  all  subjects  not  considered  technical,  to  attempt  to 
make  the  original  stock  of  names  serve  with  but  little  augmentation  to 
express  a constantly  increasing  number  of  objects  and  distinctions,  and, 
consequently,  to  express  them  in  a manner  progressively  more  and  more 
imperfect. 

To  what  a degree  this  loose  mode  of  classing  and  denominating  objects 
has  rendered  the  vocabulary  of  mental  and  moral  philosophy  unfit  for  the 
purposes  of  accurate  thinking,  is  best  known  to  whoever  has  most  medi- 
tated on  the  present  condition  of  those  branches  of  knowledge.  Since, 
however,  the  introduction  of  a new  technical  language  as  the  vehicle  of 
speculations  on  subjects  belonging  to  the  domain  of  daily  discussion,  is  ex- 
tremely difficult  to  effect,  and  would  not  be  free  from  inconvenience  even 
if  effected,  the  problem  for  the  philosopher,  and  one  of  the  most  difficult 
which  he  has  to  resolve,  is,  in  retaining  the  existing  phraseology,  how  best 
to  alleviate  its  imperfections.  This  can  only  be  accomplished  by  giving  to 
every  general  concrete  name  which  there  is  frequent  occasion  to  predicate, 
a definite  and  fixed  connotation;  in  order  that  it  may  be  known  what  attri- 
butes, when  we  call  an  object  by  that  name,  we  really  mean  to  predicate  of 
the  object.  And  the  question  of  most  nicety  is,  how  to  give  this  fixed  con- 
notation to  a name,  with  the  least  possible  change  in  the  objects  which  the 
name  is  habitually  employed  to  denote;  with  the  least  possible  disarrange- 
ment, either  by  adding  or  subtraction,  of  the  group  of  objects  which,  in 
however  imperfect  a manner,  it  serves  to  circumscribe  and  hold  together ; 
and  with  the  least  vitiation  of  the  truth  of  any  propositions  which  are  com- 
monly received  as  true. 

This  desirable  purpose,  of  giving  a fixed  connotation  where  it  is  want- 
ing, is  the  end  aimed  at  whenever  any  one  attempts  to  give  a definition  of 
a general  name  already  in  use;  every  definition  of  a connotative  name  be- 
ing an  attempt  either  merely  to  declare,  or  to  declare  and  analyze,  the  con- 
notation of  the  name.  And  the  fact,  that  no  questions  which  have  arisen 
in  the  moral  sciences  have  been  subjects  of  keener  controversy  than  the 

* “Take  the  familiar  term  Stone.  It  is  applied  to  mineral  and  rocky  materials,  to  the 
kernels  of  fruit,  to  the  accumulations  in  the  gall-bladder  and  in  the  kidney ; while  it  is  re- 
fused to  polished  minerals  (called  gems),  to  rocks  that  have  the  cleavage  suited  for  roofing 
(slates;,  and  to  baked  clay  (bricks).  It  occurs  in  the  designation  of  the  magnetic  oxide  of 
iron  (loadstone),  and  not  in  speaking  of  other  metallic  ores.  Such  a term  is  wholly  unfit  for 
accurate  reasoning,  unless  hedged  round  on  every  occasion  by  other  phrases;  as  building 
stone,  precious  stone,  gall-stone,  etc.  Moreover,  the  methods  of  definition  are  baffled  for 
want, of  sufficient  community  to  ground  upon.  There  is  no  quality  uniformly  present  in  the 
cases  where  it  is  applied,  and  uniformly  absent  where  it  is  not  applied;  hence  the  definer 
would  have  to  employ  largely  the  license  of  striking  off  existing  applications,  and  taking  in 
new  ones.” — Bain,  Logic , ii. , 172.  ■' 


NAMES. 


41 


definitions  of  almost  all  the  leading  expressions,  is  a proof  how  great  an 
extent  the  evil  to  which  we  have  adverted  has  attained. 

Names  with  indeterminate  connotation  are  not  to  be  confounded  with 
names  which  have  more  than  one  connotation,  that  is  to  say,  ambiguous 
words.  A word  may  have  several  meanings,  but  all  of  them  fixed  and  rec- 
ognized ones ; as  the  word  post,  for  example,  or  the  word  box,  the  various 
senses  of  which  it  would  be  endless  to  enumerate.  And  the  paucity  of  ex- 
isting names,  in  comparison  with  the  demand  for  them,  may  often  render 
it  advisable  and  even  necessary  to  retain  a name  in  this  multiplicity  of' ac- 
ceptations, distinguishing  these  so  clearly  as  to  prevent  their  being  con- 
founded with  one  another.  Such  a word  may  be  considered  as  two  or 
more  names,  accidentally  written  and  spoken  alike.* 

§ 6.  The  fourth  principal  division  of  names,  is  into  positive  and  nega- 
tive. Positive,  as  man,  tree,  good ; negative,  as  not-man , not-tree,  not-good. 
To  every  positive  concrete  name,  a corresponding  negative  one  might  be 
framed.  After  giving  a name  to  any  one  thing,  or  to  any  plurality  of 
things,  we  might  create  a second  name  which  should  be  a name  of  all  things 
whatever,  except  that  particular  thing  or  things.  These  negative  names 
are  employed  whenever  we  have  occasion  to  speak  collectively  of  all  things 
other  than  some  thing  or  class  of  things.  When  the  positive  name  is  con- 
notative,  the  corresponding  negative  name  is  connotative  likewise;  but  in  a 

* Before  quitting  the  subject  of  connotative  names,  it  is  proper  to  observe,  that  the  first 
writer  who,  in  our  times,  has  adopted  from  the  schoolmen  the  word  to  connote,  Mr.  James 
Mill,  in  his  Analysis  of  the  Phenomena  of  the  Human  Mind,  employs  it  in  a signification  dif- 
ferent from  that  in  which  it  is  here  used.  He  uses  the  word  in  a sense  co-extensive  with  its 
etymology,  applying  it  to  every  case  in  which  a name,  while  pointing  directly  to  one  thing 
(which  is  consequently  termed  its  signification),  includes  also  a tacit  reference  to  some  other 
thing.  In  the  case  considered  in  the  text,  that  of  concrete  general  names,  his  language  and 
mine  are  the  converse  of  one  another.  Considering  (very  justly)  the  signification  of  the  name 
to  lie  in  the  attribute,  he  speaks  of  the  word  as  noting  the  attribute,  and  connoting  the  things 
possessing  the  attribute.  And  he  describes  abstract  names  as  being  properly  coucrete  names 
with  their  connotation  dropped ; whereas,  in  my  view,  it  is  the  denotation  which  would  be 
said  to  be  dropped,  what  was  previously  connoted  becoming  the  whole  signification. 

In  adopting  a phraseology  at  variance  with  that  which  so  high  an  authority,  and  one  which 
I am  less  likely  than  any  other  person  to  undervalue,  has  deliberately  sanctioned,  I have  been 
influenced  by  the  urgent  necessity  for  a term  exclusively  appropriated  to  express  the  manner 
in  which  a concrete  general  name  serves  to  mark  the  attributes  which  are  involved  in  its  signi- 
fication. This  necessity  can  scarcely  be  felt  in  its  full  force  by  any  one  who  has  not  found  by 
experience  how  vain  is  the  attempt  to  communicate  clear  ideas  on  the  philosophy  of  language 
without  such  a word.  It  is  hardly  an  exaggeration  to  say,  that  some  of  the  most  prevalent  of 
the  errors  with  which  logic  has  been  infected,  and  a large  part  of  the  cloudiness  and  confusion 
of  ideas  which  have  enveloped  it,  would,  in  all  probability,  have  been  avoided,  if  a term  had 
been  in  common  nse  to  express  exactly  what  I have  signified  by  the  term  to  connote.  And 
the  schoolmen,  to  whom  we  are  indebted  for  the  greater  part  of  our  logical  language,  gave  us 
this  also,  and  in  this  very  sense.  Eor  though  some  of  their  general  expressions  countenance 
the  use  of  the  word  in  the  more  extensive  and  vague  acceptation  in  which  it  is  taken  by  Mr. 
Mill,  yet  when  they  had  to  define  it  specifically  as  a technical  term,  and  to  fix  its  meaning  as 
such,  with  that  admirable  precision  which  always  characterizes  their  definitions,  they  clearly 
explained  that  nothing  was  said  to  be  connoted  except  forms , which  word  may  generally,  in 
their  writings,  be  understood  as  synonymous  with  attributes. 

Now,  if  the  word  to  connote,  so  well  suited  to  the  purpose  to  which  they  applied  it,  be  di- 
verted from  that  purpose  by  being  taken  to  fulfill  another,  for  which  it  does  not  seem  to  me  to 
be  at  all  required ; I am  unable  to  find  any  expression  to  replace  it,  but  such  as  are  commonly 
employed  in  a sense  so  much  more  general,  that  it  would  be  useless  attempting  to  associate 
them  peculiarly  with  this  precise  idea.  Such  are  the  words,  to  involve,  to  imply,  etc.  By 
employing  these,  I should  fail  of  attaining  the  object  for  wrhich  alone  the  name  is  needed, 
namely,  to  distinguish  this  particular  kind  of  involving  and  implying  from  all  other  kinds,  and 
to  assure  to  it  the  degree  of  habitual  attention  which  its  importance  demands. 


42 


NAMES  AND  PROPOSITIONS. 


peculiar  way,  connoting  not  the  presence  but  the  absence  of  an  attribute. 
Thus,  not-wliite  denotes  all  things  whatever  except  white  things;  and  con- 
notes the  attribute  of  not  possessing  whiteness.  For  the  non-possession  of 
any  given  attribute  is  also  an  attribute,  and  may  receive  a name  as  such; 
and  Urns  negative  concrete  names  may  obtain  negative  abstract  names  to 
correspond  to  them.* 

Names  which  are  positive  in  form  are  often  negative  in  reality,  and  oth- 
ers are  really  positive  though  their  form  is  negative.  The  word  inconven- 
ient, foi  example,  does  not  express  the  mere  absence  of  convenience;  it  ex- 
presses a positive  attribute — that  of  being  the  cause  of  discomfort  or  an- 
no} mice.  So  the  word  unpleasant , notwithstanding  its  negative  form,  does 
not  connote  the  mere  absence  of  pleasantness,  but  a less  degree  of  what  is 
signified  by  the  word  painful , which,  it  is  hardly  necessary  to  say,  is  posi- 
tive. Idle,  on  the  other  hand,  is  a word  which,  though  positive  in  form, 
expresses  nothing  but  what  would  be  signified  either  by  the  phrase  not 
working,  or  by  the  phrase  not  disposed  to  work ; and  sober,  either  by  not 
drunk  or  by  not  drunken. 

There  is  a class  of  names  called  privative.  A privative  name  is  equiva- 
lent in  its  signification  to  a positive  and  a negative  name  taken  together ; 
being  the  name  of  something  which  has  once  had  a particular  attribute,  or 
for  some  other  reason  might  have  been  expected  to  have  it,  but  which  has 
it  not.  Such  is  the  word  blind,  which  is  not  equivalent  to  not  seeing,  or  to 
not  capable  of  seeing,  for  it  would  not,  except  by  a poetical  or  rhetorical 
figure,  be  applied  to  stocks  and  stones.  A thing  is  not  usually  said  to  be 
blind,  unless  the  class  to  which  it  is  most  familiarly  referred,  or  to  which 
it  is  referred  on  the  particular  occasion,  be  chiefly  composed  of  things 
which  can  see,  as  in  the  case  of  a blind  man,  or  a blind  horse ; or  unless  it 
is  supposed  for  any  reason  that  it  ought  to  see ; as  in  saying  of  a man,  that 
he  rushed  blindly  into  an  abyss,  or  of  philosophers  or  the  clergy  that  the 
greater  part  of  them  are  blind  guides.  The  names  called  privative,  there- 
fore, connote  two  things  ; the  absence  of  certain  attributes,  and  the  pres- 
ence of  others,  from  which  the  presence  also  of  the  former  might  naturally 
have  been  expected. 

§ 7.  The  fifth  leading  division  of  names  is  into  relative  and  absolute,  or 
let  us  rather  say,  relative  and  non-relative ; for  the  word  absolute  is  put 
upon  much  too  hard  duty  in  metaphysics,  not  to  be  willingly  spared  when 
its  services  can  be  dispensed  with.  It  resembles  the  word  civil  in  the  lan- 
guage of  jurisprudence,  which  stands  for  the  opposite  of  criminal,  the  op- 
posite of  ecclesiastical,  the  opposite  of  military,  the  opposite  of  political — 
in  short,  the  opposite  of  any  positive  word  which  wants  a negative. 

Relative  names  are  such  as  father,  son;  ruler,  subject;  like;  equal;  un- 
like; unequal;  longer,  shorter;  cause,  effect.  Their  characteristic  property 
is,  that  they  are  always  given  in  pairs.  Every  relative  name  which  is  pred- 
icated of  an  object,  supposes  another  object  (or  objects),  of  which  we  may 
predicate  either  that  same  name  or  another  relative  name  which  is  said  to 
be  the  correlative  of  the  former.  Thus,  when  we  call  any  person  a son,  we 

* Professor  Bain  (Logic,  i.,  56)  thinks  that  negative  names  are  not  names  of  all  things 
whatever  except  those  denoted  by  the  correlative  positive  name,  but  only  for  all  things  of  some 
particular  class:  not-whil.e,  for  instance,  he  deems  not  to  be  a name  for  every  thing  in  nature 
except  white  tilings,  but  only  for  every  colored  thing  other  than  white.  In  this  ease,  however, 
as  in  all  others,  the  test  of  what  a name  denotes  is  what  it  can  be  predicated  of:  and  we  can 
certainly  predicate  of  a sound,  or  a smell,  that  it  is  not  white.  The  affirmation  and  the  nega- 
tion of  the  same  attribute  can  not  but  divide  the  whole  field  of  predication  between  them. 


NAMES. 


43 


suppose  other  persons  who  must  be  called  parents.  When  we  call  any  event 
a cause,  we  suppose  another  event  which  is  an  effect.  When  we  say  of 
any  distance  that  it  is  longer,  we  suppose  another  distance  which  is  shorter. 
When  we  say  of  any  object  that  it  is  like,  we  mean  that  it  is  like  some 
other  object,  which  is  also  said  to  be  like  the  first.  In  this  last  case  both 
objects  receive  the  same  name ; the  relative  term  is  its  own  correlative. 

It  is  evident  that  these  words,  when  concrete,  are,  like  other  concrete 
general  names,  connotative;  they  denote  a subject,  and  connote  an  attri- 
bute ; and  each  of  them  has,  or  might  have,  a corresponding  abstract  name, 
to  denote  the  attribute  connoted  by  the  concrete.  Thus  the  concrete  like 
has  its  abstract  likeness / the  concretes,  father  and  son,  have,  or  might  have, 
the  abstracts,  paternity,  and  filiety,  or  sonship.  The  concrete  name  con- 
notes an  attribute,  and  the  abstract  name  which  answers  to  it  denotes  that 
attribute.  But  of  what  nature  is  the  attribute?  Wherein  consists  the 
peculiarity  in  the  connotation  of  a relative  name? 

The  attribute  signified  by  a relative  name,  say  some,  is  a relation ; and 
this  they  give,  if  not  as  a sufficient  explanation,  at  least  as  the  only  one  at- 
tainable. If  they  are  asked,  What  then  is  a relation?  they  do  not  profess 
to  be  able  to  tell.  It  is  generally  regarded  as  something  peculiarly  recondite 
and  mysterious.  I can  not,  however,  perceive  in  what  respect  it  is  more 
so  than  any  other  attribute ; indeed,  it  appears  to  me  to  be  so  in  a some- 
what less  degree.  I conceive  rather,  that  it  is  by  examining  into  the  sig- 
nification of  relative  names,  or,  in  other  words,  into  the  nature  of  the  at- 
tribute which  they  connote,  that  a clear  insight  may  best  be  obtained  into 
the  nature  of  all  attributes:  of  all  that  is  meant  by  an  attribute. 

It  is  obvious,  in  fact,  that  if  we  take  any  two  correlative  names,  father 
and  soji  for  instance,  though  the  objects  denoted  by  the  names  are  differ- 
ent, they  both,  in  a certain  sense,  connote  the  same  thing.  They  can  not, 
indeed,  be  said  to  connote  the  same  attribute:  to  be  a father,  is  not  the 
same  thing  as  to  be  a son.  But  when  we  call  one  man  a father,  another  a 
son,  what  we  mean  to  affirm  is  a set  of  facts,  which  are  exactly  the  same  in 
both  cases.  To  predicate  of  A that  he  is  the  father  of  B,  and  of  B that  he 
is  the  son  of  A,  is  to  assert  one  and  the  same  fact  in  different  words.  The 
two  propositions  are  exactly  equivalent:  neither  of  them  asserts  more  or 
asserts  less  than  the  other.  The  paternity  of  A and  the  filiety  of  B are 
not  two  facts,  but  two  modes  of  expressing  the  same  fact.  That  fact,  when 
analysed,  consists  of  a series  of  physical  events  or  phenomena,  in  which 
both  A and  B are  parties  concerned,  and  from  wffiich  they  both  derive 
names.  What  those  names  really  connote,  is  this  series  of  events : that  is 
the  meaning,  and  the  whole  meaning,  which  either  of  them  is  intended  to 
convey.  The  series  of  events  may  be  said  to  constitute  the  relation ; the 
schoolmen  called  it  the  foundation  of  the  relation,  j^ndamentitm  relationis. 

In  this  manner  any  fact,  or  series  of  facts,  in  which  two  different  objects 
are  implicated,  and  which  is  therefore  predicable  of  both  of  them,  may  be 
either  considered  as  constituting  an  attribute  of  the  one,  or  an  attribute  of 
the  other.  According  as  we  consider  it  in  the  former,  or  in  the  latter  as- 
pect, it  is  connoted  by  the  one  or  the  other  of  the  two  correlative  names. 
Father  connotes  the  fact,  regarded  as  constituting  an  attribute  of  A ; son 
connotes  the  same  fact,  as  constituting  an  attribute  of  B.  It  may  evident- 
ly be  regarded  with  equal  propriety  in  either  light.  And  all  that  appears 
necessary  to  account  for  the  existence  of  relative  names,  is,  that  whenever 
there  is  a fact  in  which  two  individuals  are  concerned,  an  attribute  ground- 
ed on  that  fact  may  be  ascribed  to  either  of  these  individuals. 


44 


NAMES  AND  PROPOSITIONS. 


A name,  therefore,  is  said  to  be  relative,  when,  over  and  above  the  object 
which  it  denotes,  it  implies  in  its  signification  the  existence  of  another  ob- 
ject, also  deriving  a denomination  from  the  same  fact  which  is  the  ground 
of  the  first  name.  Or  (to  express  the  same  meaning  in  other  words)  a 
name  is  relative,  when,  being  the  name  of  one  thing,  its  signification  can 
not  be  explained  but  by  mentioning  another.  Or  we  may  state  it  thus — 
when  the  name  can  not  be  employed  in  discourse  so  as  to  have  a meaning, 
unless  the  name  of  some  other  thing  than  what  it  is  itself  the  name  of,  be 
either  expressed  or  understood.  These  definitions  are  all,  at  bottom,  equiva- 
lent, being  modes  of  variously  expressing  this  one  distinctive  circumstance 
— that  every  other  attribute  of  an  object  might,  without  any  contradiction, 
be  conceived  still  to  exist  if  no  object  besides  that  one  had  ever  existed  ;* 
but  those  of  its  attributes  which  are  expressed  by  relative  names,  would  on 
that  supposition  be  swept  away. 

§ 8.  Names  have  been  further  distinguished  into  univocal  and  (equivocal : 
these,  however,  are  not  two  kinds  of  names,  but  two  different  modes  of 
employing  names.  A name  is  univocal,  or  applied  univocally,  with  respect 
to  all  things  of  which  it  can  be  predicated  in  the  same  sense ; it  is  tcquiv- 
ocal,  or  applied  {equivocally,  as  respects  those  things  of  which  it  is  predi- 
cated in  different  senses.  It  is  scarcely  necessary  to  give  instances  of  a 
fact  so  familiar  as  the  double  meaning  of  a word.  In  reality,  as  has  been 
already  observed,  an  {equivocal  or  ambiguous  word  is  not  one  name,  but 
two  names,  accidentally  coinciding  in  sound.  File  meaning  a steel  instru- 
ment, and  file  meaning  a line  of  soldiers,  have  no  more  title  to  be  consid- 
ed  one  word,  because  written  alike,  than  grease  and  Greece  have,  because 
they  are  pronounced  alike.  They  are  one  sound,  appropriated  to  form  two 
different  words. 

An  intermediate  case  is  that  of  a name  used  analogically  or  metaphor- 
ically; that  is,  a name  which  is  predicated  of  two  things,  not  univocally, 
or  exactly  in  the  same  signification,  but  in  significations  somewhat  similar, 
and  which  being  derived  one  from  the  other,  one  of  them  may  be  consid- 
ered the  primary,  and  the  other  a secondary  signification.  As  when  we 
speak  of  a brilliant  light  and  a brilliant  achievement.  The  word  is  not 
applied  in  the  same  sense  to  the  light  and  to  the  achievement ; but  having- 
been  applied  to  the  light  in  its  original  sense,  that  of  brightness  to  the  eye, 
it  is  transferred  to  the  achievement  in  a derivative  signification,  supposed 
to  be  somewhat  like  the  primitive  one.  The  word,  however,  is  just  as 
properly  two  names  instead  of  one,  in  this  case,  as  in  that  of  the  most  per- 
fect ambiguity.  And  one  of  the  commonest  forms  of  fallacious  reasoning- 
arising  from  ambiguity,  is  that  of  arguing  from  a metaphorical  expression 
as  if  it  were  literal;  that  is,  as  if  a word,  when  applied  metaphorically, 
were  the  same  name  as  when  taken  in  its  original  sense:  which  will  be 
seen  more  particularly  in  its  place. 

* Or  rather,  all  objects  except  itself  and  the  percipient  mind  ; for,  as  we  shall  see  hereafter, 
to  ascribe  any  attribute  to  an  object,  necessarily  implies  a mind  to  perceive  it. 

The  simple  and  clear  explanation  given  in  the  text,  of  relation  and  relative  names,  a subject 
so  long  the  opprobrium  of  metaphysics,  was  given  (as  far  as  I know)  for  the  first  time,  by  Mr. 
James  Mill,  in  his  Analysis  of  the  Phenomena  of  the  Human  Mind. 


THINGS  DENOTED  BY  NAMES. 


45 


CHAPTER  III. 

OP  THE  THINGS  DENOTED  BY  NAMES. 

§ 1.  Looking  back  now  to  the  commencement  of  our  inquiry,  let  us  at- 
tempt to  measure  how  far  it  has  advanced.  Logic,  we  found,  is  the  Theory 
of  Proof.  But  proof  supposes  something  provable,  which  must  be  a Prop- 
osition or  Assertion;  since  nothing  but  a Proposition  can  be  an  object  of 
belief,  or  therefore  of  proof.  A Proposition  is,  discourse  which  affirms  or 
denies  something  of  some  other  thing.  This  is  one  step : there  must,  it 
seems,  be  two  things  concerned  in  every  act  of  belief.  But  what  are  these 
Things  ? They  can  be  no  other  than  those  signified  by  the  two  names, 
which  being  joined  together  by  a copula  constitute  the  Proposition.  If, 
therefore,  we  knew  what  all  names  signify,  we  should  know  every  thing 
which,  in  the  existing  state  of  human  knowledge,  is  capable  either  of  being 
made  a subject  of  affirmation  or  denial,  or  of  being  itself  affirmed  or  de- 
nied of  a subject.  We  have  accordingly,  in  the  preceding  chapter,  re- 
viewed the  various  kinds  of  Names,  in  order  to  ascertain  what  is  signified 
by  each  of  them.  And  we  have  now  carried  this  survey  far  enough  to  be 
able  to  take  an  account  of  its  results,  and  to  exhibit  an  enumeration  of  all 
kinds  of  Things  which  are  capable  of  being  made  predicates,  or  of  having 
any  thing  predicated  of  them:  after  which  to  determine  the  import  of 
Predication,  that  is,  of  Propositions,  can  be  no  arduous  task. 

The  necessity  of  an  enumeration  of  Existences,  as  the  basis  of  Logic,  did 
not  escape  the  attention  of  the  schoolmen,  and  of  their  master  Aristotle, 
the  most  comprehensive,  if  not  also  the  most  sagacious,  of  the  ancient  phi- 
losophers. The  Categories,  or  Predicaments  — the  former  a Greek  word, 
the  latter  its  literal  translation  in  the  Latin  language — were  believed  to  be 
an  enumeration  of  all  things  capable  of  being  named ; an  enumeration  by 
the  summa  genera , i.  e.,  the  most  extensive  classes  into  which  things  could 
be  distributed ; which,  therefore,  were  so  many  highest  Predicates,  one  or 
other  of  which  was  supposed  capable  of  being  affirmed  with  truth  of  every 
namable  thing  whatsoever.  The  following  are  the  classes  into  which,  ac- 
cording to  this  school  of  philosophy, Things  in  general  might  be  reduced: 


0 vaia, 

Substantia. 

Tlocbv, 

Quantitas. 

Tloidv, 

Qualitas. 

IT p6q  ti, 

Relatio. 

TLoielv, 

Actio. 

TLairx£lv> 

Passio. 

II  oh, 

Ubi. 

II  6te, 

Quando. 

Kelodau, 

Situs. 

’'Exeiv, 

Habitus. 

The  imperfections  of  this  classification  are  too  obvious  to  require,  and 
its  merits  are  not  sufficient  to  reward,  a minute  examination.  It  is  a mere 
catalogue  of  the  distinctions  rudely  marked  out  by  the  language  of  familiar 
life,  with  little  or  no  attempt  to  penetrate,  by  philosophic  analysis,  to  the 
rationale  even  of  those  common  distinctions.  Such  an  analysis,  however 


46 


NAMES  AND  PROPOSITIONS. 


superficially  conducted,  would  have  shown  the  enumeration  to  be  both  re- 
dundant and  defective.  Some  objects  are  omitted,  and  others  repeated 
several  times  under  different  heads.  It  is  like  a division  of  animals  into 
men,  quadrupeds,  horses,  asses,  and  ponies.  That,  for  instance,  could  not 
be  a verv  comprehensive  view  of  the  nature  of  Relation  which  could  ex- 
clude action,  passivity,  and  local  situation  from  that  category.  The  same 
observation  applies  to  the  categories  Quando  (or  position  in  time),  and  Ubi 
(or  position  in  space);  while  the  distinction  between  the  latter  and  Situs 
is  merely  verbal.  The  incongruity  of  erecting  into  a summum  genus  the 
class  which  forms  the  tenth  category  is  manifest.  On  the  other  hand,  the 
enumeration  takes  no  notice  of  any  thing  besides  substances  and  attributes. 
In  what  category  are  we  to  place  sensations,  or  any  other  feelings  and 
states  of  mind;  as  hope,  joy,  fear;  sound,  smell,  taste;  pain,  pleasure; 
thought,  judgment,  conception,  and  the  like?  Probably  all  these  would 
have  been  placed  by  the  Aristotelian  school  in  the  categories  of  actio  and 
pctssio;  and  the  relation  of  such  of  them  as  are  active,  to  their  objects,  and 
of  such  of  them  as  are  passive,  to  their  causes,  would  rightly  be  so  placed ; 
but  the  things  themselves,  the  feelings  or  states  of  mind,  wrongly.  Feel- 
ings, or  states  of  consciousness,  are  assuredly  to  be  accounted  among  reali- 
ties, but  they  can  not  be  reckoned  either  among  substances  or  attributes.* 

§ 2.  Before  recommencing,  under  better  auspices,  the  attempt  made  with 
such  imperfect  success  by  the  early  logicians,  we  must  take  notice  of  an 
unfortunate  ambiguity  in  all  the  concrete  names  which  correspond  to  the 
most  general  of  all  abstract  terms,  the  word  Existence.  When  we  have 
occasion  for  a name  which  shall  be  capable  of  denoting  whatever  exists, 
as  contradistinguished  from  non-entity  or  Nothing,  there  is  hardly  a word 
applicable  to  the  purpose  which  is  not  also,  and  even  more  familiarly,  taken 
in  a sense  in  which  it  denotes  only  substances.  But  substances  are  not  all 
that  exists ; attributes,  if  such  things  are  to  be  spoken  of,  must  be  said  to 
exist;  feelings  certainly  exist.  Yet  when  we  speak  of  an  object,  or  of  a 

* On  the  preceding  passage  Professor  Bain  remarks  (Logic,  i.,  205) : “The  Categories  do  not 
seem  to  have  been  intended  as  a classification  of  Nainable  Tilings,  in  the  sense  of  ‘an  enu- 
meration of  all  kinds  of  Things  which  are  capable  of  being  made  predicates,  or  of  having  any 
thing  predicated  of  them.’  They  seem  to  have  been  rather  intended  as  a generalization 
of  predicates ; an  analysis  of  the  final  import  of  predication.  Viewed  in  this  light,  they 
are  not  open  to  the  objections  offered  by  Mr.  Mill.  The  proper  question  to  ask  is  not — In 
what  Category  are  we  to  place  sensations  or  other  feelings  or  states  of  mind?  but,  Under 
what  Categories  can  we  predicate  regarding  states  of  mind?  Take,  for  example,  Hope. 
When  we  say  that  it  is  a state  of  mind,  we  predicate  Substance : we  may  also  describe  how 
great  it  is  (Quantity),  what  is  the  quality  of  it,  pleasurable  or  painful  (Quality),  what  it  has 
reference  to  (Relation).  Aristotle  seems  to  have  framed  the  Categories  on  the  plan — Here  is 
an  individual ; what  is  the  final  analysis  of  all  that  we  can  predicate  about  him  ?” 

This  is  doubtless  a true  statement  of  the  leading  idea  in  the  classification.  The  Category 
O hoia  was  certainly  understood  by  Aristotle  to  be  a general  name  for  all  possible  answers  to 
the  question  Quid  sit  ? when  asked  respecting  a concrete  individual ; as  the  other  Categories 
are  names  comprehending  all  possible  answers  to  the  questions  Quantum  sit?  Quale  sit?  etc. 
In  Aristotle's  conception,  therefore,  the  Categories  may  not  have  been  a classification  of 
Things;  but  they  were  soon  converted  into  one  by  his  Scholastic  followers,  who  certainly  re- 
garded and  treated  them  as  a classification  of  Things,  and  carried  them  out  as  such,  dividing 
down  the  Category  Substance  as  a naturalist  might  do,  into  the  different  classes  of  physical 
or  metaphysical  objects  as  distinguished  from  attributes,  and  the  other  Categories  into  the 
principal  varieties  of  quantity,  quality,  relation,  etc.  It  is,  therefore,  a just  subject  of  com- 
plaint against  them,  that  they  had  no  Category  of  Feeling.  Feeling  is  assuredly  predicable  as 
a summum  genus,  of  every  particular  kind  of  feeling,  for  instance,  as  in  Mr.  Bain’s  example,  of 
Hope  : but  it  can  not  be  brought  within  any  of  the  Categories  as  interpreted  either  by  Aristo- 
tle or  by  bis  followers. 


THINGS  DENOTED  BY  NAMES. 


47 


thing , we  are  almost  always  supposed  to  mean  a substance.  There  seems 
a kind  of  contradiction  in  using  such  an  expression  as  that  one  thing  is 
merely  an  attribute  of  another  thing.  And  the  announcement  of  a Classi- 
fication of  Things  would,  I believe,  prepare  most  readers  for  an  enumera- 
tion like  those  in  natural  history,  beginning  with  the  great  divisions  of  an- 
imal, vegetable,  aud  mineral,  and  subdividing  them  into  classes  and  orders. 
If,  rejecting  the  word  Thing,  we  endeavor  to  find  another  of  a more  general 
import,  or  at  least  more  exclusively  confined  to  that  general  import,  a word 
denoting  all  that  exists,  and  connoting  only  simple  existence ; no  word 
might  be  presumed  fitter  for  such  a purpose  than  being:  originally  the 
present  participle  of  a verb  which  in  one  of  its  meanings  is  exactly  equiv- 
alent to  the  verb  exists  ; and  therefore  suitable,  even  by  its  grammatical 
formation,  to  be  the  concrete  of  the  abstract  existence.  But  this  word, 
strange  as  the  fact  may  appear,  is  still  more  completely  spoiled  for  the 
purpose  which  it  seemed  expressly  made  for,  than  the  word  Thing.  Being 
is,  by  custom,  exactly  synonymous  with  substance;  except  that  it  is  free 
from  a slight  taint  of  a second  ambiguity ; being  implied  impartially  to 
matter  and  to  mind,  while  substance,  though  originally  and  in  strictness 
applicable  to  both,  is  apt  to  suggest  in  preference  the  idea  of  matter.  At- 
tributes are  never  called  Beings;  nor  are  feelings.  A Being  is  that  which 
excites  feelings,  and  which  possesses  attributes.  The  soul  is  called  a Be- 
ing; God  and  angels  are  called  Beings;  but  if  we  were  to  say,  extension, 
color,  wisdom,  virtue,  are  beings,  we  should  perhaps  be  suspected  of  think- 
ing with  some  of  the  ancients,  that  the  cardinal  virtues  are  animals;  or,  at 
the  least,  of  holding  with  the  Platonic  school  the  doctrine  of  self-existent 
Ideas,  or  with  the  followers  of  Epicurus  that  of  Sensible  Forms,  which  de- 
tach themselves  in  every  direction  from  bodies,  and  by  coming  in  contact 
with  our  organs,  cause  our  perceptions.  We  should  be  supposed,  in  short, 
to  believe  that  Attributes  are  Substances. 

In  consequence  of  this  perversion  of  the  word  Being,  philosophers  look- 
ing about  for  something  to  supply  its  place,  laid  their  hands  upon  the  word 
Entity,  a piece  of  barbarous  Latin,  invented  by  the  schoolmen  to  be  used 
as  an  abstract  name,  in  which  class  its  grammatical  form  would  seem  to 
place  it : but  being  seized  by  logicians  in  distress  to  stop  a leak  in  their 
terminology,  it  has  ever  since  been  used  as  a concrete  name.  The  kindred 
word  essence,  born  at  the  same  time  and  of  the  same  parents,  scarcely  un- 
derwent a more  complete  transformation  when,  from  being  the  abstract 
of  the  verb  to  be,  it  came  to  denote  something  sufficiently  concrete  to  be 
inclosed  in  a glass  bottle.  The  word  Entity,  since  it  settled  down  into  a 
concrete  name,  has  retained  its  universality  of  signification  somewhat  less 
impaired  than  any  of  the  names  before  mentioned.  Yet  the  same  gradual 
decay  to  which,  after  a certain  age,  all  the  language  of  psychology  seems 
liable,  has  been  at  work  even  here.  If  you  call  virtue  an  entity,  you  are 
indeed  somewhat  less  strongly  suspected  of  believing  it  to  be  a substance 
than  if  you  called  it  a being ; but  you  are  by  no  means  free  from  the  sus- 
picion. Every  word  which  was  originally  intended  to  connote  mere  ex- 
istence, seems,  after  a time,  to  enlarge  its  connotation  to  separate  existence, 
or  existence  freed  from  the  condition  of  belonging  to  a substance;  which 
condition  being  precisely  what  constitutes  an  attribute,  attributes  are  grad- 
ually shut  out;  and  along  with  them  feelings,  which  in  ninety-nine  cases 
out  of  a hundred  have  no  other  name  than  that  of  the  attribute  which  is 
grounded  on  them.  Strange  that  when  the  greatest  embarrassment  felt  by 
all  who  have  any  considerable  number  of  thoughts  to  express,  is  to  find  a 


4S 


NAMES  AND  PROPOSITIONS. 


sufficient  variety  of  precise  words  fitted  to  express  them,  there  should  be 
no  practice  to  which  even  scientific  thinkers  are  more  addicted  than  that 
of  taking  valuable  words  to  express  ideas  which  are  sufficiently  expressed 
by  other  words  already  appropriated  to  them. 

When  it  is  impossible  to  obtain  good  tools,  the  next  best  thing  is  to  un- 
derstand thoroughly  the  defects  of  those  we  have.  I have  therefore  warn- 
ed the  reader  of  the  ambiguity  of  the  names  which,  for  want  of  better,  I 
am  necessitated  to  employ.  It  must  now  be  the  writer’s  endeavor  so  to 
emplov  them  as  in  no  case  to  leave  the  meaning  doubtful  or  obscure.  No 
one  of  the  above  terms  being  altogether  unambiguous,  I shall  not  confine 
mvself  to  any  one,  but  shall  employ  on  each  occasion  the  word  which  seems 
least  likely  in  the  particular  case  to  lead  to  misunderstanding;  nor  do  I 
pretend  to  use  either  these  or  any  other  words  with  a rigorous  adherence 
to  one  single  sense.  To  do  so  would  often  leave  us  without  a word  to  ex- 
press what  is  signified  by  a known  word  in  some  one  or  other  of  its  senses : 
unless  authors  had  an  unlimited  license  to  coin  new  words,  together  with 
(what  it  would  be  more  difficult  to  assume)  unlimited  power  of  making 
readers  understand  them.  Nor  would  it  be  wise  in  a writer,  on  a subject 
involving  so  much  of  abstraction,  to  deny  himself  the  advantage  derived 
from  even  an  improper  use  of  a term,  when,  by  means  of  it,  some  familiar 
association  is  called  up  which  brings  the  meaning  home  to  the  mind,  as  it 
were  by  a flash. 

The  difficulty  both  to  the  writer  and  reader,  of  the  attempt  which  must 
be  made  to  use  vague  words  so  as  to  convey  a precise  meaning,  is  not 
wholly  a matter  of  regret.  It  is  not  unfitting  that  logical  treatises  should 
afford  an  example  of  that,  to  facilitate  which  is  among  the  most  important 
uses  of  logic.  Philosophical  language  will  for  a long  time,  and  popular 
language  still  longer,  retain  so  much  of  vagueness  and  ambiguity,  that  logic 
would  be  of  little  value  if  it  did  not,  among  its  other  advantages,  exercise 
the  understanding  in  doing  its  work  neatly  and  correctly  with  these  im- 
perfect tools. 

After  this  preamble  it  is  time  to  proceed  to  our  enumeration.  We  shall 
commence  with  Feelings,  the  simplest  class  of  namable  things;  the  term 
Feeling  being  of  course  understood  in  its  most  enlarged  sense. 

I.  Feelings,  or  States  op  Consciousness. 

§ 3.  A Feeling  and  a State  of  consciousness  are,  in  the  language  of  phi- 
losophy, equivalent  expressions : every  thing  is  a feeling  of  which  the  mind 
is  conscious ; every  thing  which  it  feels,  or,  in  other  words,  which  forms  a 
part  of  its  own  sentient  existence.  In  popular  language  Feeling  is  not  al- 
ways synonymous  with  State  of  Consciousness;  being  often  taken  more 
peculiarly  for  those  states  which  are  conceived  as  belonging  to  the  sensi- 
tive, or  to  the  emotional,  phasis  of  our  nature,  and  sometimes,  with  a still 
narrower  restriction,  to  the  emotional  alone,  as  distinguished  from  what 
are  conceived  as  belonging  to  the  percipient  or  to  the  intellectual  phasis. 
But  this  is  an  admitted  departure  from  correctness  of  language;  just  as, 
by  a popular  perversion  the  exact  converse  of  this,  the  word  Mind  is  with- 
drawn from  its  rightful  generality  of  signification,  and  restricted  to  the 
intellect.  The  still  greater  perversion  by  which  Feeling  is  sometimes  con- 
fined not  only  to  bodily  sensations,  but  to  the  sensations  of  a single  sense, 
that  of  touch,  needs  not  be  more  particularly  adverted  to. 

Feeling,  in  the  proper  sense  of  the  term,  is  a genus,  of  which  Sensation, 
Emotion,  and  Thought,  are  subordinate  species.  Under  the  word  Thought 


THINGS  DENOTED  BY  NAMES. 


49 


is  here  to  be  included  whatever  we  are  internally  conscious  of  when  we  are 
said  to  think;  from  the  consciousness  we  have  when  we  think  of  a red  col- 
or without  having  it  before  our  eyes,  to  the  most  recondite  thoughts  of  a 
philosopher  or  poet.  Be  it  remembered,  however,  that  by  a thought  is  to 
be  understood  what  passes  in  the  mind  itself,  and  not  any  object  external 
to  the  mind,  which  the  person  is  commonly  said  to  be  thinking  of.  He  may 
be  thinking  of  the  sun,  or  of  God,  but  the  sun  and  God  are  not  thoughts*; 
his  mental  image,  however,  of  the  sun,  and  his  idea  of  God,  are  thoughts ; 
states  of  his  mind,  not  of  the  objects  themselves;  and  so  also  is  his  belief 
of  the  existence  of  the  sun,  or  of  God  ; or  his  disbelief,  if  the  case  be  so. 
Even  imaginary  objects  (which  are  said  to  exist  only  in  our  ideas)  are  to  be 
distinguished  from  our  ideas  of  them.  I may  think  of  a hobgoblin,  as  I may 
think  of  the  loaf  which  was  eaten  yesterday,  or  of  the  flower  which  will 
bloom  to-morrow.  But  the  hobgoblin  which  never  existed  is  not  the  same 
thing  with  my  idea  of  a hobgoblin,  any  more  than  the  loaf  which  once  ex- 
isted is  the  same  thing  with  my  idea  of  a loaf,  or  the  flower  which  does  not 
yet  exist,  but  which  will  exist,  is  the  same  with  my  idea  of  a flower.  They 
are  all, not  thoughts,  but  objects  of  thought;  though  at  the  present  time  all 
the  objects  are  alike  non-existent. 

In  like  manner,  a Sensation  is  to  be  carefully  distinguished  from  the  ob- 
ject which  causes  the  sensation;  our  sensation  of  white  from  a white  object: 
nor  is  it  less  to  be  distinguished  from  the  attribute  whiteness,  which  we 
ascribe  to  the  object  in  consequence  of  its  exciting  the  sensation.  Unfor- 
tunately for  clearness  and  due  discrimination  in  considering  these  subjects, 
our  sensations  seldom  receive  separate  names.  We  have  a name  for  the 
objects  which  produce  in  us  a certain  sensation : the  word  white.  We 
have  a name  for  the  quality  in  those  objects,  to  which  we  ascribe  the  sen- 
sation : the  name  whiteness.  But  when  we  speak  of  the  sensation  itself 
(as  we  have  not  occasion  to  do  this  often  except  in  our  scientific  specula- 
tions), language,  which  adapts  itself  for  the  most  part  only  to  the  common 
uses  of  life,  has  provided  us  with  no  single-worded  or  immediate  designa- 
tion; we  must  employ  a circumlocution,  and  say,  The  sensation  of  white, 
or  The  sensation  of  whiteness;  we  must  denominate  the  sensation  either 
from  the  object,  or  from  the  attribute,  by  wThich  it  is  excited.  Yet  the 
sensation,  though  it  never  does,  might  very  well  be  conceived  to  exist,  with- 
out any  thing  whatever  to  excite  it.  We  can  conceive  it  as  arising  spon- 
taneously in  the  mind.  But  if  it  so  arose,  we  should  have  no  name  to  de- 
note it  which  would  not  be  a misnomer.  In  the  case  of  our  sensations  of 
hearing  we  are  better  provided ; we  have  the  word  Sound,  and  a whole 
vocabulary  of  words  to  denote  the  various  kinds  of  sounds.  For  as  we 
are  often  conscious  of  these  sensations  in  the  absence  of  any  perceptible 
object,  we  can  more  easily  conceive  having  them  in  the  absence  of  any 
object  whatever.  We  need  only  shut  our  eyes  and  listen  to  music,  to  have 
a conception  of  a universe  with  nothing  in  it  except  sounds,  and  ourselves 
hearing  them : and  what  is  easily  conceived  separately,  easily  obtains  a 
separate  name.  But  in  general  our  names  of  sensations  denote  indiscrim- 
inately the  sensation  and  the  attribute.  Thus,  color  stands  for  the  sensa- 
tions of  white,  red,  etc.,  but  also  for  the  quality  in  the  colored  object.  We 
talk  of  the  colors  of  things  as  among  their  'properties. 

§ 4.  In  the  case  of  sensations,  another  distinction  has  also  to  be  kept  in 
view,  which  is  often  confounded,  and  never  without  mischievous  conse- 
quences. This  is,  the  distinction  between  the  sensation  itself,  and  the  state 

4 


50 


NAMES  AND  PROPOSITIONS. 


of  the  bodily  organs  which  precedes  the  sensation,  and  which  constitutes 
the  physical  agency  by  which  it  is  produced.  One  of  the  sources  of  con- 
fusion on  this  subject  is  the  division  commonly  made  of  feelings  into  Bodily 
and  Mental.  Philosophically  speaking,  there  is  no  foundation  at  all  for  this 
distinction:  even  sensations  are  states  of  the  sentient  mind,  not  states  of 
the  body,  as  distinguished  from  it.  What  I am  conscious  of  when  I see 
the  color  blue,  is  a feeling  of  blue  color,  which  is  one  thing ; the  picture  on 
my  retina,  or  the  phenomenon  of  hitherto  mysterious  nature  which  takes 
place  in  my  optic  nerve  or  in  my  brain,  is  another  thing,  of  which  I am 
not  at  all  conscious,  and  which  scientific  investigation  alone  could  have  ap- 
prised me  of.  These  are  states  of  my  body;  but  the  sensation  of  blue, 
which  is  the  consequence  of  these  states  of  body,  is  not  a state  of  body: 
that  which  perceives  and  is  conscious  is  called  Mind.  When  sensations 
are  called  bodily  feeling's,  it  is  only  as  being  the  class  of  feelings  which  are 
immediately  occasioned  by  bodily  states;  whereas  the  other  kinds  of  feel- 
ings, thoughts,  for  instance,  or  emotions,  are  immediately  excited  not  by 
any  thing  acting  upon  the  bodily  organs,  but  by  sensations,  or  by  previous 
thoughts.  This,  however,  is  a distinction  not  in  our  feelings,  but  in  the 
agency  which  produces  our  feelings:  all  of  them  when  actually  produced 
are  states  of  mind. 

Besides  the  affection  of  our  bodily  organs  from  without,  and  the  sensa- 
tion thereby  produced  in  our  minds,  many  writers  admit  a third  link  in  the 
chain  of  phenomena,  which  they  call  a Perception,  and  which  consists  in 
the  recognition  of  an  external  object  as  the  exciting  cause  of  the  sensation. 
This  perception,  they  say,  is  an  act  of  the  mind,  proceeding  from  its  own 
spontaneous  activity ; while  in  a sensation  the  mind  is  passive,  being  mere- 
ly acted  upon  by  the  outward  object.  And  according  to  some  metaphysi 
cians,  it  is  by  an  act  of  the  mind,  similar  to  perception,  except  in  not  being 
preceded  by  any  sensation,  that  the  existence  of  God,  the  soul,  and  other 
hyperphysical  objects,  is  recognized. 

These  acts  of  what  is  termed  perception,  whatever  be  the  conclusion  ul- 
timately come  to  respecting  their  nature,  must,  4 conceive,  take  their  place 
among  the  varieties  of  feelings  or  states  of  mind.  In  so  classing  them, 
I have  not  the  smallest  intention  of  declaring  or  insinuating  any  theory 
as  to  the  law  of  mind  in  which  these  mental  processes  may  be  supposed 
to  originate,  or  the  conditions  under  which  they  may  be  legitimate  or  the 
reverse.  Far  less  do  I mean  (as  Dr.  Whewell  seems  to  suppose  must  be 
meant  in  an  analogous  case*)  to  indicate  that  as  they  are  “ merely  states  of 
mind,”  it  is  superfluous  to  inquire  into  their  distinguishing  peculiarities. 
I abstain  from  the  inquiry  as  irrelevant  to  the  science  of  logic.  In  these 
so-called  perceptions,  or  direct  recognitions  by  the  mind,  of  objects,  wheth- 
er physical  or  spiritual,  which  are  external  to  itself,  I can  see  only  cases  of 
belief ; but  of  belief  which  claims  to  be  intuitive,  or  independent  of  exter- 
nal evidence.  When  a stone  lies  before  me,  I am  conscious  of  certain  sen- 
sations which  I receive  from  it ; but  if  I say  that  these  sensations  come  to 
me  from  an  external  object  which  I perceive,  the  meaning  of  these  words 
is,  that  receiving  the  sensations,  I intuitively  believe  that  an  external  cause 
of  those  sensations  exists.  The  laws  of  intuitive  belief,  and  the  conditions 
under  which  it  is  legitimate,  are  a subject  which,  as  we  have  already  so 
often  remarked,  belongs  not  to  logic,  but  to  the  science  of  the  ultimate  laws 
of  the  human  mind. 


Philosophy  of  the  Inductive  Sciences,  vol.  i.,  p.  40. 


THINGS  DENOTED  BY  NAMES. 


51 


To  the  same  region  of  speculation  belongs  all  that  can  be  said  respecting 
the  distinction  which  the  German  metaphysicians  and  their  French  and 
English  followers  so  elaborately  draw  between  the  acts  of  the  mind  and  its 
merely  passive  states • between  what  it  receives  from,  and  what  it  gives  to, 
the  crude  materials  of  its  experience.  I am  aware  that  with  reference  to 
the  view  which  those  writers  take  of  the  primary  elements  of  thought  and 
knowledge,  this  distinction  is  fundamental.  But  for  the  present  purpose, 
which  is  to  examine,  not  the  original  groundwork  of  our  knowledge,  but 
how  we  come  by  that  portion  of  it  which  is  not  original ; the  difference  be- 
tween active  and  passive  states  of  mind  is  of  secondary  importance.  For 
us,  they  all  are  states  of  mind,  they  all  are  feelings ; by  which,  let  it  be 
said  once  more,  I mean  to  imply  nothing  of  passivity,  but  simply  that  they 
are  psychological  facts,  facts  which  take  place  in  the  mind,  and  are  to  be 
carefully  distinguished  from  the  external  or  physical  facts  with  which  they 
may  be  connected  either  as  effects  or  as  causes. 

§ 5.  Among  active  states  of  mind,  there  is,  however,  one  species  which 
merits  particular  attention,  because  it  forms  a principal  part  of  the  conno- 
tation of  some  important  classes  of  names.  I mean  volitions,  or  acts  of 
the  will.  When  we  speak  of  sentient  beings  by  relative  names,  a large 
portion  of  the  connotation  of  the  name  usually  consists  of  the  actions  of 
those  beings ; actions  past,  present,  and  possible  or  probable  future.  Take, 
for  instance,  the  words  Sovereign  and  Subject.  What  meaning  do  these 
words  convey,  but  that  of  innumerable  actions,  done  or  to  be  done  by  the 
sovereign  and  the  subjects,  to  or  in  regard  to  one  another  reciprocally? 
So  with  the  words  physician  and  patient,  leader  and  follower,  tutor  and 
pupil.  In  many  cases  the  words  also  connote  actions  which  would  be 
done  under  certain  contingencies  by  persons  other  than  those  denoted:  as 
the  words  mortgagor  and  mortgagee,  obligor  and  obligee,  and  many  other 
.words  expressive  of  legal  relation,  which  connote  what  a court  of  justice 
would  do  to  enforce  the  legal  obligation  if  not  fulfilled.  There  are  also 
words  which  connote  actions  previously  done  by  persons  other  than  those 
denoted  either  by  the  name  itself  or  by  its  correlative ; as  the  word  brother. 
From  these  instances,  it  may  be  seen  how  large  a portion  of  the  connota- 
tion of  names  consists  of  actions.  Now  what  is  an  action?  Not  one  thing, 
but  a series  of  two  things : the  state  of  mind  called  a volition,  followed  by 
an  effect.  The  volition  or  intention  to  produce  the  effect,  is  one  thing; 
the  effect  produced  in  consequence  of  the  intention,  is  another  thing ; the 
two  together  constitute  the  action.  I form  the  purpose  of  instantly  mov- 
ing my  arm ; that  is  a state  of  my  mind : my  arm  (not  being  tied  or  par- 
alytic) moves  in  obedience  to  my  purpose ; that  is  a physical  fact,  conse- 
quent on  a state  of  mind.  The  intention,  followed  by  the  fact,  or  (if  we 
prefer  the  expression)  the  fact  Avhen  preceded  and  caused  by  the  intention, 
is  called  the  action  of  moving  my  arm. 

§ 6.  Of  the  first  leading  division  of  namable  things,  viz.,  Feelings  or 
States  of  Consciousness,  we  began  by  recognizing  three  subdivisions ; Sen- 
sations, Thoughts,  and  Emotions.  The  first  two  of  these  we  have  illustrated 
at  considerable  length  ; the  third,  Emotions,  not  being  perplexed  by  similar 
ambiguities,  does  not  require  similar  exemplification.  And,  finally,  we  have 
found  it  necessary  to  add  to  these  three  a fourth  species,  commonly  known 
by  the  name  Volitions.  We  shall  now  proceed  to  the  two  remaining  class- 
es of  namable  things ; all  things  which  are  regarded  as  external  to  the 


NAMES  AND  PROPOSITIONS. 


52 

mind  being  considered  as  belonging  either  to  the  class  of  Substances  or  to 
that  of  Attributes. 

II.  Substances. 

Logicians  have  endeavored  to  define  Substance  and  Attribute ; but  their 
definitions  are  not  so  much  attempts  to  draw  a distinction  between  the 
things  themselves,  as  instructions  what  difference  it  is  customary  to  make 
in  the  grammatical  structure  of  the  sentence,  according  as  we  are  speak- 
ing of  substances  or  of  attributes.  Such  definitions  are  rather  lessons  of 
English,  or  of  Greek,  Latin,  or  German,  than  of  mental  philosophy.  An 
attribute,  say  the  school  logicians,  must  be  the  attribute  of  something; 
color,  for  example,  must  be  the  color  of  something ; goodness  must  be  the 
goodness  of  something ; and  if  this  something  should  cease  to  exist,  or 
should  cease  to  be  connected  with  the  attribute,  the  existence  of  the  attri- 
bute would  be  at  an  end.  A substance,  on  the  contrary,  is  self-existent ; in 
speaking  about  it,  we  need  not  put  of  after  its  name.  A stone  is  not  the 
stone  of  any  thing;  the  moon  is  not  the  moon  o/‘any  thing,  but  simply  the 
moon.  Unless,  indeed,  the  name  which  we  choose  to  give  to  the  substance 
be  a relative  name ; if  so,  it  must  be  followed  either  by  of  or  by  some 
other  particle,  implying,  as  that  preposition  does,  a reference  to  something 
else : but  then  the  other  characteristic  peculiarity  of  an  attribute  would 
fail;  the  something  might  be  destroyed,  and  the  substance  might  still  sub- 
sist. Thus,  a father  must  be  the  father  of  something,  and  so  far  resembles 
an  attribute,  in  being  referred  to  something  besides  himself : if  there  were 
no  child,  there  would  be  no  father:  but  this,  when  we  look  into  the  matter, 
only  means  that  we  should  not  call  him  father.  The  man  called  father 
might  still  exist  though  there  were  no  child,  as  he  existed  before  there  was 
a child ; and  there  would  be  no  contradiction  in  supposing  him  to  exist, 
though  the  whole  universe  except  himself  were  destroyed.  But  destroy 
all  white  substances,  and  where  would  be  the  attribute  whiteness?  White- 
ness, without  any  white  thing,  is  a contradiction  in  terms. 

This  is  the  nearest  approach  to  a solution  of  the  difficulty,  that  will  be 
found  in  the  common  treatises  on  logic.  It  will  scarcely  be  thought  to  be 
a satisfactory  one.  If  an  attribute  is  distinguished  from  a substance  by 
being  the  attribute  of  something,  it  seems  highly  necessary  to  understand 
what  is  meant  by  of/  a particle  which  needs  explanation  too  much  itself, 
to  be  placed  in  front  of  the  explanation  of  any  thing  else.  And  as  for  the 
self-existence  of  substance,  it  is  very  true  that  a substance  may  be  con- 
ceived to  exist  without  any  other  substance,  but  so  also  may  an  attribute 
without  any  other  attribute : and  we  can  no  more  imagine  a substance 
without  attributes  than  we  can  imagine  attributes  without  a substance. 

Metaphysicians,  however,  have  probed  the  question  deeper,  and  given  an 
account  of  Substance  considerably  more  satisfactory  than  this.  Substances 
are  usually  distinguished  as  Bodies  or  Minds.  Of  each  of  these,  philoso- 
phers have  at  length  provided  us  with  a definition  which  seems  unexcep- 
tionable. 

§ 7.  A body,  according  to  the  received  doctrine  of  modern  metaphysi 
cians,  may  be  defined,  the  external  cause  to  which  we  ascribe  our  sensa- 
tions. When  I see  and  touch  a piece  of  gold,  I am  conscious  of  a sensa- 
tion of  yellow  color,  and  sensations  of  hardness  and  weight ; and  by  vary- 
ing the  mode  of  handling,  I may  add  to  these  sensations  many  others  com- 
pletely distinct  from  them.  The  sensations  are  all  of  which  I am  directly 


THINGS  DENOTED  BY  NAMES. 


53 


conscious ; but  I consider  them  as  produced  by  something  not  only  exist- 
ing independently  of  my  will,  but  external  to  my  bodily  oi’gans  and  to  my 
mind.  This  external  something  I call  a body. 

It  may  be  asked,  how  come  we  to  ascribe  our  sensations  to  any  exter- 
nal cause?  And  is  there  sufficient  ground  for  so  ascribing  them?  It  is 
known,  that  there  are  metaphysicians  who  have  raised  a controversy  on 
the  point;  maintaining  that  we  are  not  warranted  in  referring  our  sensa- 
tions to  a cause  such  as  we  understand  by  the  word  Body,  or  to  any  ex- 
ternal cause  whatever.  Though  we  have  no  concern  here  with  this  con- 
troversy, nor  with  the  metaphysical  niceties  on  which  it  turns,  one  of  the 
best  ways  of  showing  what  is  meant  by  Substance  is,  to  consider  what  po- 
sition it  is  necessary  to  take  up,  in  order  to  maintain  its  existence  against 
opponents. 

It  is  certain,  then,  that  a part  of  our  notion  of  a body  consists  of  the 
notion  of  a number  of  sensations  of  our  own,  or  of  other  sentient  beings, 
habitually  occurring  simultaneously.  My  conception  of  the  table  at  which 
I am  writing  is  compounded  of  its  visible  form  and  size,  which  are  com- 
plex sensations  of  sight;  its  tangible  form  and  size,  which  are  complex 
sensations  of  our  organs  of  touch  and  of  our  muscles ; its  weight,  which 
is  also  a sensation  of  touch  and  of  the  muscles ; its  color,  which  is  a sensa- 
tion of  sight ; its  hardness,  which  is  a sensation  of  the  muscles ; its  com- 
position, which  is  another  word  for  all  the  varieties  of  sensation  which  we 
receive  under  various  circumstances  from  the  wood  of  which  it  is  made, 
and  so  forth.  All  or  most  of  these  various  sensations  frequently  are,  and, 
as  we  learn  by  experience,  always  might  be,  experienced  simultaneously,  or 
in  many  different  orders  of  succession  at  our  own  choice : and  hence  the 
thought  of  any  one  of  them  makes  us  think  of  the  others,  and  the  whole 
becomes  mentally  amalgamated  into  one  mixed  state  of  consciousness, 
which,  in  the  language  of  the  school  of  Locke  and  Hartley,  is  termed  a 
Complex  Idea. 

Now,  there  are  philosophers  who  have  argued  as  follows:  If  we  con- 
ceive an  orange  to  be  divested  of  its  natural  color  without  acquiring  any 
new  one ; to  lose  its  softness  without  becoming  hard,  its  roundness  without 
becoming  square  or  pentagonal,  or  of  any  other  regular  or  irregular  figure 
whatever ; to  be  deprived  of  size,  of  weight,  of  taste,  of  smell ; to  lose  all 
its  mechanical  and  all  its  chemical  properties,  and  acquire  no  new  ones ; to 
become,  in  short,  invisible,  intangible,  imperceptible  not  only  by  all  our 
senses,  but  by  the  senses  of  all  other  sentient  beings,  real  or  possible ; 
nothing,  say  these  thinkers,  would  remain.  For  of  what  nature,  they  ask, 
could  be  the  residuum?  and  by  what  token  could  it  manifest  its  presence? 
To  the  unreflecting  its  existence  seems  to  rest  on  the  evidence  of  the  senses. 
But  to  the  senses  nothing  is  apparent  except  the  sensations.  We  know, 
indeed,  that  these  sensations  are  bound  together  by  some  law ; they  do  not 
come  together  at  random,  but  according  to  a systematic  order,  which  is 
part  of  the  order  established  in  the  universe.  When  we  experience  one  of 
these  sensations,  we  usually  experience  the  others  also,  or  know  that  we 
have  it  in  our  power  to  experience  them.  But  a fixed  law  of  connection, 
making  the  sensations  occur  together,  does  not,  say  these  philosophers, 
necessarily  require  what  is  called  a substratum  to  support  them.  The  con- 
ception of  a substratum  is  but  one  of  many  possible  forms  in  which  that 
connection  presents  itself  to  our  imagination ; a mode  of,  as  it  were,  real- 
izing the  idea.  If  there  be  such  a substratum,  suppose  it  at  this  instant 
miraculously  annihilated,  and  let  the  sensations  continue  to  occur  in  the 


o4 


NAMES  AND  PROPOSITIONS. 


same  order,  and  how  would  the  substratum  be  missed?  By  what  signs 
should  we  be  able  to  discover  that  its  existence  had  terminated  ? Should 
we  not  have  as  much  reason  to  believe  that  it  still  existed  as  we  now  have? 
And  if  we  should  not  then  be  warranted  in  believing  it,  how  can  we  be  so 
now  ? A body,  therefore,  according  to  these  metaphysicians,  is  not  any 
thing  intrinsically  different  from  the  sensations  which  the  body  is  said  to 
produce  in  us ; it  is,  in  short,  a set  of  sensations,  or  rather,  of  possibilities 
of  sensation,  joined  together  according  to  a fixed  law. 

The  controversies  to  which  these  speculations  have  given  rise,  and  the 
doctrines  which  have  been  developed  in  the  attempt  to  find  a conclusive 
answer  to  them,  have  been  fruitful  of  important  consequences  to  the  Science 
of  Mind.  The  sensations  (it  was  answered)  which  we  are  conscious  of,  and 
which  we  receive,  not  at  random,  but  joined  together  in  a certain  uniform 
manner,  imply  not  only  a law  or  laws  of  connection,  but  a cause  external  to 
our  mind,  which  cause,  by  its  own  laws,  determines  the  laws  according  to 
which  the  sensations  are  connected  and  experienced.  The  schoolmen  used 
to  call  this  external  cause  by  the  name  we  have  already  employed,  a sub- 
stratum• and  its  attributes  (as  they  expressed  themselves)  inhered , literally 
stuck,  in  it.  To  this  substratum  the  name  Matter  is  usually  given  in  phil- 
osophical discussions.  It  was  soon,  however,  acknowledged  by  all  who  re- 
flected on  the  subject,  that  the  existence  of  matter  can  not  be  proved  by  ex- 
trinsic evidence.  The  answer,  therefore,  now  usually  made  to  Berkeley  and 
his  followers,  is,  that  the  belief  is  intuitive ; that  mankind,  in  all  ages,  have 
felt  themselves  compelled,  by  a necessity  of  their  nature,  to  refer  their  sen- 
sations to  an  external  cause:  that  even  those  who  deny  it  in  theory, yield 
to  the  necessity  in  practice,  and  both  in  speech,  thought,  and  feeling,  do, 
equally  with  the  vulgar,  acknowledge  their  sensations  to  be  the  effects  of 
something  external  to  them  : this  knowledge,  therefore,  it  is  affirmed,  is  as 
evidently  intuitive  as  our  knowledge  of  our  sensations  themselves  is  intui- 
tive. And  here  the  questiou  merges  in  the  fundamental  problem  of  meta- 
physics properly  so  called : to  which  science  we  leave  it. 

But  although  the  extreme  doctrine  of  the  Idealist  metaphysicians,  that 
objects  are  nothing  but  our  sensations  and  the  laws  which  connect  them, 
has  not  been  generally  adopted  by  subsequent  thinkers ; the  point  of  most 
real  importance  is  one  on  which  those  metaphysicians  are  now  very  gen- 
erally considered  to  have  made  out  their  case : viz.,  that  all  toe  know  of  ob- 
jects is  the  sensations  which  they  give  us,  and  the  order  of  the  occurrence 
of  those  sensations.  Ivant  himself,  on  this  point,  is  as  explicit  as  Berke- 
ley or  Locke.  Howrever  firmly  convinced  that  there  exists  a universe  of 
“Things  in  themselves,”  totally  distinct  from  the  universe  of  phenomena, 
or  of  things  as  they  appear  to  our  senses;  and  even  when  bringing  into 
use  a technical  expression  ( Noumenon ) to  denote  what  the  thing  is  in  it- 
self, as  contrasted  with  the  representation  of  it  in  our  minds ; he  allows 
that  this  representation  (the  matter  of  which,  he  says,  consists  of  our  sen- 
sations, though  the  form  is  given  by  the  laws  of  the  mind  itself)  is  all  we 
know  of  the  object:  and  that  the  real  nature  of  the  Thing  is,  and  by  the 
constitution  of  our  faculties  ever  must  remain,  at  least  in  the  present  state 
of  existence,  an  impenetrable  mystery  to  us.  “ Of  things  absolutely  or  in 
themselves,”  says  Sir  William  Hamilton,*  “be  they  external,  be  they  in- 
ternal, we  know  nothing,  or  know  them  only  as  incognizable ; and  become 
aware  of  their  incomprehensible  existence,  only  as  this  is  indirectly  and 


Discussions  on  Philosophy,  etc.  Appendix  I.,  pp.  G43,  644. 


THINGS  DENOTED  BY  NAMES. 


55 


accidentally  revealed  to  us,  through  certain  qualities  related  to  our  faculties 
of  knowledge,  and  which  qualities,  again,  we  can  not  think  as  uncondition- 
al, irrelative,  existent  in  aud  of  ourselves.  All  that  we  know  is  therefore 
phenomenal — phenomenal  of  the  unknown.”*  The  same  doctrine  is  laid 
down  in  the  clearest  and  strongest  terms  by  M.  Cousin,  whose  observations 
on  the  subject  are  the  more  worthy  of  attention,  as,  in  consequence  of  the 
ultra-German  and  ontological  character  of  his  philosophy  in  other  respects, 
they  may  be  regarded  as  the  admissions  of  an  opponent. f 

There  is  not  the  slightest  reason  for  believing  that  what  we  call  the  sen- 
sible qualities  of  the  object  are  a type  of  any  thing  inherent  in  itself,  or 
bear  any  affinity  to  its  own  nature.  A cause  does  not,  as  such,  resemble 
its  effects ; an  east  wind  is  not  like  the  feeling  of  cold,  nor  heat  like  the 
steam  of  boiling  water.  Why  then  should  matter  resemble  our  sensations? 
Why  should  the  inmost  nature  of  fire  or  water  resemble  the  impressions 
made  by  those  objects  upon  our  senses  ?t  Or  on  what  principle  are  we 

* It  is  to  be  regretted  that  Sir  William  Hamilton,  though  he  often  strenuous!}'  insists  on 
this  doctrine,  and  though,  in  the  passage  quoted,  he  states  it  with  a comprehensiveness  and 
force  which  leave  nothing  to  be  desired,  did  not  consistently  adhere  to  his  own  doctrine,  but 
maintained  along  with  it  opinions  with  which  it  is  utterly  irreconcilable.  See  the  third  and 
other  chapters  of  An  Examination  of  Sir  William  Hamiltonls  Philosophy. 

t “ Nous  savons  qu’il  existe  quelque  chose  hors  de  nous,  parceque  nous  ne  pouvons  expli- 
quer  nos  perceptions  sans  les  rattaeher  a des  causes  distinctes  de  nous  memes ; nous  savons 
de  plus  que  ces  causes,  dont  nous  ne  connaissons  pas  d’ailleurs  l’essence,  produisent  les  effets 
les  plus  variables,  les  plus  divers,  et  meme  les  plus  contraires,  seloti  qu'elles  rencontrent  telle 
nature  ou  telle  disposition  du  sujet.  Mais  savons-nous  quelque  chose  de  plus?  et  meme,  vu 
le  caractere  indetermine  des  causes  que  nous  eoncevons  dans  les  corps,  y a-t-il  quelque  chose 
de  plus  a savoir?  Y a-t-il  lieu  de  nous  enquerir  si  nous  pereevons  les  choses  telles  qu’elles 

sont?  Non  evidemment Je  ne  dis  pas  que  le  probleme  est  insoluble,  ye  dis 

quit,  est  absurde  et  enferme  une  contradiction.  Nous  ne  savons  pas  ce  que  ces  causes  sont  en 
elles-memes,  et  la  raison  nous  de'fend  de  chercher  a le  connaitre : mais  ii  est  bien  e'vident  a 
priori,  qa'el/es  ne  sont  pas  en  elles-memes  ce  quelles  sont  par  rapport  a nous,  puisque  la  pre- 
sence du  sujet  modifie  ne'cessairement  leur  action.  Supprimez  tout  sujet  sentant,  il  est  certain 
que  ces  causes  agiraient  encore  puisqu’elles  continueraient  d’exister ; mais  elles  agiraient  au- 
trement ; elles  seraient  encore  des  qualites  et  des  proprietes,  mais  qui  ne  ressembleraient  a 
l ien  de  ce  que  nous  connaissons.  Le  feu  ne  manifesterait  plus  aucune  des  proprietes  que  nous 
lui  connaissons  : que  serait-il  ? C’est  ce  que  nous  ne  saurons  jamais.  C’est  d'ailleurs  peut- 
etre  un  probleme  qui  ne  repugne  pas  seulement  a la  nature  de  notre  esprit , mais  a T essence  meme 
des  choses.  Quand  meme  en  effet  on  supprimerait  par  le  pense'e  tons  les  sujets  sentants,  il 
faudrait  encore  admettre  que  nul  corps  ne  manifesterait  ses  proprietes  autrement  qu’en  rela- 
tion avec  un  sujet  quelconque,  et  dans  ce  cas  ses  proprietes  ne  seraient  encore  que  relatives: 
en  sorte  qu’il  me  parait  fort  raisonnable  d’admettre  que  les  propriete's  determine'es  des  corps 
n’existent  pas  independamment  d’un  sujet  quelconque,  et  que  quand  on  demande  si  les  pro- 
prietes de  la  matiere  sont  telles  que  nous  les  pereevons,  il  faudrait  voir  auparavant  si  elles  sont 
en  tant  que  determinees,  et  dans  quel  sens  il  est  vrai  de  dire  qu’elles  sont.” — Cours  d'Histoire 
de  la  Philosophic  Morale  au  18me  siecle,  8me  le<;on. 

f An  attempt,  indeed,  has  been  made  by  Reid  and  others,  to  establish  that  although  some 
of  the  properties  we  ascribe  to  objects  exist  only  in  our  sensations,  others  exist  in  the  things 
themselves,  being  such  as  can  not  possibly  be  copies  of  any  impression  upon  the  senses;  and 
they  ask,  from  what  sensations  our  notions  of  extension  and  figure  have  been  derived?  The 
gauntlet  thrown  down  by  Reid  was  taken  up  by  Brown,  who,  applying  greater  powers  of  anal- 
ysis than  had  previously  been  applied  to  the  notions  of  extension  and  figure,  pointed  out  that 
the  sensations  from  which  those  notions  are  derived,  are  sensations  of  touch,  combined  with 
sensations  of  a class  previously  too  little  adverted  to  by  metaphysicians,  those  which  have  their 
seat  in  our  muscular  frame.  His  analysis,  which  was  adopted  and  followed  up  by  James  Mill, 
has  been  further  and  greatly  improved  upon  in  Professor  Bain’s  profound  work,  The  Senses 
and  the  Intellect,  and  in  the  chapters  on  “Perception”  of  a work  of  eminent  analytic  power, 
Mr.  Herbert  Spencer’s  Principles  of  Psychology. 

On  this  point  M.  Cousin  may  again  be  cited  in  favor  of  the  better  doctrine.  M.  Cousin 
recognizes,  in  opposition  to  Reid,  the  essential  subjectivity  of  our  conceptions  of  what  are  called 
the  primary  qualities  of  matter,  as  extension,  solidity,  etc.,  equally  with  those  of  color,  heat, 
and  the  remainder  of  the  so-called  secondary  qualities. — Cours,  ut  supra,  9me  le$on. 


5G 


NAMES  AND  PROPOSITIONS. 


authorized  to  deduce  from  the  effects,  any  tiling  concerning  the  cause,  ex- 
cept that  it  is  a cause  adequate  to  produce  those  effects?  It  may,  there- 
fore, safely  be  laid  clown  as  a truth  both  obvious  in  itself,  and  admitted  by 
all  whom  it  is  at  present  necessary  to  take  into  consideration,  that,  of  the 
outward  world,  we  know  and  can  know  absolutely  nothing,  except  the  sen- 
sations which  we  experience  from  it.* 

§ 8.  Body  having  now  been  defined  the  external  cause,  and  (according 
to  the  more  reasonable  opinion)  the  unknown  external  cause,  to  which  we 
refer  our  sensations;  it  remains  to  frame  a definition  of  Mind.  Nor,  after 
the  preceding  observations,  will  this  be  difficult.  For,  as  our  conception 
of  a body  is  that  of  an  unknown  exciting  cause  of  sensations,  so  our  con- 
ception of  a mind  is  that  of  an  unknown  recipient  or  percipient,  of  them ; 
and  not  of  them  alone,  but  of  all  our  other  feelings.  As  body  is  under- 
stood to  be  the  mysterious  something  which  excites  the  mind  to  feel,  so 
mind  is  the  mysterious  something  which  feels  and  thinks.  It  is  unneces- 
sary to  give  in  the  case  of  mind,  as  we  gave  in  the  case  of  matter,  a par- 
ticular statement  of  the  skeptical  system  by  which  its  existence  as  a Thing 
in  itself,  distinct  from  the  series  of  what  are  denominated  its  states,  is  call- 
ed in  question.  But  it  is  necessary  to  remark,  that  on  the  inmost  nature 
(whatever  be  meant  by  inmost  nature)  of  the  thinking,  principle,  as  well 
as  on  the  inmost  nature  of  matter,  we  are,  and  with  our  faculties  must  al- 
ways remain,  entirely  in  the  dark.  All  which  we  are  aware  of,  even  in  our 
own  minds,  is  (in  the  words  of  James  Mill)  a certain  “thread  of  conscious- 
ness a series  of  feelings,  that  is,  of  sensations,  thoughts,  emotions,  and 
volitions,  more  or  less  numerous  and  complicated.  There  is  a something 
I call  Myself,  or,  by  another  form  of  expression,  my  mind,  which  I consider 
as  distinct  from  these  sensations,  thoughts,  etc. ; a something  which  I con- 
ceive to  be  not  the  thoughts,  but  the  being  that  has  the  thoughts,  and 


* This  doctrine,  which  is  the  most  complete  form  of  the  philosophical  theory  known  as  the 
Relativity  of  Human  Knowledge,  has,  since  the  recent  revival  in  this  country  of  an  active  in- 
terest in  metaphysical  speculation,  been  the  subject  of  a greatly  increased  amount  of  discussion 
and  controversy ; and  dissentients  have  manifested  themselves  in  considerably  greater  number 
than  I had  any  knowledge  of  when  the  passage  in  the  text  was  written.  The  doctrine  has 
been  attacked  from  two  sides.  Some  thinkers,  among  whom  are  the  late  Professor  Perrier, 
in  his  Institutes  of  Metaphysic,  and  Professor  Jojjn  Grote,  in  his  Ex/>loratio  Philosophica , ap- 
pear to  deny  altogether  the  reality  of  Noumena,  or  Things  in  themselves — of  an  unknowable 
substratum  or  support  for  the  sensations  which  we  experience,  and  which,  according  to  the 
theory,  constitute  all  our  knowledge  of  an  external  worid.  It  seems  to  me,  however,  that  in 
Professor  Grote’s  case  at  least,  the  denial  of  Noumena  is  only  apparent,  and  that  he  does  not 
essentially  differ  from  the  other  class  of  objectors,  including  Mr.  Bailey  in  his  valuable  Let- 
ters on  the  Philosophy  of  the  Human  Mind,  and  (in  spite  of  the  striking  passage  quoted  in 
the  text)  also  Sir  William  Hamilton,  who  contend  for  a direct  knowledge  by  the  human  mind 
of  more  than  the  sensations — of  certain  attributes  or  properties  as  they  exist  not  in  us,  but 
in  the  Things  themselves. 

With  the  first  of  these  opinions,  that  which  denies  Noumena,  I have,  as  a metaphysician, 
no  quarrel ; but,  whether  it  be  true  or  false,  it  is  irrelevant  to  Logic.  And  since  all  the  forms 
of  language  are  in  contradiction  to  it,  nothing  but  confusion  could  result  from  its  unnecessary 
introduction  into  a treatise,  every  essential  doctrine  of  which  could  stand  equally  -well  with 
the  opposite  and  accredited  opinion.  The  other  and  rival  doctrine,  that  of  a direct  perception 
or  intuitive  knowledge  of  the  outward  object  as  it  is  in  itself,  considered  as  distinct  from  the 
sensations  we  receive  from  it,  is  of  far  greater  practical  moment.  But  even  this  question, 
depending  on  the  nature  and  laws  of  Intuitive  Knowledge,  is  not  within  the  province  of  Logic. 
For  the  grounds  of  my  own  opinion  concerning  it,  I must  content  myself  with  referring  to  a 
work  already  mentioned — An  Examination  of  Sir  William  Hamilton's  Philosophy ; several 
chapters  of  which  arc  devoted  to  a full  discussion  of  the  questions  and  theories  relating  to 
the  supposed  direct  perception  of  external  objects. 


THINGS  DENOTE!?  BY  NAMES. 


51 


which  I can  conceive  as  existing  forever  in  a state  of  quiescence,  without 
any  thoughts  at  all.  But  what  this  being  is,  though  it  is  myself,  I have  no 
knowledge,  other  than  the  series  of  its  states  of  consciousness.  As  bodies 
manifest  themselves  to  me  only  through  the  sensations  of  which  I regard 
them  as  the  causes,  so  the  thinking  principle,  or  mind,  in  my  own  nature, 
makes  itself  known  to  me  only  by  the  feelings  of  which  it  is  conscious.  I 
know  nothing  about  myself,  save  my  capacities  of  feeling  or  being  con- 
scious (including,  of  course,  thinking  and  willing) : and  were  I to  learn 
any  thing  new  concerning  my  own  nature,  I can  not  with  my  present  facul- 
ties conceive  this  new  information  to  be  any  thing  else,  than  that  I have 
some  additional  capacities,  as  yet  unknown  to  me,  of  feeling,  thinking,  or 
willing. 

Thus,  then,  as  body  is  the  unsentient  cause  to  which  we  are  naturally 
prompted  to  refer  a certain  portion  of  our  feelings,  so  mind  may  be  de- 
scribed as  the  sentient  subject  (in  the  scholastic  sense  of  the  term)  of  all 
feelings;  that  which  has  or  feels  them.  But  of  the  nature  of  either  body 
or  mind,  further  than  the  feelings  which  the  former  excites,  and  which  the 
latter  experiences,  we  do  not,  according  to  the  best  existing  doctrine,  know 
any  thing;  and  if  any  thing,  logic  has  nothing  to  do  with  it,  or  with  the 
manner  in  which  the  knowledge  is  acquired.  AVith  this  result  we  may 
conclude  this  portion  of  our  subject,  and  pass  to  the  third  and  only  remain- 
ing class  or  division  of  Namable  Things. 

III.  Attributes  : and,  first,  Qualities. 

§ 9.  From  what  has  already  been  said  of  Substance,  what  is  to  be  said 
of  Attribute  is  easily  deducible.  For  if  we  know  not,  and  can  not  know, 
any  thing  of  bodies  but  the  sensations  which  they  excite  in  us  or  in  others, 
those  sensations  must  be  all  that  we  can,  at  bottom,  mean  by  their  attri- 
butes; and  the  distinction  which  we  verbally  make  between  the  properties 
of  things  and  the  sensations  we  receive  from  them,  must  originate  in  the 
convenience  of  discourse  rather  than  in  the  nature  of  what  is  signified  by 
the  terms. 

Attributes  are  usually  distributed  under  the  three  heads  of  Quality, 
Quantity,  and  Relation.  We  shall  come  to  the  two  latter  presently:  in  the 
first  place  we  shall  confine  ourselves  to  the  former. 

Let  us  take,  then,  as  our  example,  one  of  what  are  termed  the  sensible 
qualities  of  objects,  and  let  that  example  be  whiteness.  When  we  ascribe 
whiteness  to  any  substance,  as,  for  instance,  snow ; when  we  say  that  snow 
has  the  quality  whiteness,  what  do  we  really  assert?  Simply,  that  when 
snow  is  present  to  our  organs,  we  have  a particular  sensation,  which  we 
are  accustomed  to  call  the  sensation  of  white.  But  how  do  I know  that 
snow  is  present?  Obviously  by  the  sensations  which  I derive  from  it,  and 
not  otherwise.  I infer  that  the  object  is  present,  because  it  gives  me  a 
certain  assemblage  or  series  of  sensations.  And  when  I ascribe  to  it  the 
attribute  whiteness,  my  meaning  is  only,  that,  of  the  sensations  composing 
this  group  or  series,  that  which  I call  the  sensation  of  white  color  is  one. 

This  is  one  view  which  may  be  taken  of  the  subject.  But  there  is  also 
another  and  a different  view.  It  may  be  said,  that  it  is  true  we  knoio  noth- 
ing of  sensible  objects,  except  the  sensations  they  excite  in  us ; that  the 
fact  of  our  receiving  from  snow  the  particular  sensation  which  is  called  a 
sensation  of  white,  is  the  ground  on  which  we  ascribe  to  that  substance  the 
quality  whiteness;  the  sole  proof  of  its  possessing  that  quality.  But  be- 
cause one  thing  may  be  the  sole  evidence  of  the  existence  of  another  thing, 


58 


NAMES  AND  PROPOSITIONS. 


it  does  not  follow  that  the  two  are  one  and  the  same.  The  attribute  white- 
ness (it  may  be  said)  is  not  the  fact  of  receiving  the  sensation,  but  some- 
thing in  the  object  itself;  a power  inherent  in  it;  something  in  virtue  of 
which  the  object  produces  the  sensation.  And  when  we  affirm  that  snow 
possesses  the  attribute  whiteness,  we  do  not  merely  assert  that  the  pres- 
ence of  snow  produces  in  us  that  sensation,  but  that  it  does  so  through, 
and  by  reason  of,  that  power  or  quality. 

For  the  purposes  of  logic  it  is  not  of  material  importance  which  of  these 
opinions  we  adopt.  The  full  discussion  of  the  subject  belongs  to  the  other 
department  of  scientific  inquiry,  so  often  alluded  to  under  the  name  of  met- 
aphysics ; but  it  may  be  said  here,  that  for  the  doctrine  of  the  existence  of 
a peculiar  species  of  entities  called  qualities,  I can  see  no  foundation  ex- 
cept in  a tendency  of  the  human  mind  which  is  the  cause  of  many  delu- 
sions. I mean,  the  disposition,  wherever  we  meet  with  two  names  which 
are  not  precisely  synonymous,  to  suppose  that  they  must  be  the  names  of 
two  different  things ; whereas  in  reality  they  may  be  names  of  the  same 
thing  viewed  in  two  different  lights,  or  under  different  suppositions  as  to 
surrounding  circumstances.  Because  quality  and  sensation  can  not  be  put 
indiscriminately  one  for  the  other,  it  is  supposed  that  they  can  not  both 
signify  the  same  thing,  namely,  the  impression  or  feeling  with  which  we 
are  affected  through  our  senses  by  the  presence  of  an  object;  though  there 
is  at  least  no  absurdity  in  supposing  that  this  identical  impression  or  feel- 
ing may  be  called  a sensation  when  considered  merely  in  itself,  and  a quali- 
ty when  looked  at  in  relation  to  any  one  of  the  numerous  objects,  the  pres- 
ence of  which  to  our  organs  excites  in  our  minds  that  among  various  other 
sensations  or  feelings.  And  if  this  be  admissible  as  a supposition,  it  rests 
with  those  who  contend  for  an  entity  per  se  called  a quality,  to  show  that 
their  opinion  is  preferable,  or  is  any  thing  in  fact  but  a lingering  remnant 
of  the  old  doctrine  of  occult  causes ; the  very  absurdity  which  Moliere  so 
happily  ridiculed  when  he  made  one  of  his  pedantic  physicians  account  for 
the  fact  that  opium  produces  sleep  by  the  maxim,  Because  it  has  a soporific 
virtue. 

It  is  evident  that  when  the  physician  stated  that  opium  has  a soporific 
virtue,  he  did  not  account  for,  but  merely  asserted  over  again,  the  fact  that 
it  produces  sleep.  In  like  manner,  when  we  say  that  snow  is  white  because 
it  has  the  quality  of  whiteness,  we  are  only  re-asserting  in  more  technical 
language  the  fact  that  it  excites  in  us  the  sensation  of  white.  If  it  be  said 
that  the  sensation  must  have  some  cause,  I answer,  its  cause  is  the  presence 
of  the  assemblage  of  phenomena  which  is  termed  the  object.  When  we 
have  asserted  that  as  often  as  the  object  is  present,  and  our  organs  in  their 
normal  state,  the  sensation  takes  place,  we  have  stated  all  that  we  know 
about  the  matter.  There  is  no  need,  after  assigning  a certain  and  intelli- 
gible cause,  to  suppose  an  occult  cause  besides,  for  the  purpose  of  enabling 
the  real  cause  to  produce  its  effect.  If  I am  asked,  why  does  the  presence 
of  the  object  cause  this  sensation  in  me, I can  not  tell:  I can  only  say  that 
such  is  my  nature,  and  the  nature  of  the  object ; that  the  fact  forms  a part 
of  the  constitution  of  things.  And  to  this  we  must  at  last  come,  even  after 
interpolating  the  imaginary  entity.  Whatever  number  of  links  the  chain 
of  causes  and  effects  may  consist  of,  how  any  one  link  produces  the  one 
which  is  next  to  it,  remains  equally  inexplicable  to  us.  It  is  as  easy  to 
comprehend  that  the  object  should  produce  the  sensation  directly  and  at 
once,  as  that  it  should  produce  the  same  sensation  by  the  aid  of  something 
else  called  the  power  of  jn-oducing  it. 


THINGS  DENOTED  BY  NAMES. 


59 


But,  as  the  difficulties  which  may  be  felt  in  adopting  this  view  of  the 
subject  can  not  be  removed  without  discussions  transcending  the  bounds 
of  our  science,  I content  myself  with  a passing  indication,  and  shall,  for  the 
purposes  of  logic,  adopt  a language  compatible  with  either  view  of  the  na- 
ture of  qualities.  I shall  say — what  at  least  admits  of  no  dispute — that 
the  quality  of  whiteness  ascribed  to  the  object  snow,  is  grounded  on  its 
exciting  in  us  the  sensation  of  white ; and  adopting  the  language  already 
used  by  the  school  logicians  in  the  case  of  the  kind  of  attributes  called 
Relations,  I shall  term  the  sensation  of  white  the  foundation  of  the  quality 
whiteness.  For  logical  purposes  the  sensation  is  the  only  essential  part  of 
what  is  meant  by  the  word ; the  only  part  which  we  ever  can  be  concerned 
in  proving.  When  that  is  proved,  the  quality  is  proved ; if  an  object  ex- 
cites a sensation,  it  has,  of  course,  the  power  of  exciting  it. 

IV.  Relations. 

§ 10.  The  qualities  of  a body,  we  have  said,  are  the  attributes  grounded 
on  the  sensations  which  the  presence  of  that  particular  body  to  our  organs 
excites  in  our  minds.  But  when  we  ascribe  to  any  object  the  kind  of  at- 
tribute called  a Relation,  the  foundation  of  the  attribute  must  be  some- 
thing in  which  other  objects  are  concerned  besides  itself  and  the  percipient. 

As  there  may  with  propriety  be  said  to  be  a relation  between  any  two 
things  to  which  two  correlative  names  are  or  may  be  given,  we  may  ex- 
pect to  discover  what  constitutes  a relation  in  general,  if  we  enumerate  the 
principal  cases  in  which  mankind  have  imposed  correlative  names,  and  ob- 
serve what  these  cases  have  in  common. 

What,  then,  is  the  character  which  is  possessed  in  common  by  states  of 
circumstances  so  heterogeneous  and  discordant  as  these : one  thing  like 
another;  one  thing  unlike  another;  one  thing  near  another;  one  thing 
far  from,  another;  one  thing  before,  after,  along  with  another;  one  thing 
greater,  equal,  less,  than  another ; one  thing  the  cause  of  another,  the  effect 
of  another;  one  person  the  master,  servant,  child,  parent,  debtor,  creditor, 
sovereign,  subject,  attorney,  client,  of  another,  and  so  on  ? 

Omitting,  for  the  present,  the  case  of  Resemblance,  (a  relation  which  re- 
quires to  be  considered  separately,)  there  seems  to  be  one  thing  common 
to  all  these  cases,  and  only  one ; that  in  each  of  them  there  exists  or  occurs, 
or  has  existed  or  occurred,  or  may  be  expected  to  exist  or  occur,  some  fact 
or  phenomenon,  into  which  the  two  things  which  are  said  to  be  related  to 
each  other,  both  enter  as  parties  concerned.  This  fact,  or  phenomenon,  is 
what  the  Aristotelian  logicians  called  the  fundamentum  relationis.  Thus 
in  the  relation  of  greater  and  less  between  two  magnitudes,  the  f undamen- 
tum relationis  is  the  fact  that  one  of  the  two  magnitudes  could,  under  cer- 
tain conditions,  be  included  in,  without  entirely  filling,  the  space  occupied 
by  the  other  magnitude.  In  the  relation  of  master  and  servant,  the  fun- 
damentum relationis  is  the  fact  that  the  one  has  undertaken,  or  is  com- 
pelled, to  perform  certain  services  for  the  benefit  and  at  the  bidding  of  the 
other.  Examples  might  be  indefinitely  multiplied ; but  it  is  already  obvi- 
ous that  whenever  two  things  are  said  to  be  related,  there  is  some  fact,  or 
series  of  facts,  into  which  they  both  enter;  and  that  whenever  any  two 
things  are  involved  in  some  one  fact,  or  series  of  facts,  we  may  ascribe  to 
those  two  things  a mutual  relation  grounded  on  the  fact.  Even  if  they 
have  nothing  in  common  but  what  is  common  to  all  things,  that  they  are 
members  of  the  universe,  we  call  that  a relation,  and  denominate  them 
fellow-creatures,  fellow-beings,  or  fellow-denizens  of  the  universe.  But  in 


60 


NAMES  AND  PROPOSITIONS. 


proportion  as  the  fact  into  which  the  two  objects  enter  as  parts  is  of  a 
more  special  and  peculiar,  or  of  a more  complicated  nature,  so  also  is  the 
relation  grounded  upon  it.  And  there  are  as  many  conceivable  relations 
as  there  are  conceivable  kinds  of  fact  in  which  two  things  can  be  jointly 
concerned. 

In  the  same  manner,  therefore,  as  a quality  is  an  attribute  grounded  on 
the  fact  that  a certain  sensation  or  sensations  are  produced  in  us  by  the 
object,  so  an  attribute  grounded  on  some  fact  into  which  the  object  enters 
jointly  with  another  object,  is  a relation  between  it  and  that  other  object. 
But  the  fact  in  the  latter  case  consists  of  the  very  same  kind  of  elements 
as  the  fact  in  the  former ; namely,  states  of  consciousness.  In  the  case, 
for  example,  of  any  legal  relation,  as  debtor  and  creditor,  principal  and 
agent,  guardian  and  ward,  the  fundamentum  relationis  consists  entirely  of 
thoughts,  feelings,  and  volitions  (actual  or  contingent),  either  of  the  persons 
themselves  or  of  other  persons  concerned  in  the  same  series  of  transactions; 
as,  for  instance,  the  intentions  which  would  be  formed  by  a judge,  in  case 
a complaint  were  made  to  his  tribunal  of  the  infringement  of  any  of  the 
legal  obligations  imposed  by  the  relation;  and  the  acts  which  the  judge 
would  perform  in  consequence;  acts  being  (as  we  have  already  seen)  an- 
other word  for  intentions  followed  by  an  effect,  and  that  effect  being  but 
another  word  for  sensations,  or  some  other  feelings,  occasioned  either  to 
the  agent  himself  or  to  somebody  else.  There  is  no  part  of  what  the  names 
expressive  of  the  relation  imply,  that  is  not  resolvable  into  states  of  con- 
sciousness; outward  objects  being,  no  doubt,  supposed  throughout  as  the 
causes  by  which  some  of  those  states  of  consciousness  are  excited,  and 
minds  as  the  subjects  by  which  all  of  them  are  experienced,  but  neither 
the  external  objects  nor  the  minds  making  their  existence  known  other- 
wise than  by  the  states  of  consciousness. 

Cases  of  relation  are  not  always  so  complicated  as  those  to  which  we 
last  alluded.  The  simplest  of  all  cases  of  relation  are  those  expressed  by 
the  words  antecedent  and  consequent,  and  by  the  word  simultaneous.  If 
we  say,  for  instance,  that  dawn  preceded  sunrise,  the  fact  in  which  the  two 
things,  dawn  and  sunrise,  were  jointly  concerned,  consisted  only  of  the  two 
things  themselves;  no  third  thing  entered  into  the  fact  or  phenomenon  at 
all.  Unless,  indeed,  we  choose  to  call  the  succession  of  the  two  objects  a 
third  thing;  but  their  succession  is  not  something  added  to  the  things 
themselves ; it  is  something  involved  in  them.  Dawn  and  sunrise  announce 
themselves  to  our  consciousness  by  two  successive  sensations.  Our  con- 
sciousness of  the  succession  of  these  sensations  is  not  a third  sensation  or 
feeling  added  to  them;  we  have  not  first  the  two  feelings,  and  then  a feel- 
ing of  their  succession.  To  have  two  feelings  at  all,  implies  having  them 
either  successively,  or  else  simultaneously.  Sensations,  or  other  feelings, 
being  given,  succession  and  simultaneousness  are  the  two  conditions,  to  the 
alternative  of  which  they  are  subjected  by  the  nature  of  our  faculties ; and 
no  one  has  been  able,  or  needs  expect,  to  analyze  the  matter  any  further. 

§ 11.  In  a somewhat  similar  position  are  two  other  sorts  of  relations, 
Likeness  and  Unlikeness.  I have  two  sensations ; we  will  suppose  them 
to  be  simple  ones;  two  sensations  of  white,  or  one  sensation  of  white  and 
another  of  black.  I call  the  first  two  sensations  like  ; the  last  two  unlike. 
What  is  the  fact  or  phenomenon  constituting  the  fundamentum  of  this 
relation?  The  two  sensations  first,  and  then  what  we  call  a feeling  of  re- 
semblance, or  of  want  of  resemblance.  Let  us  confine  ourselves  to  the  few 


THINGS  DENOTED  BY  NAMES. 


61 


mer  case.  Resemblance  is  evidently  a feeling ; a state  of  the  consciousness 
of  the  observer.  Whether  the  feeling  of  the  resemblance  of  the  two  colors 
be  a third  state  of  consciousness,  which  I have  after  having  the  two  sensa- 
tions of  color,  or  whether  (like  the  feeling  of  their  succession)  it  is  involved 
in  the  sensations  themselves,  may  be  a matter  of  discussion.  But  in  either 
case,  these  feelings  of  resemblance,  and  of  its  opposite  dissimilarity,  are 
parts  of  our  nature ; and  parts  so  far  from  being  capable  of  analysis,  that 
they  are  presupposed  in  every  attempt  to  analyze  any  of  our  other  feelings. 
Likeness  and  unlikeness,  therefore,  as  well  as  antecedence,  sequence,  and 
simultaneousness,  must  stand  apart  among  relations,  as  things  sui  generis. 
They  are  attributes  grounded  on  facts,  that  is,  on  states  of  consciousness, 
but  on  states  which  are  peculiar,  unresolvable,  and  inexplicable. 

But,  though  likeness  or  unlikeness  can  not  be  resolved  into  any  thing 
else,  complex  cases  of  likeness  or  unlikeness  can  be  resolved  into  simpler 
ones.  When  we  say  of  two  things  which  consist  of  parts,  that  they  are 
like  one  another,  the  likeness  of  the  wholes  does  admit  of  analysis ; it  is 
compounded  of  likenesses  between  the  various  parts  respectively,  and  of 
likeness  in  their  arrangement.  Of  how  vast  a variety  of  resemblances  of 
parts  must  that  resemblance  be  composed,  which  induces  us  to  say  that  a 
portrait,  or  a landscape,  is  like  its  original.  If  one  person  mimics  another 
with  any  success,  of  how  many  simple  likenesses  must  the  general  or  com- 
plex likeness  be  compounded : likeness  in  a succession  of  bodily  postures ; 
likeness  in  voice,  or  in  the  accents  and  intonations  of  the  voice ; likeness 
in  the  choice  of  words,  and  in  the  thoughts  or  sentiments  expressed,  wheth- 
er by  word,  countenance,  or  gesture. 

All  likeness  and  unlikeness  of  which  wTe  have  any  cognizance,  resolve 
themselves  into  likeness  and  unlikeness  between  states  of  our  own,  or  some 
other,  mind.  When  we  say  that  one  body  is  like  another,  (since  we  know 
nothing  of  bodies  but  the  sensations  which  they  excite,)  we  mean  really 
that  there  is  a resemblance  between  the  sensations  excited  by  the  two 
bodies,  or  between  some  portions  at  least  of  those  sensations.  If  we  say 
that  two  attributes  are  like  one  another  (since  we  know  nothing  of  attri- 
butes except  the  sensations  or  states  of  feeling  on  which  they  are  ground- 
ed), we  mean  really  that  those  sensations,  or  states  of  feeling,  resemble  each 
other.  We  may  also  say  that  two  relations  are  alike.  The  fact  of  resem- 
blance between  relations  is  sometimes  called  analogy , forming  one  of  the 
numerous  meanings  of  that  word.  The  relation  in  which  Priam  stood  to 
Hector,  namely,  that  of  father  and  son,  resembles  the  relation  in  which 
Philip  stood  to  Alexander;  resembles  it  so  closely  that  they  are  called  the 
same  relation.  The  relation  in  which  Cromwell  stood  to  England  resem- 
bles the  relation  in  which  Napoleon  stood  to  France,  though  not  so  closely 
as  to  be  called  the  same  relation.  The  meaning  in  both  these  instances 
must  be,  that  a resemblance  existed  between  the  facts  which  constituted 
the  fundamentum  relationis. 

This  resemblance  may  exist  in  all  conceivable  gradations,  from  perfect 
undistinguisliableness  to  something  extremely  slight.  When  we  say,  that 
a thought  suggested  to  the  mind  of  a person  of  genius  is  like  a seed  cast 
into  the  ground,  because  the  former  produces  a multitude  of  other  thoughts, 
and  the  latter  a multitude  of  other  seeds,  this  is  saying  that  between  the 
relation  of  an  inventive  mind  to  a thought  contained  in  it,  and  the  relation 
of  a fertile  soil  to  a seed  contained  in  it,  there  exists  a resemblance : the 
real  resemblance  being  in  the  two  fundamenta  relationis,  in  each  of  which 
there  occurs  a germ,  producing  by  its  development  a multitude  of  other 


62 


NAMES  AND  PROPOSITIONS. 


things  similar  to  itself.  And  as,  whenever  two  objects  are  jointly  concern- 
ed in  a phenomenon,  this  constitutes  a relation  between  those  objects,  so, 
if  we  suppose  a second  pair  of  objects  concerned  in  a second  phenomenon, 
the  slightest  resemblance  between  the  two  phenomena  is  sufficient  to  ad- 
mit of  its  being  said  that  the  two  relations  resemble;  provided,  of  course, 
the  points  of  resemblance  are  found  in  those  portions  of  the  two  phenom- 
ena respectively  which  are  connoted  by  the  relative  names. 

While  speaking  of  resemblance,  it  is  necessary  to  take  notice  of  an  am- 
biguity of  language,  against  which  scarcely  any  one  is  sufficiently  on  his 
guard.  Resemblance,  when  it  exists  in  the  highest  degree  of  all,  amount- 
ing to  undistinguish  ableness,  is  often  called  identity,  and  the  two  similar 
things  are  said  to  be  the  same.  I say  often,  not  always;  for  we  do  not  say 
that  two  visible  objects,  two  persons,  for  instance,  are  the  same,  because 
they  are  so  much  alike  that  one  might  be  mistaken  for  the  other:  but  we 
constantly  use  this  mode  of  expression  when  speaking  of  feelings ; as  when 
I say  that  the  sight  of  any  object  gives  me  the  same  sensation  or  emotion 
to-day  that  it  did  yesterday,  or  the  same  which  it  gives  to  some  other  per- 
son. This  is  evidently  an  incorrect  application  of  the  word  same • for  the 
feeling  which  I had  yesterday  is  gone,  never  to  return  ; what  I have  to- 
day is  another  feeling,  exactly  like  the  former,  perhaps,  but  distinct  from  it ; 
and  it  is  evident  that  two  different  persons  can  not  be  experiencing  the 
same  feeling,  in  the  sense  in  which  we  say  that  they  are  both  sitting  at  the 
same  table.  By  a similar  ambiguity  we  say,  that  two  persons  are  ill  of  the 
same  disease ; that  two  persons  hold  the  same  office ; not  in  the  sense  in 
which  we  say  that  they  are  engaged  in  the  same  adventure,  or  sailing  in 
the  same  ship,  but  in  the  sense  that  they  fill  offices  exactly  similar,  though, 
perhaps,  in  distant  places.  Great  confusion  of  ideas  is  often  produced,  and 
many  fallacies  engendered,  in  otherwise  enlightened  understandings,  by 
not  being  sufficiently  alive  to  the  fact  (in  itself  not  always  to  be  avoided), 
that  they  use  the  same  name  to  express  ideas  so  different  as  those  of  iden- 
tity and  undistinguishable  resemblance.  Among  modern  writers,  Arch- 
bishop Whately  stands  almost  alone  in  having  drawn  attention  to  this  dis- 
tinction, and  to  the  ambiguity  connected  with  it. 

Several  relations,  generally  called  by  other  names,  are  really  cases  of 
resemblance.  As,  for  example,  equality ; which  is  but  another  word  for 
the  exact  resemblance  commonly  called  identity,  considered  as  subsisting 
between  things  in  respect  of  their  quantity.  And  this  example  forms  a 
suitable  transition  to  the  third  and  last  of  the  three  heads  under  which,  as 
already  remarked,  Attributes  are  commonly  arranged. 

V.  Quantity. 

§ 12.  Let  us  imagine  two  things,  between  which  there  is  no  difference 
(that  is,  no  dissimilarity),  except  in  quantity  alone ; for  instance,  a gallon 
of  water,  and  more  than  a gallon  of  water.  A gallon  of  water,  like  any 
other  external  object,  makes  its  presence  known  to  us  by  a set  of  sensa- 
tions which  it  excites.  Ten  gallons  of  water  are  also  an  external  object, 
making  its  presence  known  to  us  in  a similar  manner;  and  as  we  do  not 
mistake  ten  gallons  of  water  for  a gallon  of  water,  it  is  plain  that  the  set 
of  sensations  is  more  or  less  different  in  the  two  cases.  In  like  manner, 
a gallon  of  water,  and  a gallon  of  wine,  are  two  external  objects,  making 
their  presence  known  by  two  sets  of  sensations,  which  sensations  are  dif- 
ferent from  each  other.  In  the  first  case,  however,  we  say  that  the  differ- 
ence is  in  quantity ; in  the  last  there  is  a difference  in  quality,  while  the 


THINGS  DENOTED  BY  NAMES. 


63 


quantity  of  the  water  and  of  the  wine  is  the  same.  What  is  the  real  dis- 
tinction between  the  two  cases?  It  is  not  within  the  province  of  Logic  to 
analyze  it ; nor  to  decide  whether  it  is  susceptible  of  analysis  or  not.  For 
us  the  following  considerations  are  sufficient:  It  is  evident  that  the  sen- 
sations I receive  from  the  gallon  of  water,  and  those  I receive  from  the 
gallon  of  wine,  are  not  the  same,  that  is,  not  precisely  alike ; neither  are 
they  altogether  unlike : they  are  partly  similar,  partly  dissimilar  ; and  that 
in  which  they  resemble  is  precisely  that  in  which  alone  the  gallon  of  wa- 
ter and  the  ten  gallons  do  not  resemble.  That  in  which  the  gallon  of  wa- 
ter and  the  gallon  of  wine  are  like  each  other,  and  in  which  the  gallon 
and  the  ten  gallons  of  water  are  unlike  each  other,  is  called  their  quan- 
tity. This  likeness  and  unlikeness  I do  not  pretend  to  explain,  no  more 
than  any  other  kind  of  likeness  or  unlikeness.  But  my  object  is  to  show, 
that  when  we  say  of  two  things  that  they  differ  in  quantity,  just  as  when 
we  say  that  they  differ  in  quality,  the  assertion  is  always  grounded  on  a 
difference  in  the  sensations  which  they  excite.  Nobody,  I presume,  will 
say,  that  to  see,  or  to  lift,  or  to  drink,  ten  gallons  of  water,  does  not  include 
in  itself  a different  set  of  sensations  from  those  of  seeing,  lifting,  or  drink- 
ing one  gallon ; or  that  to  see  or  handle  a foot-rule,  and  to  see  or  handle  a 
yard-measure  made  exactly  like  it,  are  the  same  sensations.  I do  not  un- 
dertake to  say  what  the  difference  in  the  sensations  is.  Every  body  knows, 
and  nobody  can  tell;  no  more  than  any  one  could  tell  what  white  is  to  a 
person  who  had  never  had  the  sensation.  But  the  difference,  so  far  os 
cognizable  by  our  faculties,  lies  in  the  sensations.  Whatever  difference 
we  say  there  is  in  the  things  themselves,  is,  in  this  as  in  all  other  cases, 
grounded,  and  grounded  exclusively,  on  a difference  in  the  sensations  ex- 
cited by  them. 

VI.  Attributes  Concluded. 

§ 13.  Thus,  then,  all  the  attributes  of  bodies  which  are  classed  under 
Quality  or  Quantity,  are  grounded  on  the  sensations  which  we  receive  from 
those  bodies,  and  may  be  defined,  the  powers  which  the  bodies  have  of  ex- 
citing those  sensations.  And  the  same  general  explanation  has  been  found 
to  apply  to  most  of  the  attributes  usually  classed  under  the  head  of  Rela- 
tion. They,  too,  are  grounded  on  some  fact  or  phenomenon  into  which  the 
related  objects  enter  as  parts;  that  fact  or  phenomenon  having  no  mean- 
ing and  no  existence  to  us,  except  the  series  of  sensations  or  other  states 
of  consciousness  by  which  it  makes  itself  known ; and  the  relation  being 
simply  the  power  or  capacity  which  the  object  possesses  of  taking  part 
along  with  the  correlated  object  in  the  production  of  that  series  of  sensa- 
tions or  states  of  consciousness.  We  have  been  obliged,  indeed,  to  recog- 
nize a somewhat  different  character  in  certain  peculiar  relations,  those  of 
succession  and  simultaneity,  of  likeness  and  unlikeness.  These,  not  being 
grounded  on  any  fact  or  phenomenon  distinct  from  the  related  objects 
themselves,  do  not  admit  of  the  same  kind  of  analysis.  But  these  relations, 
though  not,  like  other  relations,  grounded  on  states  of  consciousness,  are 
themselves  states  of  consciousness:  resemblance  is  nothin"  but  our  feelin" 
of  resemblance;  succession  is  nothing  but  our  feeling  of  succession.  Or, 
if  this  be  disputed  (and  ive  can  not,  without  transgressing  the  bounds  of 
our  science,  discuss  it  here),  at  least  our  knowledge  of  these  relations,  and 
even  our  possibility  of  knowledge,  is  confined  to  those  which  subsist  be- 
tween sensations,  or  other  states  of  consciousness ; for,  though  we  ascribe 
resemblance,  or  succession,  or  simultaneity,  to  objects  and  to  attributes,  it 


04 


NAMES  AND  PROPOSITIONS. 


is  always  in  virtue  of  resemblance  or  succession  or  simultaneity  in  the  sen- 
sations or  states  of  consciousness  which  those  objects  excite,  and  on  which 
those  attributes  are  grounded. 

§ 14.  In  the  preceding  investigation  rve  have,  for  the  sake  of  simplicity, 
considered  bodies  only,  and  omitted  minds.  But  what  we  have  said,  is  ap- 
plicable, mutatis  mutandis,  to  the  latter.  The  attributes  of  minds,  as  wTell 
as  those  of  bodies,  are  grounded  on  states  of  feeling  or  consciousness.  But 
in  the  case  of  a mind,  we  have  to  consider  its  own  states,  as  well  as  those 
which  it  produces  in  other  minds.  Every  attribute  of  a mind  consists  either 
in  being  itself  affected  in  a certain  way,  or  affecting  other  minds  in  a certain 
way.  Considered  in  itself,  we  can  predicate  nothing  of  it  but  the  series 
of  its  own  feelings.  When  we  say  of  any  mind,  that  it  is  devout,  or  super- 
stitious, or  meditative,  or  cheerful,  we  mean  that  the  ideas,  emotions,  or 
volitions  implied  in  those  words,  form  a frequently  recurring  part  of  the 
series  of  feelings,  or  states  of  consciousness,  which  fill  up  the  sentient  ex- 
istence of  that  mind. 

In  addition,  however,  to  those  attributes  of  a mind  which  are  grounded 
on  its  own  states  of  feeling,  attributes  may  also  be  ascribed  to  it,  in  the 
same  manner  as  to  a body,  grounded  on  the  feelings  which  it  excites  in 
other  minds.  A mind  does  not,  indeed,  like  a body,  excite  sensations,  but 
it  may  excite  thoughts  or  emotions.  The  most  important  example  of  attri- 
butes ascribed  on  this  ground,  is  the  employment  of  terms  expressive  of 
approbation  or  blame.  When,  for  example,  we  say  of  any  character,  or  (in 
other  words)  of  any  mind,  that  it  is  admirable,  we  mean  that  the  contem- 
plation of  it  excites  the  sentiment  of  admiration ; and  indeed  somewhat 
more,  for  the  word  implies  that  we  not  only  feel  admiration,  but  approve 
that  sentiment  in  ourselves.  In  some  cases,  under  the  semblance  of  a sin- 
gle attribute,  two  are  really  predicated : one  of  them,  a state  of  the  mind 
itself;  the  other,  a state  with  which  other  minds  are  affected  by  thinking 
of  it.  As  when  we  say  of  any  one  that  he  is  generous.  The  word  gene- 
rosity expresses  a certain  state  of  mind,  but  being  a term  of  praise,  it  also 
expresses  that  this  state  of  mind  excites  in  us  another  mental  state,  called 
approbation.  The  assertion  made,  therefore,  is  twofold,  and  of  the  follow- 
ing purport:  Certain  feelings  form  habitually  a part  of  this  person’s  sen- 
tient existence;  and  the  idea  of  those  feelings  of  his,  excites  the  sentiment 
of  approbation  in  ourselves  or  others. 

As  we  thus  ascribe  attributes  to  minds  on  the  ground  of  ideas  and  emo- 
tions, so  may  we  to  bodies  on  similar  grounds,  and  not  solely  on  the  ground 
of  sensations : as  in  speaking  of  the  beauty  of  a statue ; since  this  attribute 
is  grounded  on  the  peculiar  feeling  of  pleasure  which  the  statue  produces 
in  our  minds;  which  is  not  a sensation,  but  an  emotion. 

VII.  General  Results. 

§ 15.  Our  survey  of  the  varieties  of  Things  which  have  been,  or  which 
are  capable  of  being,  named — which  have  been,  or  are  capable  of  being, 
either  predicated  of  other  Things,  or  themselves  made  the  subject  of  predi- 
cations— is  now  concluded. 

Our  enumeration  commenced  with  Feelings.  These  we  scrupulously  dis- 
tinguished from  the  objects  which  excite  them,  and  from  the  organs  by 
which  they  are,  or  may  be  supposed  to  be,  conveyed.  Feelings  are  of  four 
sorts:  Sensations,  Thoughts,  Emotions,  and  Volitions.  What  are  called 
Perceptions  are  merely  a particular  case  of  Belief,  and  Belief  is  a kind  of 
thought.  Actions  are  merely  volitions  followed  by  an  effect. 


THINGS  DENOTED  BY  NAMES. 


65 


After  Feelings  we  proceeded  to  Substances.  These  are  either  Bodies  or 
Minds.  Without  entering  into  the  grounds  of  the  metaphysical  doubts 
which  have  been  raised  concerning  the  existence  of  Matter  and  Mind  as  ob- 
jective realities,  we  stated  as  sufficient  for  us  the  conclusion  in  which  the 
best  thinkers  are  now  for  the  most  part  agreed,  that  all  we  can  know  of 
Matter  is  the  sensations  which  it  gives  us,  and  the  order  of  occurrence  of 
those  sensations ; and  that  while  the  substance  Body  is  the  unknown  cause 
of  our  sensations,  the  substance  Mind  is  the  unknown  recipient. 

The  only  remaining  class  of  Namable  Things  is  Attributes;  and  these 
are  of  three  kinds,  Quality,  Relation,  and  Quantity.  Qualities,  like  sub- 
stances, are  known  to  us  no  otherwise  than  by  the  sensations  or  other 
states  of  consciousness  which  they  excite : and  while,  in  compliance  with 
common  usage,  we  have  continued  to  speak  of  them  as  a distinct  class  of 
Things,  we  showed  that  in  predicating  them  no  one  means  to  predicate  any 
thing  but  those  sensations  or  states  of  consciousness,  on  which  they  may  be 
said  to  be  grounded,  and  by  which  alone  they  can  be  defined  or  described. 
Relations,  except  the  simple  cases  of  likeness  and  unlikeness,  succession 
and  simultaneity,  are  similarly  grounded  on  some  fact  or  phenomenon,  that 
is,  on  some  series  of  sensations  or  states  of  consciousness,  more  or  less 
complicated.  The  third  species  of  Attribute,  Quantity,  is  also  manifestly 
grounded  on  something  in  our  sensations  or  states  of  feeling,  since  there  is 
an  indubitable  difference  in  the  sensations  excited  by  a larger  and  a smaller 
bulk,  or  by  a greater  or  a less  degree  of  intensity,  in  any  object  of  sense  or 
of  consciousness.  All  attributes,  therefore,  are  to  us  nothing  but  either 
our  sensations  and  other  states  of  feeling,  or  something  inextricably  in- 
volved therein;  and  to  this  even  the  peculiar  and  simple  relations  just  ad- 
verted to  are  not  exceptions.  Those  peculiar  relations,  however,  are  so  im- 
portant, and,  even  if  they  might  in  strictness  be  classed  among  states  of 
consciousness,  are  so  fundamentally  distinct  from  any  other  of  those  states, 
that  it  would  be  a vain  subtlety  to  bring  them  under  that  common  descrip- 
tion, and  it  is  necessary  that  they  should  be  classed  apart.* 

As  the  result,  therefore,  of  our  analysis,  we  obtain  the  following  as  an 
enumeration  and  classification  of  all  Namable  Things : 

1st.  Feelings,  or  States  of  Consciousness. 

2d.  The  Minds  which  experience  those  feelings. 

3d.  The  Bodies,  or  external  objects  which  excite  certain  of  those  feelings, 
together  with  the  powers  or  properties  whereby  they  excite  them ; these 
latter  (at  least)  being  included  rather  in  compliance  with  common  opinion, 
and  because  their  existence  is  taken  for  granted  in  the  common  language 
from  which  I can  not  prudently  deviate,  than  because  the  recognition  of 
such  powers  or  properties  as  real  existences  appears  to  be  warranted  by  a 
sound  philosophy. 

4th,  and  last.  The  Successions  and  Co-existences,  the  Likenesses  and  Un- 
likenesses, between  feelings  or  states  of  consciousness.  Those  relations, 
when  considered  as  subsisting  between  other  things,  exist  in  reality  only 
between  the  states  of  consciousness  which  those  things,  if  bodies,  excite,  if 
minds,  either  excite  or  experience. 

* Professor  Bain  {Logic,  i.,  49)  defines  attributes  as  “points  of  community  among  classes.” 
This  definition  expresses  well  one  point  of  view,  but  is  liable  to  the  objection  that  it  applies 
only  to  the  attributes  of  classes ; though  an  object,  unique  in  its  kind,  may  be  said  to  have  at- 
tributes. Moreover,  the  definition  is  not  ultimate,  since  the  points  of  community  themselves 
admit  of,  and  require,  further  analysis ; and  Mr.  Bain  does  analyze  them  into  resemblances  in 
the  sensations,  or  other  states  of  consciousness  excited  by  the  object. 

5 


00 


NAMES  AND  PROPOSITIONS. 


This,  until  a better  can  be  suggested,  may  serve  as  a substitute  for  the 
Categories  of  Aristotle  considered  as  a classification  of  Existences.  The 
practical  application  of  it  will  appear  when  we  commence  the  inquiry  into 
the  Import  of  Propositions;  in  other  words,  when  we  inquire  what  it  is 
which  the  mind  actually  believes,  when  it  gives  what  is  called  its  assent  to 
a proposition. 

These  four  classes  comprising,  if  the  classification  be  correct,  all  Namable 
Things,  these  or  some  of  them  must  of  course  compose  the  signification  of 
all  names : and  of  these,  or  some  of  them,  is  made  up  whatever  we  call  a 
fact. 

For  distinction’s  sake,  every  fact  which  is  solely  composed  of  feelings  or 
states  of  consciousness  considered  as  such,  is  often  called  a Psychological 
or  Subjective  fact;  while  every  fact  which  is  composed,  either  wholly  or  in 
part,  of  something  different  from  these,  that  is,  of  substances  and  attri- 
butes, is  called  an  Objective  fact.  We  may  say,  then,  that  every  objective 
fact  is  grounded  on  a corresponding  subjective  one ; and  has  no  meaning  - 
to  us  (apart  from  the  subjective  fact  which  corresponds  to  it),  except  as  a 
name  for  the  unknown  and  inscrutable  process  by  which  that  subjective  or 
psychological  fact  is  brought  to  pass. 


CHAPTER  IV. 

OF  PROPOSITIONS. 

§ 1.  In  treating  of  Propositions,  as  already  in  treating  of  Names,  some 
considerations  of  a comparatively  elementary  nature  respecting  their  form 
and  varieties  must  be  premised,  before  entering  upon  that  analysis  of  the 
import  conveyed  by  them,  which  is  the  real  subject  and  purpose  of  this 
preliminary  book. 

A proposition,  we  have  before  said,  is  a portion  of  discourse  in  which  a 
predicate  is  affirmed  or  denied  of  a subject.  A predicate  and  a subject  are 
all  that  is  necessarily  required  to  make  up  a proposition : but  as  we  can  not 
conclude  from  merely  seeing  two  names  put  together,  that  they  are  a predi- 
cate and  a subject,  that  is,  that  one  of  them  is  intended  to  be  affirmed  or 
denied  of  the  other,  it  is  necessary  that  there  should  be  some  mode  or  form 
of  indicating  that  such  is  the  intention;  some  sign  to  distinguish  a predi- 
cation from  any  other  kind  of  discourse.  This  is  sometimes  done  by  a 
slight  alteration  of  one  of  the  words,  called  an  inflection ; as  when  we  say, 
Fire  burns ; the  change  of  the  second  word  from  burn  to  burns  showing 
that  we  mean  to  affirm  the  predicate  burn  of  the  subject  fire.  But  this 
function  is  more  commonly  fulfilled  by  the  word  is,  when  an  affirmation  is 
intended,  is  not,  when  a negation;  or  by  some  other  part  of  the  verb  to  be. 
The  word  which  thus  serves  the  purpose  of  a sign  of  predication  is  called, 
as  we  formerly  observed,  the  cojmla.  It  is  important  that  there  should  be 
no  indistinctness  in  our  conception  of  the  nature  and  office  of  the  copula; 
for  confused  notions  respecting  it  are  among  the  causes  which  have  spread 
mysticism  over  the  field  of  logic,  and  perverted  its  speculations  into  logoma- 
chies. 

It  is  apt  to  be  supposed  that  the  copula  is  something  more  than  a mere 
sign  of  predication  ; that  it  also  signifies  existence.  In  the  proposition, 
Socrates  is  just,  it  may  seem  to  be  implied  not  only  that  the  quality  just 
can  be  affirmed  of  Socrates,  but  moreover  that  Socrates  is,  that  is  to  say, 


PROPOSITIONS. 


67 


exists.  This,  however,  only  shows  that  there  is  an  ambiguity  in  the  word 
is;  a word  which  not  only  performs  the  function  of  the  copula  in  affirma- 
tions, but  has  also  a meaning  of  its  own,  in  virtue  of  which  it  may  itself  be 
made  the  predicate  of  a proposition.  That  the  employment  of  it  as  a cop- 
ula does  not  necessarily  include  the  affirmation  of  existence,  appears  from 
such  a proposition  as  this,  A centaur  is  a fiction  of  the  poets  ; where  it  can 
not  possibly  be  implied  that  a centaur  exists,  since  the  proposition  itself  ex- 
pressly asserts  that  the  thing  has  no  real  existence. 

Many  volumes  might  be  filled  with  th.e  frivolous  speculations  concerning 
the  nature  of  Being  (to  ov,  obtriu,  Ens,  Entitas,  Essentia,  and  the  like),  which 
have  arisen  from  overlooking  this  double  meaning  of  the  word  to  be ; from 
supposing  that  when  it  signifies  to  exist,  and  when  it  signifies  to  be  some 
specified  thing,  as  to  be  a man,  to  be  Socrates,  to  be  seen  or  spoken  of,  to  be 
a phantom,  even  to  be  a nonentity,  it  must  still,  at  bottom,  answer  to  the 
same  idea ; and  that  a meaning  must  be  found  for  it  which  shall  suit  all 
these  cases.  The  fog  which  rose  from  this  narrow  spot  diffused  itself  at 
an  early  period  over  the  whole  surface  of  metaphysics.  Yet  it  becomes 
us  not  to  triumph  over  the  great  intellects  of  Plato  and  Aristotle  because 
we  are  now  able  to  preserve  ourselves  from  many  errors  into  which  they, 
perhaps  inevitably,  fell.  The  fire-teazer  of  a modern  steam-engine  produces 
by  his  exertions  far  greater  effects  than  Milo  of  Crotona  could,  but  he  is 
not  therefore  a stronger  man.  The  Greeks  seldom  knew  any  language  but 
their  own.  This  rendered  it  far  more  difficult  for  them  than  it  is  for  us,  to 
acquire  a readiness  in  detecting  ambiguities.  One  of  the  advantages  of 
having  accurately  studied  a plurality  of  languages,  especially  of  those  lan- 
guages which  eminent  thinkers  have  used  as  the  vehicle  of  their  thoughts, 
is  the  practical  lesson  we  learn  respecting  the  ambiguities  of  words,  by  find- 
ing that  the  same  word  in  one  language  corresponds,  on  different  occasions, 
to  different  words  in  another.  When  not  thus  exercised,  even  the  strong- 
est understandings  find  it  difficult  to  believe  that  things  which  have  a com- 
mon name,  have  not  in  some  respect  or  other  a common  nature ; and  often 
expend  much  labor  very  unprofitably  (as  was  frequently  done  by  the  two 
philosophers  just  mentioned)  in  vain  attempts  to  discover  in  what  this  com- 
mon nature  consists.  But,  the  habit  once  formed,  intellects  much  inferior 
are  capable  of  detecting  even  ambiguities  which  are  common  to  many  lan- 
guages: and  it  is  surprising  that  the  one  now  under  consideration,  though 
it  exists  in  the  modern  languages  as  well  as  in  the  ancient,  should  have 
been  overlooked  by  almost  all  authors.  The  quantity  of  futile  speculation 
which  had  been  caused  by  a misapprehension  of  the  nature  of  the  copula, 
was  hinted  at  by  Hobbes ; but  Mr.  James  Mill*, was,  I believe,  the  first  who 
distinctly  characterized  the  ambiguity,  and  pointed  out  how  many  errors  in 
the  received  systems  of  philosophy  it  has  had  to  answer  for.  It  has,  indeed, 
misled  the  moderns  scarcely  less  than  the  ancients,  though  their  mistakes, 
because  our  understandings  are  not  yet  so  completely  emancipated  from 
their  influence,  do  not  appear  equally  irrational. 

We  shall  now  briefly  review  the  principal  distinctions  which  exist  among 
propositions,  and  the  technical  terms  most  commonly  in  use  to  express 
those  distinctions. 

§ 2.  A proposition  being  a portion  of  discourse  in  which  something  is 
affirmed  or  denied  of  something,  the  first  division  of  propositions  is  into 


Analysis  of  the  Human  Mind , i.,  126  et  seq. 


OS 


NAMES  AND  PROPOSITIONS. 


affirmative  and  negative.  An  affirmative  proposition  is  that  in  which  the 
predicate  is  affirmed  of  the  subject;  as,  Caesar  is  dead.  A negative  prop- 
osition is  that  in  which  the  predicate  is  denied  of  the  subject;  as,  Caesar 
is  not  dead.  The  copula,  in  this  last  species  of  proposition,  consists  of 
the  words  is  not,  which  are  the  sign  of  negation ; is  being  the  sign  of 
affirmation. 

Some  logicians,  among  whom  may  be  mentioned  Hobbes,  state  this  dis- 
tinction differently;  they  recognize  only  one  form  of  copula,  is,  and  attach 
the  negative  sign  to  the  predicate.  “ Caesar  is  dead,”  and  “ Caesar  is  not 
dead,”  according  to  these  writers,  are  propositions  agreeing  not  in  the  sub- 
ject and  predicate,  but  in  the  subject  only.  They  do  not  consider  “dead,” 
but  “not  dead,”  to  be  the  predicate  of  the  second  proposition,  and  they  ac- 
cordingly define  a negative  proposition  to  be  one  in  which  the  predicate  is 
a negative  name.  The  point,  though  not  of  much  practical  moment,  de- 
serves notice  as  an  example  (not  unfrequent  in  logic)  where  by  means  of 
an  apparent  simplification,  but  which  is  merely  verbal,  matters  are  made 
more  complex  than  before.  The  notion  of  these  writers  was,  that  they 
could  get  rid  of  the  distinction  between  affirming  and  denying,  by  treating 
every  case  of  denying  as  the  affirming  of  a negative  name.  But  what  is 
meant  by  a negative  name?  A name  expressive  of  the  absence  of  an  attri- 
bute. So  that  when  we  affirm  a negative  name,  what  we  are  really  predi- 
cating is  absence  and  not  presence;  we  are  asserting  not  that  any  thing  is, 
but  that  something  is  not;  to  express  which  operation  no  word  seems  so 
proper  as  the  word  denying.  The  fundamental  distinction  is  between  a 
fact  and  the  non-existence  of  that  fact;  between  seeing  something  and 
not  seeing  it,  between  Caesar’s  being  dead  and  his  not  being  dead ; and  if 
this  were  a merely  verbal  distinction,  the  generalization  which  brings  both 
within  the  same  form  of  assertion  would  be  a real  simplification  : the  dis- 
tinction, however,  being  real,  and  in  the  facts,  it  is  the  generalization  con- 
founding the  distinction  that  is  merely  verbal ; and  tends  to  obscure  the 
subject,  by  treating  the  difference  between  two  kinds  of  truths  as  if  it  were 
only  a difference  between  two  kinds  of  words.  To  put  things  together, 
and  to  put  them  or  keep  them  asunder,  will  remain  different  operations, 
whatever  tricks  we  may  play  with  language. 

A remark  of  a similar  nature  may  be  applied  to  most  of  those  distinc- 
tions among  propositions  which  are  said  to  have  reference  to  their  modali- 
ty ' as,  difference  of  tense  or  time;  the  sun  did  rise,  the  sun  is  rising,  the 
sun  will  rise.  These  differences,  like  that  between  affirmation  and  nega- 
tion, might  be  glossed  over  by  considering  the  incident  of  time  as  a mere 
modification  of  the  predicate : thus,  The  sun  is  an  object  having  risen,  The 
sun  is  an  object  now  rising,  The  sun  is  an  object  to  rise  hereafter.  But  the 
simplification  would  be  merely  verbal.  Past,  present,  and  future,  do  not 
constitute  so  many  different  kinds  of  rising ; they  are  designations  belong- 
ing to  the  event  asserted,  to  the  sun's  rising  to-day.  They  affect,  not  the 
predicate,  but  the  applicability  of  the  predicate  to  the  particular  subject. 
That  which  we  affirm  to  be  past,  present,  or  future,  is  not  what  the  subject 
signifies,  nor  what  the  predicate  signifies,  but  specifically  and  expressly 
what  the  predication  signifies ; what  is  expressed  only  by  the  proposition 
as  such,  and  not  by  either  or  both  of  the  terms.  Therefore  the  circum- 
stance of  time  is  properly  considered  as  attaching  to  the  copula,  which  is 
the  sign  of  predication,  and  not  to  the  predicate.  If  the  same  can  not  be 
said  of  such' modifications  as  these,  Caesar  may  be  dead  ; Caesar  is  perhaps 
dead ; it  is  possible  that  Caesar  is  dead ; it  is  only  because  these  fall  alto- 


PROPOSITIONS. 


69 


gether  under  another  head,  being  properly  assertions  not  of  any  thing  re- 
lating to  the  fact  itself,  but  of  the  state  of  our  own  mind  in  regard  to  it ; 
namely,  our  absence  of  disbelief  of  it.  Thus  “ Caesar  may  be  dead”  means 
“ I am  not  sure  that  Caesar  is  alive.” 

§ 3.  The  next  division  of  propositions  is  into  Simple  and  Complex ; more 
aptly  (by  Professor  Bain*)  termed  Compound.  A simple  proposition  is 
that  in  which  one  predicate  is  affirmed  or  denied  of  one  subject.  A com- 
pound proposition  is  that  in  wffiich  there  is  more  than  one  predicate,  or 
more  than  one  subject,  or  both. 

At  first  sight  this  division  has  the  air  of  an  absurdity;  a solemn  distinc- 
tion of  things  into  one  and  more  than  one;  as  if  we  were  to  divide  horses 
into  single  horses  and  teams  of  horses.  And  it  is  true  that  what  is  called 
a complex  (or  compound)  proposition  is  often  not  a proposition  at  all,  but 
several  propositions,  held  together  by  a conjunction.  Such,  for  example,  is 
this : Caesar  is  dead,  and  Brutus  is  alive : or  even  this,  Caesar  is  dead,  but 
Brutus  is  alive.  There  are  here  two  distinct  assertions ; and  we  might  as 
well  call  a street  a complex  house,  as  these  two  propositions  a complex 
proposition.  It  is  true  that  the  syncategorematic  words  and  and  but  have 
a meaning ; but  that  meaning  is  so  far  from  making  the  two  propositions 
one,  that  it  adds  a third  proposition  to  them.  All  particles  are  abbrevia- 
tions, and  generally  abbreviations  of  pi’opositions ; a kind  of  short-hand, 
whereby  something  which,  to  be  expressed  fully,  would  have  required  a 
proposition  or  a series  of  propositions,  is  suggested  to  the  mind  at  once. 
Thus  the  words,  Caesar  is  dead  and  Brutus  is  alive,  are  equivalent  to  these : 
Caesar  is  dead ; Brutus  is  alive ; it  is  desired  that  the  two  preceding  prop- 
ositions should  be  thought  of  together.  If  the  words  were,  Caesar  is  dead, 
but  Brutus  is  alive,  the  sense  would  be  equivalent  to  the  same  three  propo- 
sitions together  with  a fourth ; “ between  the  two  preceding  propositions 
there  exists  a contrast :”  viz.,  either  between  the  two  facts  themselves,  or 
between  the  feelings  with  which  it  is  desired  that  they  should  be  regarded. 

In  the  instances  cited  the  two  propositions  are  kept  visibly  distinct,  each 
subject  having  its  separate  predicate,  and  each  predicate  its  separate  sub- 
ject. For  brevity,  however,  and  to  avo’d  repetition,  the  propositions  are 
often  blended  together:  as  in  this,  “Peter  and  James  preached  at  Jerusa- 
lem and  in  Galilee,”  which  contains  four  propositions : Peter  preached  at 
Jerusalem,  Peter  preached  in  Galilee,  James  preached  at  Jerusalem,  James 
preached  in  Galilee. 

AVe  have  seen  that  when  the  two  or  more  propositions  comprised  in 
what  is  called  a complex  proposition  are  stated  absolutely,  and  not  under 
any  condition  or  proviso,  it  is  not  a proposition  at  all,  but  a plurality  of 
propositions ; since  what  it  expresses  is  not  a single  assertion,  but  several 
assertions,  which,  if  true  when  joined,  are  true  also  when  separated.  But 
there  is  a kind  of  proposition  which,  though  it  contains  a plurality  of  sub- 
jects and  of  predicates,  and  may  be  said  in  one  sense  of  the  word  to  con- 
sist of  several  propositions,  contains  but  one  assertion ; and  its  truth  does 
not  at  all  imply  that  of  the  simple  propositions  which  compose  it.  An  ex- 
ample of  this  is,  when  the  simple  propositions  are  connected  by  the  parti- 
cle or  • as,  either  A is  B or  C is  D ; or  by  the  particle  if,"  as,  A is  B if  C 
is  D.  In  the  former  case,  the  proposition  is  called  disjunctive,  in  the  lat- 
ter, conditional:  the  name  hypotheticcd  was  originally  common  to  both. 


Logic,  i.,  85. 


NAMES  AND  PROPOSITIONS. 


TO 


As  1ms  been  well  remarked  by  Archbishop  Wliately  and  others,  the  dis- 
junctive form  is  resolvable  into  the  conditional;  every  disjunctive  proposi- 
tion being  equivalent  to  two  or  more  conditional  ones.  “Either  A is  B or 
C is  D,”  means,  “ if  A is  not  B,  C is  D ; and  if  C is  not  D,  A is  B.”  All 
hypothetical  propositions,  therefore,  though  disjunctive  in  form,  are  condi- 
tional in  meaning;  and  the  words  hypothetical  and  conditional  may  be,  as 
indeed  they  generally  are,  used  synonymously.  Propositions  in  which  the 
assertion  is  not  dependent  on  a condition,  are  said,  in  the  language  of  logi- 
cians, to  be  categorical. 

A hypothetical  proposition  is  not,  like  the  pretended  complex  proposi- 
tions which  we  previously  considered,  a mere  aggregation  of  simple  propo- 
sitions. The  simple  propositions  which  form  part  of  the  words  in  which 
it  is  couched,  form  no  part  of  the  assertion  which  it  conveys.  When  we 
say,  If  the  Koran  comes  from  God,  Mohammed  is  the  prophet  of  God,  we 
do  not  intend  to  affirm  either  that  the  Koran  does  come  from  God,  or  that 
Mohammed  is  really  his  prophet.  Neither  of  these  simple  propositions  may 
be  true,  and  yet  the  truth  of  the  hypothetical  proposition  may  be  indis- 
putable. What  is  asserted  is  not  the  truth  of  either  of  the  propositions, 
but  the  inferribility  of  the  one  from  the  other.  What,  then,  is  the  subject, 
and  what  the  predicate  of  the  hypothetical  proposition  ? “ The  Koran  ” 

is  not  the  subject  of  it,  nor  is  “ Mohammed for  nothing  is  affirmed  or  de- 
nied either  of  the  Koran  or  of  Mohammed.  The  real  subject  of  the  pred- 
ication is  the  entire  proposition,  “Mohammed  is  the  prophet  of  God;”  and 
the  affirmation  is,  that  this  is  a legitimate  inference  from  the  proposi- 
tion, “ The  Koran  comes  from  God.”  The  subject  and  predicate,  therefore, 
of  a hypothetical  proposition  are  names  of  propositions.  The  subject  is 
some  one  proposition.  The  predicate  is  a general  relative  name  applicable 
to  propositions ; of  this  form — “ an  inference  from  so  and  so.”  A fresh 
instance  is  here  afforded  of  the  remark,  that  particles  are  abbreviations ; 
since  “If  A is  B,  C is  D,”  is  found  to  be  an  abbreviation  of  the  follow- 
ing : “ The  proposition  C is  D,  is  a legitimate  inference  from  the  proposi- 
tion A is  B.” 

The  distinction,  therefore,  between  hypothetical  and  categorical  proposi- 
tions is  not  so  great  as  it  at  first  appears.  In  the  conditional,  as  well  as  in 
the  categorical  form,  one  predicate  is  affirmed  of  one  subject,  and  no  more: 
but  a conditional  proposition  is  a proposition  concerning  a proposition ; 
the  subject  of  the  assertion  is  itself  an  assertion.  Nor  is  this  a property 
peculiar  to  hypothetical  propositions.  There  are  other  classes  of  assertions 
concerning  propositions.  Like  other  things,  a proposition  has  attributes 
which  may  be  predicated  of  it.  The  attribute  predicated  of  it  in  a hypo- 
thetical proposition,  is  that  of  being  an  inference  from  a certain  other  prop- 
osition. But  this  is  only  one  of  many  attributes  that  might  be  predicated. 
We  may  say,  That  the  whole  is  greater  than  its  part,  is  an  axiom  in  math- 
ematics: That  the  Holy  Ghost  proceeds  from  the  Father  alone,  is  a tenet 
of  the  Greek  Church:  The  doctrine  of  the  divine  right  of  kings  was  re- 
nounced by  Parliament  at  the  Revolution : The  infallibility  of  the  Pope 
has  no  countenance  from  Scripture.  In  all  these  cases  the  subject  of  the 
predication  is  an  entire  proposition.  That  which  these  different  predicates 
are  affirmed  of,  is  the  proposition,  “ the  whole  is  greater  than  its  part;”  the 
proposition,  “ the  Holy  Ghost  proceeds  from  the  Father  alone ;”  the  propo- 
sition, “ kings  have  a divine  right ;”  the  proposition,  “ the  Pope  is  infallible.” 

Seeing,  then,  that  there  is  much  less  difference  between  hypothetical 
propositions  and  auy  others,  than  one  might  be  led  to  imagine  from  their 


PROPOSITIONS. 


71 


form,  we  should  be  at  a loss  to  account  for  the  conspicuous  position  which 
they  have  been  selected  to  fill  in  treatises  on  logic,  if  we  did  not  remem- 
ber that  what  they  predicate  of  a proposition,  namely,  its  being  an  inference 
from  something  else,  is  precisely  that  one  of  its  attributes  with  which  most 
of  all  a logician  is  concerned. 

§ 4.  The  next  of  the  common  divisions  of  Propositions  is  into  Universal, 
Particular,  Indefinite,  and  Singular : a distinction  founded  on  the  degree 
of  generality  in  which  the  name,  which  is  the  subject  of  the  proposition, 
is  to  be  understood.  The  following  are  examples : 


The  proposition  is  Singular,  when  the  subject  is  an  individual  name. 
The  individual  name  needs  not  be  a proper  name.  “The  Founder  of 
Christianity  was  crucified,”  is  as  much  a singular  proposition  as  “ Christ 
was  crucified.” 

When  the  name  which  is  the  subject  of  the  proposition  is  a general 
name,  we  may  intend  to  affirm  or  deny  the  predicate,  either  of  all  the 
things  that  the  subject  denotes,  or  only  of  some.  When  the  predicate  is 
affirmed  or  denied  of  all  and  each  of  the  things  denoted  by  the  subject, 
the  proposition  is  universal;  when  of  some  undefined  portion  of  them  only, 
it  is  particular.  Thus,  All  men  are  mortal ; Every  man  is  mortal ; are  uni- 
versal propositions.  No  man  is  immortal,  is  also  a universal  proposition, 
since  the  predicate,  immortal,  is  denied  of  each  and  every  individual  de- 
noted by  the  term  man ; the  negative  proposition  being  exactly  equivalent 
to  the  following,  Every  man  is  not-im  mortal.  But  “some  men  are  wise,” 
“ some  men  are  not  wise,”  are  particular  propositions ; the  predicate  wise 
being  in  the  one  case  affirmed  and  in  the  other  denied  not  of  each  and  ev- 
ery individual  denoted  by  the  term  man,  but  only  of  each  and  every  one 
of  some  portion  of  those  individuals,  without  specifying  what  portion ; for 
if  this  were  specified,  the  proposition  would  be  changed  either  into  a singu- 
lar proposition,  or  into  a universal  proposition  with  a different  subject ; 
as,  for  instance,  “ all  -properly  instructed  men  are  wise.”  There  are  other 
forms  of  particular  propositions;  as,  u Most  men  are  imperfectly  educated:” 
it  being  immaterial  how  large  a portion  of  the  subject  the  predicate  is  as- 
serted of,  as  long  as  it  is  left  uncertain  how  that  portion  is  to  be  distin- 
guished from  the  rest.* 

When  the  form  of  the  expression  does  not  clearly  show  whether  the 
general  name  which  is  the  subject  of  the  proposition  is  meant  to  stand  for 
all  the  individuals  denoted  by  it,  or  only  for  some  of  them,  the  proposition 
is,  by  some  logicians,  called  Indefinite ; but  this,  as  Archbishop  Whately  ob- 

* Instead  of  Universal  and  Particular  as  applied  to  propositions,  Professor  Bain  proposes 
(Logic,  i.,  81)  the  terms  Total  and  Partial;  reserving  the  former  pair  of  terms  for  their  in- 
ductive meaning,  “the  contrast  between  a general  proposition  and  the  particulars  or  individ- 
uals that  we  derive  it  from.”  This  change  in  nomenclature  would  be  attended  with  the  further 
advantage,  that  Singular  propositions,  which  in  the  Syllogism  follow  the  same  rules  as  Univer- 
sal, would  be  included  along  with  them  in  the  same  class,  that  of  Total  predications.  It  is  not 
the  Subject’s  denoting  many  things  or  only  one,  that  is  of  importance  in  reasoning,  it  is  that 
the  assertion  is  made  of  the  whole  or  a part  only  of  what  the  Subject  denotes.  The  words 
Universal  and  Particular,  however,  are  so  familiar  and  so  well  understood  in  both  the  senses 
mentioned  by  Mr.  Bain,  that  the  double  meaning  does  not  produce  any  material  inconvenience. 


All  men  are  mortal — 
Some  men  are  mortal — 
Man  is  mortal — - 
Julius  Caesar  is  mortal — 


Universal. 

Particular." 

Indefinite. 

Singular. 


NAMES  AND  PROPOSITIONS. 


serves,  is  a solecism,  of  the  same  nature  as  that  committed  by  some  gram- 
marians  w hen  in  their  list  of  genders  they  enumerate  the  doubtful  gender. 
The  speaker  must  mean  to  assert  the  proposition  either  as  a universal  or 
as  a particular  proposition,  though  he  lias  failed  to  declare  which : and  it 
often  happens  that  though  the  words  do  not  show  which  of  the  two  he  in- 
tends, the  context,  or  the  custom  of  speech,  supplies  the  deficiency.  Thus, 
when  it  is  affirmed  that  “ Man  is  mortal,”  nobody  doubts  that  the  asser- 
tion is  intended  of  all  human  beings  ; and  the  word  indicative  of  universal- 
ity is  commonly  omitted,  only  because  the  meaning  is  evident  without  it. 
In  the  proposition,  “ Wine  is  good,”  it  is  understood  with  equal  readiness, 
though  for  somewhat  different  reasons,  that  the  assertion  is  not  intended 
to  be  universal,  but  particular.*  As  is  observed  by  Professor  Bain,f  the 
chief  examples  of  Indefinite  propositions  occur  “ with  names  of  material, 
which  are  the  subjects  sometimes  of  universal,  and  at  other  times  of  partic- 
ular predication.  ‘Food  is  chemically  constituted  by  carbon,  oxygen,  etc.,’ 
is  a proposition  of  universal  quantity ; the  meaning  is  all  food — all  kinds 
of  food.  ‘Food  is  necessary  to  animal  life’  is  a case  of  particular  quan- 
tity; the  meaning  is  some  sort  of  food,  not  necessarily  all  sorts.  ‘Metal 
is  requisite  in  order  to  strength  ’ does  not  mean  all  kinds  of  metal.  ‘ Gold 
will  make  a way,’  means  a portion  of  gold.” 

When  a general  name  stands  for  each  and  every  individual  which  it  is  a 
name  of,  or  in  other  words,  which  it  denotes,  it  is  said  by  logicians  to  be 
distributed , or  taken  distributively.  Thus,  in  the  proposition,  All  men  are 
mortal,  the  subject,  Man,  is  distributed,  because  mortality  is  affirmed  of 
each  and  every  man.  The  predicate,  Mortal,  is  not  distributed,  because 
the  only  mortals  who  are  spoken  of  in  the  proposition  are  those  who  hap- 
pen to  be  men;  while  the  word  may,  for  aught  that  appears,  and  in  fact 
does,  comprehend  within  it  an  indefinite  number  of  objects  besides  men. 
In  the  proposition,  Some  men  are  mortal,  both  the  predicate  and  the  sub- 
ject are  undistributed.  In  the  following,  No  men  have  wings,  both  the 
predicate  and  the  subject  are  distributed.  Not  only  is  the  attribute  of 
having  wings  denied  of  the  entire  class  Man,  but  that  class  is  severed  and 
cast  out  from  the  whole  of  the  class  Winged,  and  not  merely  from  some 
part  of  that  class. 

This  phraseology,  which  is  of  great  service  in  stating  and  demonstrating 
the  rules  of  the  syllogism,  enables  us  to  express  very  concisely  the  defini- 
tions of  a universal  and  a particular  proposition.  A universal  proposition 
is  that  of  which  the  subject  is  distributed;  a particular  proposition  is  that 
of  which  the  subject  is  undistributed. 

There  are  many  more  distinctions  among  propositions  than  those  we 
have  here  stated,  some  of  them  of  considerable  importance.  But,  for  ex- 
plaining and  illustrating  these,  more  suitable  opportunities  will  occur  in  the 
sequel. 

* It.  may,  however,  be  considered  as  equivalent  to  a universal  proposition  with  a different 
predicate,  viz.  : “All  wine  is  good  qua  wine,”  or  “is  good  in  respect  of  the  qualities  which 
constitute  it  wine.” 

t Logic,  i.,  82. 


IMPORT  OF  PROPOSITIONS. 


73 


CHAPTER  Y. 

OP  THE  IMPORT  OP  PROPOSITIONS. 

§ 1.  An  inquiry  into  the  nature  of  propositions  must  have  one  of  two 
objects:  to  analyze  the  state  of  mind  called  Belief,  or  to  analyze  what  is 
believed.  All  language  recognizes  a difference  between  a doctrine  or  opin- 
ion, and  the  fact  of  entertaining  the  opinion ; between  assent,  and  what  is 
assented  to. 

Logic,  according  to  the  conception  here  formed  of  it,  has  no  concern 
with  the  nature  of  the  act  of  judging  or  believing;  the  consideration  of 
that  act,  as  a phenomenon  of  the  mind,  belongs  to  another  science.  Phi- 
losophers, however,  from  Descartes  downward,  and  especially  from  the  era 
of  Leibnitz  and  Locke,  have  by  no  means  observed  this  distinction  ; and 
would  have  treated  with  great  disrespect  any  attempt  to  analyze  the  im- 
port of  Propositions,  unless  founded  on  an  analysis  of  the  act  of  Judgment. 
A proposition,  they  would  have  said,  is  but  the  expression  in  words  of  a 
Judgment.  The  thing  expressed,  not  the  mere  verbal  expression,  is  the 
important  matter.  When  the  mind  assents  to  a proposition,  it  judges. 
Let  us  find  out  what  the  mind  does  when  it  judges,  and  we  shall  know 
what  propositions  mean,  and  not  otherwise. 

Conformably  to  these  views,  almost  all  the  writers  on  Logic  in  the  last 
two  centuries,  whether  English,  German,  or  French,  have  made  their  the- 
ory of  Propositions,  from  one  end  to  the  other,  a theory  of  Judgments. 
They  considered  a Proposition,  or  a Judgment,  for  they  used  the  two 
words  indiscriminately,  to  consist  in  affirming  or  denying  one  idea  of  an- 
other. To  judge,  was  to  put  two  ideas  together,  or  to  bring  one  idea  un- 
der another,  or  to  compare  two  ideas,  or  to  perceive  the  agreement  or  disa- 
greement between  two  ideas : and  the  whole  doctrine  of  Propositions,  to- 
gether with  the  theory  of  Reasoning  (always  necessarily  founded  on  the 
theory  of  Propositions),  was  stated  as  if  Ideas,  or  Coriceptions,  or  whatever 
other  term  the  writer  preferred  as  a name  for  mental  representations  gen- 
erally, constituted  essentially  the  subject-matter  and  substance  of  those  op- 
erations. 

It  is,  of  course,  true,  that  in  any  case  of  judgment,  as  for  instance  when 
we  judge  that  gold  is  yellow,  a process  takes  place  in  our  minds,  of  which 
some  one  or  other  of  these  theories  is  a partially  correct  account.  "We 
must  have  the  idea  of  gold  and  the  idea  of  yellow,  and  these  two  ideas 
must  be  brought  together  in  our  mind.  But  in  the  first  place,  it  is  evident 
that  this  is  only  a part  of  what  takes  place ; for  we  may  put  two  ideas  to- 
gether without  any  act  of  belief;  as  when  we  merely  imagine  something, 
such  as  a golden  mountain ; or  when  we  actually  disbelieve  : for  in  order 
even  to  disbelieve  that  Mohammed  was  an  apostle  of  God,  we  must  put  the 
idea  of  Mohammed  and  that  of  an  apostle  of  God  together.  To  determine 
what  it  is  that  happens  in  the  case  of  assent  or  dissent  besides  putting  two 
ideas  together,  is  one  of  the  most  intricate  of  metaphysical  problems.  But 
whatever  the  solution  may  be,  we  may  venture  to  assert  that  it  can  have 
nothing  whatever  to  do  with  the  import  of  propositions;  for  this  reason, 


74 


NAMES  AND  PROPOSITIONS. 


that  propositions  (except  sometimes  when  the  mind  itself  is  the  subject 
treated  of)  are  not  assertions  respecting  our  ideas  of  things,  but  assertions 
respecting  the  things  themselves.  In  order  to  believe  that  gold  is  yellow, 
I must,  indeed,  have  the  idea  of  gold,  and  the  idea  of  yellow,  and  some- 
thing; having  reference  to  those  ideas  must  take  place  in  my  mind;  but 
mv  belief  has  not  reference  to  the  ideas,  it  has  reference  to  the  things. 
W1  lat  I believe,  is  a fact  relating  to  the  outward  thing,  gold,  and  to  the 
impression  made  by  that  outward  thing  upon  the  human  organs;  not  a 
fact  relating  to  my  conception  of  gold,  which  would  be  a fact  in  my  mental 
history,  not  a fact  of  external  nature.  It  is  true,  that  in  order  to  believe 
this  fact  in  external  nature,  another  fact  must  take  place  in  my  mind,  a 
process  must  be  performed  upon  my  ideas  ; but  so  it  must  in  every  thing 
else  that  I do.  I can  not  dig  the  ground  unless  I have  the  idea  of  the 
ground,  and  of  a spade,  and  of  all  the  other  things  I am  operating  upon, 
and  unless  I put  those  ideas  together.*  But  it  would  be  a very  ridiculous 
description  of  digging  the  ground  to  say  that  it  is  putting  one  idea  into  an- 
other. Digging  is  an  operation  which  is  performed  upon  the  things  them- 
selves, though  it  can  not  be  performed  unless  I have  in  my  mind  the  ideas 
of  them.  And  in  like  manner,  believing  is  an  act  which  has  for  its  subject 
the  facts  themselves,  though  a previous  mental  conception  of  the  facts  is 
an  indispensable  condition.  When  I say  that  fire  causes  heat,  do  I mean 
that  my  idea  of  fire  causes  my  idea  of  heat?  No : I mean  that  the  natural 
phenomenon,  fire,  causes  the  natural  phenomenon,  heat.  When  I mean  to 
assert  any  thing  respecting  the  ideas,  I give  them  their  proper  name,  I 
call  them  ideas : as  when  I say,  that  a child’s  idea  of  a battle  is  unlike  the 
reality,  or  that  the  ideas  entertained  of  the  Deity  have  a great  effect  on  the 
characters  of  mankind. 

The  notion  that  what  is  of  primary  importance  to  the  logician  in  a prop- 
osition, is  the  relation  between  the  two  ideas  corresponding  to  the  subject 
and  predicate  (instead  of  the  relation  between  the  two  phenomena  which 
they  respectively  express),  seems  to  me  one  of  the  most  fatal  errors  ever 
introduced  into  the  philosophy  of  Logic;  and  the  principal  cause  why  the 
theory  of  the  science  has  made  such  inconsiderable  progress  during  the  last 
two  centuries.  The  treatises  on  Logic,  and  on  the  branches  of  Mental  Phi- 
losophy connected  with  Logic,  which  have  been  produced  since  the  intru- 
sion of  this  cardinal*  error,  though  sometimes  written  by  men  of  extraor- 
dinary abilities  and  attainments,  almost  always  tacitly  imply  a theory  that 
the  investigation  of  truth  consists  in  contemplating  and  handling  our  ideas, 
or  conceptions  of  things,  instead  of  the  things  themselves:  a doctrine  tan- 
tamount to  the  assertion,  that  the  only  mode  of  acquiring  knowledge  of 
nature  is  to  study  it  at  second  hand,  as  represented  in  our  own  minds. 
Meanwhile,  inquiries  into  every  kind  of  natural  phenomena  were  incessant- 
ly establishing  great  and  fruitful  truths  on  most  important  subjects,  by 
processes  upon  which  these  views  of  the  nature  of  Judgment  and  Reason- 
ing threw  no  light,  and  in  which  they  afforded  no  assistance  whatever.  No 
wonder  that  those  who  knew  by  practical  experience  how  truths  are  ar- 
rived at,  should  deem  a science  futile,  which  consisted  chiefly  of  such  spec- 

* Dr.  Whewell  ( Philosophy  of  Discovery,  p.  242)  questions  this  statement,  and  asks,  “Are 
we  to  say  that  a mole  can  not  dig  the  ground,  except  he  has  an  idea  of  the  ground,  and  of 
the  snout  and  paws  with  which  he  digs  it?”  I do  not  know  what  passes  in  a mole’s  mind, 
nor  what  amount  of  mental  apprehension  may  or  may  not  accompany  his  instinctive  actions. 
But  a human  being  does  not  use  a spade  by  instinct ; and  he  certainly  could  not  use  it  unless 
lie  had  knowledge  of  a spade,  and  of  the  earth  which  he  uses  it  upon. 


IMPORT  OF  PROPOSITIONS. 


75 


ulations.  What  has  been  done  for  the  advancement  of  Logic  since  these 
doctrines  came  into  vogue,  has  been  done  not  by  professed  logicians,  but 
by  discoverers  in  the  other  sciences ; in  whose  methods  of  investigation 
many  principles  of  logic,  not  previously  thought  of,  have  successively  come 
forth  into  light,  but  who  have  generally  committed  the  error  of  supposing 
that  nothing  whatever  was  known  of  the  art  of  philosophizing  by  the  old 
logicians,  because  their  modern  interpreters  have  written  to  so  little  pur- 
pose respecting  it. 

We  have  to  inquire,  then,  on  the  present  occasion,  not  into  Judgment, 
but  judgments;  not  into  the  act  of  believing,  but  into  the  thing  believed. 
What  is  the  immediate  object  of  belief  in  a Proposition?  What  is  the 
matter  of  fact  signified  by  it?  What  is  it  to  which,  when  I assert  the 
proposition,  I give  my  assent,  and  call  upon  others  to  give  theirs?  AVhat  is 
that  which  is  expressed  by  the  form  of  discourse  called  a Proposition,  and 
the  conformity  of  which  to  fact  constitutes  the  truth  of  the  proposition  ? 

§ 2.  One  of  the  clearest  and  most  consecutive  thinkers  whom  this  coun- 
try or  the  world  has  produced,  I mean  Hobbes,  has  given  the  following  an- 
swer to  this  question.  In  every  proposition  (says  he)  what  is  signified  is, 
the  belief  of  the  speaker  that  the  predicate  is  a name  of  the  same  thing  of 
which  the  subject  is  a name;  and  if  it  really  is  so,  the  proposition  is  true. 
Thus  the  proposition,  All  men  are  living  beings  (he  would  say)  is  true, 
because  living  being  is  a name  of  every  thing  of  which  man  is  a name. 
All  men  are  six  feet  high,  is  not  true,  because  six  feet  high  is  not  a name 
of  every  thing  (though  it  is  of  some  things)  of  which  man  is  a name. 

What  is  stated  in  this  theory  as  the  definition  of  a true  proposition,  must 
be  allowed  to  be  a property  which  all  true  propositions  possess.  The  sub- 
ject and  predicate  being  both  of  them  names  of  things,  if  they  were  names 
of  quite  different  things  the  one  name  could  not,  consistently  with  its  sig- 
nification, be  predicated  of  the  other.  If  it  be  true  that  some  men  are  cop- 
per-colored, it  must  be  true — and  the  proposition  does  really  assert — that 
among  the  individuals  denoted  by  the  name  man,  there  are  some  who  are 
also  among  those  denoted  by  the  name  copper-colored.  If  it  be  true  that 
all  oxen  ruminate,  it  must  be  true  that  all  the  individuals  denoted  by  the 
name  ox  are  also  among  those  denoted  by  the  name  ruminating;  and  who- 
ever asserts  that  all  oxen  ruminate,  undoubtedly  does  assert  that  this  rela- 
tion subsists  between  the  two  names. 

The  assertion,  therefore,  which,  according  to  Hobbes,  is  the  only  one 
made  in  any  proposition,  really  is  made  in  every  proposition : and  his  anal- 
ysis has  consequently  one  of  the  requisites  for  being  the  true  one.  We 
may  go  a step  further;  it  is  the  only  analysis  that  is  rigorously  true  of  all 
propositions  without  exception.  What  he  gives  as  the  meaning  of  propo- 
sitions, is  part  of  the  meaning  of  all  propositions,  and  the  whole  meaning 
of  some.  This,  however,  only  shows  what  an  extremely  minute  fragment 
of  meaning  it  is  quite  possible  to  include  within  the  logical  formula  of  a 
proposition.  It  does  not  show  that  no  proposition  means  more.  To  war- 
rant us  in  putting  together  two  words  with  a copula  between  them,  it  is 
really  enough  that  the  thing  br  things  denoted  by  one  of  the  names  should 
be  capable,  without  violation  of  usage,  of  being  called  by  the  other  name  also. 
If,  then,  this  be  all  the  meaning  necessarily  implied  in  the  form  of  discourse 
called  a Proposition,  why  do  I object  to  it  as  the  scientific  definition  of  what 
a proposition  means?  Because,  though  the  mere  collocation  which  makes 
the  proposition  a proposition,  conveys  no  more  than  this  scanty  amount  of 


76 


NAMES  AND  PROPOSITIONS. 


meaning,  that  same  collocation  combined  with  other  circumstances,  that 
form  combined  with  other  matter , does  convey  more,  and  the  proposition 
in  those  other  circumstances  does  assert  more,  than  merely  that  relation 
between  the  two  names. 

The  only  propositions  of  which  Hobbes’s  principle  is  a sufficient  account, 
are  that  limited  and  unimportant  class  in  which  both  the  predicate  and 
the  subject  are  proper  names.  For,  as  has  already  been  remarked,  proper 
names  have  strictly  no  meaning;  they  are  mere  marks  for  individual  ob- 
jects: and  when  a proper  name  is  predicated  of  another  proper  name,  all 
the  signification  conveyed  is,  that  both  the  names  are  marks  for  the  same 
object.  But  this  is  precisely  what  Hobbes  produces  as  a theory  of  predi- 
cation in  general.  His  doctrine  is  a full  explanation  of  such  predications 
as  these : Hyde  was  Clarendon,  or,  Tally  is  Cicero.  It  exhausts  the  mean- 
ing of  those  propositions.  But  it  is  a sadly  inadequate  theory  of  any  oth- 
ers. That  it  should  ever  have  been  thought  of  as  such,  can  be  accounted 
for  only  by  the  fact,  that  Hobbes,  in  common  with  the  other  Nominalists, 
bestowed  little  or  no  attention  upon  the  connotation  of  words ; and  sought 
for  their  meaning  exclusively  in  what  they  denote:  as  if  all  names  had  been 
(what  none  but  proper  names  really  are)  marks  put  upon  individuals ; and 
as  if  there  were  no  difference  between  a proper  and  a general  name,  except 
that  the  first  denotes  only  one  individual,  and  the  last  a greater  number. 

It  has  been  seen,  however,  that  the  meaning  of  all  names,  except  proper 
names  and  that  portion  of  the  class  of  abstract  names  which  are  not  conno- 
tative,  resides  in  the  connotation.  When,  therefore,  we  are  analyzing  the 
meaning  of  any  proposition  in  which  the  predicate  and  the  subject,  or 
either  of  them,  are  connotative  names,  it  is  to  the  connotation  of  those 
terms  that  we  must  exclusively  look,  and  not  to  what  they  denote , or  in  the 
language  of  Hobbes  (language  so  far  correct)  are  names  of. 

In  asserting  that  the  truth  of  a proposition  depends  on  the  conformity  of 
import  between  its  terms,  as,  for  instance,  that  the  proposition,  Socrates  is 
wise,  is  a true  proposition,  because  Socrates  and  wise  are  names  applicable 
to,  or,  as  he  expresses  it,  names  of,  the  same  person;  it  is  very  remarkable 
that  so  powerful  a thinker  should  not  have  asked  himself  the  question,  But 
how  came  they  to  be  names  of  the  same  person  ? Surely  not  because  such 
was  the  intention  of  those  who  invented  the  words.  When  mankind  fixed 
the  meaning  of  the  word  wise,  they  were  not  thinking  of  Socrates,  nor, 
when  his  parents  gave  him  the  name  of  Socrates,  were  they  thinking  of 
wisdom.  The  names  happen  to  fit  the  same  person  because  of  a certain 
fact , which  fact  was  not  known,  nor  in  being,  when  the  names  were  in- 
vented. If  we  want  to  know  what  the  fact  is,  we  shall  find  the  clue  to  it 
in  the  connotation  of  the  names. 

A bird  or  a stone,  a man,  or  a wise  man,  means  simply,  an  object  having 
such  and  such  attributes.  The  real  meaning  of  the  word  man,  is  those  at- 
tributes, and  not  Smith,  Brown,  and  the  remainder  of  the  individuals.  The 
word  mortal , in  like  manner  connotes  a certain  attribute  or  attributes ; and 
when  we  say,  All  men  are  mortal,  the  meaning  of  the  proposition  is,  that  all 
beings  which  possess  the  one  set  of  attributes,  possess  also  the  other.  If, 
in  our  experience,  the  attributes  connoted  by  man  are  always  accompanied 
by  the  attribute  connoted  by  mortal , it  will  follow  as  a consequence,  that 
the  class  man  will  be  wholly  included  in  the  class  mortal,  and  that  mortal 
will  be  a name  of  all  things  of  which  man  is  a name : but  why  ? Those 
objects  are  brought  under  the  name,  by  possessing  the  attributes  connoted 
by  it : but  their  possession  of  the  attributes  is  the  real  condition  on  which 


IMPORT  OF  PROPOSITIONS. 


77 

the  truth  of  the  proposition  depends ; not  their  being  called  by  the  name. 
Connotative  names  do  not  precede,  but  follow,  the  attributes  which  they 
connote.  If  one  attribute  happens  to  be  always  found  in  conjunction  with 
another  attribute,  the  concrete  names  which  answer  to  those  attributes  will 
of  course  be  predicable  of  the  same  subjects,  and  may  be  said,  in  Hobbes’s 
language  (in  the  propriety  of  which  on  this  occasion  I fully  concur),  to  be 
two  names  for  the  same  things.  But  the  possibility  of  a concurrent  appli- 
cation of  the  two  names,  is  a mere  consequence  of  the  conjunction  between 
the  two  attributes,  and  was,  in  most  cases,  never  thought  of  when  the 
names  were  introduced  and  their  signification  fixed.  That  the  diamond  is 
combustible,  was  a proposition  certainly  not  dreamed  of  when  the  words 
Diamond  and  Combustible  first  received  their  meaning;  and  could  not 
have  been  discovered  by  the  most  ingenious  and  refined  analysis  of  the  sig- 
nification of  those  words.  It  was  found  out  by  a very  different  process, 
namely,  by  exerting  the  senses,  and  learning  from  them,  that  the  attribute 
of  combustibility  existed  in  the  diamonds  upon  which  the  experiment  was 
tried ; the  number  or  character  of  the  experiments  being  such,  that  what 
was  true  of  those  individuals  might  be  concluded  to  be  true  of  all  sub- 
stances “ called  by  the  name,”  that  is,  of  all  substances  possessing  the  at- 
tributes which  the  name  connotes.  The  assertion,  therefore,  when  ana- 
lyzed, is,  that  wherever  we  find  certain  attributes,  there  will  be  found  a cer- 
tain other  attribute:  which  is  not  a question  of  the  signification  of  names, 
but  of  laws  of  nature ; the  order  existing  among  phenomena. 

§ 3.  Although  Hobbes’s  theory  of  Predication  has  not,  in  the  terms  in 
which  he  stated  it,  met  with  a very  favorable  reception  from  subsequent 
thinkers,  a theory  virtually  identical  with  it,  and  not  by  any  means  so  per- 
spicuously expressed,  may  almost  be  said  to  have  taken  the  rank  of  an  es- 
tablished opinion.  The  most  generally  received  notion  of  Predication  de- 
cidedly is  that  it  consists  in  referring  something  to  a class,  i.  e.,  either  pla- 
cing an  individual  under  a class,  or  placing  one  class  under  another  class. 
Thus,  the  proposition,  Man  is  mortal,  asserts,  according  to  this  view  of  it, 
that  the  class  man  is  included  in  the  class  mortal  “ Plato  is  a philoso- 
pher,” asserts  that  the  individual  Plato  is  one  of  those  wrho  compose  the 
class  philosopher.  If  the  proposition  is  negative,  then  instead  of  placing 
something  in  a class,  it  is  said  to  exclude  something  from  a class.  Thus, 
if  the  following  be  the  proposition,  The  elephant  is  not  carnivorous ; what 
is  asserted  (according  to  this  theory)  is,  that  the  elephant  is  excluded  from 
the  class  carnivorous,  or  is  not  numbered  among  the  things  comprising  that, 
class.  There  is  no  real  difference,  except  in  language,  between  this  theory 
of  Predication  and  the  theory  of  Hobbes.  For  a class  is  absolutely  noth- 
ing but  an  indefinite  number  of  individuals  denoted  by  a general  name. 
The  name  given  to  them  in  common,  is  what  makes  them  a class.  To  re- 
fer any  thing  to  a class,  therefore,  is  to  look  upon  it  as  one  of  the  things 
which  are  to  be  called  by  that  common  name.  To  exclude  it  from  a class, 
is  to  say  that  the  common  name  is  not  applicable  to  it. 

How  widely  these  views  of  predication  have  prevailed,  is  evident  from 
this,  that  they  are  the  basis  of  the  celebrated  dictum  de  omni  et  nullo. 
When  the  syllogism  is  resolved,  by  all  who  treat  of  it,  into  an  inference 
that  what  is  true  of  a class  is  true  of  all  things  whatever  that  belong  to  the 
class;  and  when  this  is  laid  down  by  almost  all  professed  logicians  as  the 
ultimate  principle  to  which  all  reasoning  owes  its  validity ; it  is  clear  that 
in  the  general  estimation  of  logicians,  the  propositions  of  which  reasonings 


NAMES  AND  PROPOSITIONS. 


78 

are  composed  can  be  the  expression  of  nothing  but  the  process  of  dividing 
things  into  classes,  and  referring  every  thing  to  its  proper  class. 

This  theory  appears  to  me  a signal  example  of  a logical  error  very  often 
committed  in  logic,  that  of  varepoi'  it porepoi',  or  explaining  a thing  by  some- 
thing which  presupposes  it.  When  I say  that  snow  is  white,  I may  and 
ought  to  be  thinking  of  snow  as  a class,  because  I am  asserting  a proposi- 
tion as  true  of  all  snow:  but  I am  certainly  not  thinking  of  white  objects 
as  a class ; I am  thinking  of  no  white  object  whatever  except  snow,  but 
only  of  that,  and  of  the  sensation  of  white  which  it  gives  me.  When,  in- 
deed, I have  judged,  or  assented  to  the  propositions,  that  snow  is  white, 
and  that  several  other  things  are  also  white,  I gradually  begin  to  think  of 
white  objects  as  a class,  including  snow  and  those  other  things.  But  this 
is  a conception  which  followed,  not  preceded,  those  judgments,  and  there- 
fore can  not  be  given  as  an  explanation  of  them.  Instead  of  explaining  the 
effect  by  the  cause,  this  doctrine  explains  the  cause  by  the  effect,  and  is,  I 
conceive,  founded  on  a latent  misconception  of  the  nature  of  classification. 

There  is  a sort  of  language  very  generally  prevalent  in  these  discussions, 
which  seems  to  suppose  that  classification  is  an  arrangement  and  grouping 
of  definite  and  known  individuals:  that  when  names  were  imposed,  man- 
kind took  into  consideration  all  the  individual  objects  in  the  universe,  dis- 
tributed them  into  parcels  or  lists,  and  gave  to  the  objects  of  each  list  a 
common  name,  repeating  this  operation  toties  quoties  until  they  had  invent- 
ed all  the  general  names  of  which  language  consists;  which  having  been 
once  done,  if  a question  subsequently  arises  whether  a certain  general 
name  can  be  truly  predicated  of  a certain  particular  object,  we  have  only 
(as  it  were)  to  read  the  roll  of  the  objects  upon  which  that  name  was  con- 
ferred, and  see  whether  the  object  about  which  the  question  arises  is  to  be 
found  among  them.  The  framers  of  language  (it  would  seem  to  be  sup- 
posed) have  predetermined  all  the  objects  that  are  to  compose  each  class, 
and  we  have  only  to  refer  to  the  record  of  an  antecedent  decision. 

So  absurd  a doctrine  will  be  owned  by  nobody  when  thus  nakedly  stated; 
but  if  the  commonly  received  explanations  of  classification  and  naming  do 
not  imply  this  theory,  it  requires  to  be  shown  how  they  admit  of  being  rec- 
onciled with  any  other. 

General  names  are  not  marks  put  upon  definite  objects;  classes  are  not 
made  by  drawing  a line  round  a given  number  of  assignable  individuals. 
The  objects  which  compose  any  given  class  are  perpetually  fluctuating. 
We  may  frame  a class  without  knowing  the  individuals,  or  even  any  of  the 
individuals,  of  which  it  may  be  composed;  we  may  do  so  while  believing 
that  no  such  individuals  exist.  If  by  the  meaning  of  a general  name  are 
to  be  understood  the  things  which  it  is  the  name  of,  no  general  name,  ex- 
cept by  accident,  has  a fixed  meaning  at  all,  or  ever  long  retains  the  same 
meaning.  The  only  mode  in  which  any  general  name  has  a definite  mean- 
ing, is  by  being  a name  of  an  indefinite  variety  of  things;  namely,  of  all 
things,  known  or  unknown,  past,  present,  or  future,  which  possess  certain 
definite  attributes.  When,  by  studying  not  the  meaning  of  words,  but  the 
phenomena  of  nature,  we  discover  that  these  attributes  are  possessed  by 
some  object  not  previously  known  to  possess  them  (as  when  chemists 
found  that  the  diamond  was  combustible),  we  include  this  new  object  in 
the  class;  but  it  did  not  already  belong  to  the  class.  We  place  the  indi- 
vidual in  the  class  because  the  proposition  is  true;  the  proposition  is  not 
true  because  the  object  is  placed  in  the  class.* 

* Professor  Bain  remarks,  in  qualification  of  the  statement  in  the  text  ( Logic , i.,  50),  that 


IMPORT  OF  PROPOSITIONS. 


19 


It  will  appear  hereafter,  in  treating  of  reasoning,  how  much  the  theory 
of  that  intellectual  process  has  been  vitiated  by  the  influence  of  these  erro- 
neous notions,  and  by  the  habit  which  they  exemplify  of  assimilating  all 
the  operations  of  the  human  understanding  which  have  truth  for  their  ob- 
ject, to  processes  of  mere  classification  and  naming.  Unfortunately,  the 
minds  which  have  been  entangled  in  this  net  are  precisely  those  which  have 
escaped  the  other  cardinal  error  commented  upon  in  the  beginning  of  the 
present  chapter.  Since  the  revolution  which  dislodged  Aristotle  from  the 
schools,  logicians  may  almost  be  divided  into  those  who  have  looked  upon 
reasoning  as  essentially  an  affair  of  Ideas,  and  those  who  have  looked  upon 
it  as  essentially  an  affair  of  Names. 

Although,  however,  Plobbes’s  theory  of  Predication,  according  to  the 
well-known  remark  of  Leibnitz,  and  the  avowal  of  Hobbes  himself,*  renders 
truth  and  falsity  completely  arbitrary,  with  no  standard  but  the  will  of 
men,  it  must  not  be  concluded  that  either  Hobbes,  or  any  of  the  other 
thinkers  who  have  in  the  main  agreed  with  him,  did  in  fact  consider  the 
distinction  between  truth  and  error  as  less  real,  or  attached  less  importance 
to  it,  than  other  people.  To  suppose  that  they  did  so  would  argue  total 
unacquaintance  with  their  other  speculations.  But  this  shows  how  little 
hold  their  doctrine  possessed  over  their  own  minds.  No  person,  at  bot- 
tom, ever  imagined  that  there  was  nothing  more  in  truth  than  propriety  of 
expression ; than  using  language  in  conformity  to  a previous  convention. 
When  the  inquiry  was  brought  down  from  generals  to  a particular  case,  it 
has  always  been  acknowledged  that  there  is  a distinction  between  verbal 
and  real  questions ; that  some  false  propositions  are  uttered  from  ignorance 
of  the  meaning  of  words,  but  that  in  others  the  source  of  the  error  is  a 
misapprehension  of  things ; that  a person  who  has  not  the  use  of  language 
at  all  may  form  propositions  mentally,  and  that  they  may  be  untrue — that 
is,  he  may  believe  as  matters  of  fact  what  are  not  really  so.  This  last  ad- 
mission can  not  be  made  in  stronger  terms  than  it  is  by  Hobbes  himself, j 
though  he  will  not  allow  such  erroneous  belief  to  be  called  falsity,  but  only 
error.  And  he  has  himself  laid  down,  in  other  places,  doctrines  in  which 
the  true  theory  of  predication  is  by  implication  contained.  He  distinctly 

the  word  Class  has  two  meanings;  “the  class  definite,  and  the  class  indefinite.  The  class 
definite  is  an  enumeration  of  actual  individuals,  as  the  Peers  of  the  Realm,  the  oceans  of  the 
globe,  the  known  planets.  . . . The  class  indefinite  is  unenumerated.  Such  classes  are 
stars,  planets,  gold-bearing  rocks,  men,  poets,  virtuous.  ...  In  this  last  acceptation  of  the 
word,  class  name  and  general  name  are  identical.  The  class  name  denotes  an  indefinite  num- 
ber of  individuals,  and  connotes  the  points  of  community  or  likeness.” 

The  theory  controverted  in  the  text,  tacitly  supposes  all  classes  to  be  definite.  I have  as- 
sumed them  to  be  indefinite ; because,  for  the  purposes  of  Logic,  definite  classes,  as  such,  are 
almost  useless  ; though  often  serviceable  as  means  of  abridged  expression.  (Vide  infra,  book 
iii. , chap,  ii.) 

* “From  hence  also  this  may  be  deduced,  that  the  first  truths  were  arbitrarily  made  by 
those  that  first  of  all  imposed  names  upon  things,  or  received  them  from  the  imposition  of  oth- 
ers. For  it  is  true  (for  example)  that  man  is  a living  creature , but  it  is  for  this  reason,  that  it 
pleased  men  to  impose  both  these  names  on  the  same  thing.” — Computation  or  Logic,  chap, 
iii.,  sect.  8. 

t “ Men  are  subject  to  err  not  only  in  affirming  and  denying,  but  also  in  perception,  and  in 
silent  cogitation.  . . . Tacit  errors,  or  the  errors  of  sense  and  cogitation,  are  made  bv  pass- 
ing from  one  imagination  to  the  imagination  of  another  different  thing ; or  by  feigning  that  to 
be  past,  or  future,  which  never  was,  nor  ever  shall  be ; as  when  by  seeing  the  image  of  the 
sun  in  water,  we  imagine  the  sun  itself  to  be  there  ; or  by  seeing  swords,  that  there  has  been, 
or  shall  be,  fighting,  because  it  uses  to  be  so  for  the  most  part ; or  when  from  promises  we 
feign  the  mind  of  the  promiser  to  be  such  and  such  ; or,  lastly,  when  from  any  sign  we  vainly 
imagine  something  to  be  signified  which  is  not.  And  errors  of  this  sort  are  common  to  all 
things  that  have  sense.” — Computation  or  Logic , chap,  v.,  sect.  1. 


so 


NAMES  AND  PROPOSITIONS. 


says  that  general  names  are  given  to  things  on  account  of  their  attributes, 
and  that  abstract  names  are  the  names  of  those  attributes.  “ Abstract  is 

that  which  in  any  subject  denotes  the  cause  of  the  concrete  name 

And  these  causes  of  names  are  the  same  with  the  causes  of  our  conceptions, 
namely,  some  power  of  action,  or  affection,  of  the  thing  conceived,  which 
some  call  the  manner  by  which  any  thing  works  upon  our  senses,  but  by 
most  men  they  are  called  accidents It  is  strange  that  having  gone  so 
far,  he  should  not  have  gone  one  step  further,  and  seen  that  what  he  calls 
the  cause  of  the  concrete  name,  is  in  reality  the  meaning  of  it;  and  that 
when  we  predicate  of  any  subject  a name  which  is  given  because  of  an  at- 
tribute (or,  as  he  calls  it,  an  accident),  our  object  is  not  to  affirm  the  name, 
but,  by  means  of  the  name,  to  affirm  the  attribute. 

§ 4.  Let  the  predicate  be,  as  we  have  said,  a connotative  term ; and  to 
take  the  simplest  case  first,  let  the  subject  be  a proper  name:  “The  sum- 
mit of  Chimborazo  is  white.”  The  word  white  connotes  an  attribute  which 
is  possessed  by  the  individual  object  designated  by  the  words  “summit  of 
Chimborazo which  attribute  consists  in  the  physical  fact,  of  its  exciting 
in  human  beings  the  sensation  which  we  call  a sensation  of  white.  It  will 
be  admitted  that,  by  asserting  the  proposition,  we  wish  to  communicate  in- 
formation of  that  physical  fact,  and  are  not  thinking  of  the  names,  except 
as  the  necessary  means  of  making  that  communication.  The  meaning  of 
the  proposition,  therefore,  is,  that  the  individual  thing  denoted  by  the  sub- 
ject, has  the  attributes  connoted  by  the  predicate. 

If  we  now  suppose  the  subject  also  to  be  a connotative  name,  the  mean- 
ing expressed  by  the  proposition  has  advanced  a step  further  in  complica- 
tion. Let  us  first  suppose  the  proposition  to  be  universal,  as  well  as  affirm- 
ative: “All  men  are  mortal.”  In  this  case,  as  in  the  last,  what  the  propo- 
sition asserts  (or  expresses  a belief  of)  is,  of  course,  that  the  objects  de- 
noted by  the  subject  (man)  possess  the  attributes  connoted  by  the  predi- 
cate (mortal).  But  the  characteristic  of  this  case  is,  that  the  objects  are 
no  longer  individually  designated.  They  are  pointed  out  only  by  some  of 
their  attributes:  they  are  the  objects  called  men,  that  is,  possessing  the  at- 
tributes connoted  by  the  name  man ; and  the  only  thing  known  of  them 
may  be  those  attributes:  indeed,  as  the  proposition  is  general,  and  the  ob- 
jects denoted  by  the  subject  are  therefore  indefinite  in  number,  most  of 
them  are  not  known  individually  at  all.  The  assertion,  therefore,  is  not,  as 
before,  that  the  attributes  which  the  predicate  connotes  are  possessed  by 
any  given  individual,  or  by  any  number  of  individuals  previously  known  as 
John,  Thomas,  etc.,  but  that  those  attributes  are  possessed  by  each  and  ev- 
ery individual  possessing  certain  other  attributes ; that  whatever  has  the 
attributes  connoted  by  the  subject,  has  also  those  connoted  by  the  predi- 
cate; that  the  latter  set  of  attributes  constantly  accompany  the  former  set. 
Whatever  has  the  attributes  of  man  has  the  attribute  of  mortality;  mortal- 
ity constantly  accompanies  the  attributes  of  man.f 

* Chap,  iii.,  sect.  3. 

t To  the  preceding  statement  it  has  been  objected,  that  “ we  naturally  construe  the  subject 
of  a proposition  in  its  extension,  and  the  predicate  (which  therefore  may  be  an  adjective)  in 
its  intension  (connotation) : and  that  consequently  co-existence  of  attributes  does  not,  any 
more  than  the  opposite  theory  of  equation  of  groups,  correspond  with  the  living  processes  of 
thought  and  language.”  I acknowledge  the  distinction  here  drawn,  which,  indeed,  I had  my- 
self laid  down  and  exemplified  a few  pages  back  (p.  77).  But  though  it  is  true  that  we  nat- 
urally “construe  the  subject  of  a proposition  in  its  extension,”  this  extension,  or  in  other 
words,  the  extent  of  the  class  denoted  by  the  name,  is  not  apprehended  or  indicated  directly. 


IMPORT  OF  PROPOSITIONS. 


81 


If  it  be  remembered  that  every  attribute  is  grounded  on  some  fact  of 
phenomenon,  either  of  outward  sense  or  of  inward  consciousness,  and  that 
to  possess  an  attribute  is  another  phrase  for  being  the  cause  of,  or  forming 
part  of.  the  fact  or  phenomenon  upon  which  the  attribute  is  grounded ; we 
may  add  one  more  step  to  complete  the  analysis.  The  proposition  which 
asserts  that  one  attribute  always  accompanies  another  attribute,  really  as- 
serts thereby  no  other  thing  than  this,  that  one  phenomenon  always  accom- 
panies another  phenomenon;  insomuch  that  -where  we  find  the  latter,  we 
have  assurance  of  the  existence  of  the  former.  Thus, 'in  the  proposition, 
All  men  are  mortal,  the  word  man  connotes  the  attributes  which  we  ascribe 
to  a certain  kind  of  living  creatures,  on  the  ground  of  certain  phenomena 
which  they  exhibit,  and  which  are  partly  physical  phenomena,  namely  the 
impressions  made  on  our  senses  by  their  bodily  form  and  structure,  and 
partly  mental  phenomena,  namely  the  sentient  and  intellectual  life  which 
they  have  of  their  own.  All  this  is  understood  when  we  utter  the  word 
man,  by  any  one  to  whom  the  meaning  of  the  word  is  known.  Now,  when 
we  say,  Man  is  mortal,  we  mean  that  wherever  these  various  physical  and 
mental  phenomena  are  all  found,  there  we  have  assurance  that  the  other 
physical  and  mental  phenomenon,  called  death,  will  not  fail  to  take  place. 
The  proposition  does  not  affirm  ichen ; for  the  connotation  of  the  word 
mortal  goes  no  further  than  to  the  occurrence  of  the  phenomenon  at  some 
time  or  other,  leaving  the  particular  time  undecided. 

§ 5.  We  have  already  proceeded  far  enough,  not  only  to  demonstrate  the 
error  of  Hobbes,  but  to  ascertain  the  real  import  of  by  far  the  most  numer- 
ous class  of  propositions.  The  object  of  belief  in  a proposition,  when  it 
asserts  any  thing  more  than  the  meaning  of  words,  is  generally,  as  in  the 
cases  which  we  have  examined,  either  the  co-existence  or  the  sequence  of 
two  phenomena.  At  the  very  commencement  of  our  inquiry,  we  found  that 
every  act  of  belief  implied  two  Things:  we  have  now  ascertained  what,  in 
the  most  frequent  case,  these  two  things  are,  namely,  two  Phenomena;  in 
other  words,  two  states  of  consciousness ; and  what  it  is  which  the  propo- 
sition affirms  (or  denies)  to  subsist  between  them,  namely,  either  succession 
or  co-existence.  And  this  case  includes  innumerable  instances  which  no 
one,  previous  to  reflection,  would  think  of  referring  to  it.  Take  the  follow- 
ing example:  A generous  person  is  worthy  of  honor.  Who  would  expect 
to  recognize  here  a case  of  co-existence  between  phenomena  ? But  so  it  is. 
The  attribute  which  causes  a person  to  be  termed  generous,  is  ascribed  to 
him  on  the  ground  of  states  of  his  mind,  and  particulars  of  his  conduct: 
both  are  phenomena : the  former  are  facts  of  internal  consciousness ; the 
latter,  so  far  as  distinct  from  the  former,  are  physical  facts,  or  perceptions 
of  the  senses.  Worthy  of  honor  admits  of  a similar  analysis.  Honor,  as 
here  used,  means  a state  of  approving  and  admiring  emotion,  followed  on 
occasion  by  corresponding  outward  acts.  “ Worthy  of  honor”  connotes  all 
this,  together  with  our  approval  of  the  act  of  showing  honor.  All  these 
are  phenomena ; states  of  internal  consciousness,  accompanied  or  followed 
by  physical  facts.  When  we  say,  A generous  person  is  worthy  of  honor, 

It  is  both  apprehended  and  indicated  solely  through  the  attributes.  In  the  “living  processes 
of  thought  and  language”  the  extension,  though  in  this  case  really  thought  of  (which  in  the 
case  of  the  predicate  it  is  not),  is  thought  of  only  through  the  medium  of  what  my  acute  and 
courteous  critic  terms  the  “intension.” 

For  further  illustrations  of  this  subject,  see  Examination  of  Sir  William  Hamilton’s  Phi- 
losophy, chap.  xxii. 


6 


82 


NAMES  AND  PROPOSITIONS. 


we  affirm  co-existence  between  the  two  complicated  phenomena  connoted 
by  the  two  terms  respectively.  We  affirm,  that  wherever  and  whenever 
the  inward  feelings  and  outward  facts  implied  in  the  word  generosity 
have  place,  then  and  there  the  existence  and  manifestation  of  an  inward 
feeling,  honor,  would  be  followed  in  our  minds  by  another  inward  feeling, 
approval. 

After  the  analysis,  in  a former  chapter,  of  the  import  of  names,  many 
examples  are  not  needed  to  illustrate  the  import  of  propositions.  When 
there  is  any  obscurity,  or  difficulty,  it  does  not  lie  in  the  meaning  of  the 
proposition,  but  in  the  meaning  of  the  names  which  compose  it;  in  the 
extremely  complicated  connotation  of  many  words;  the  immense  multitude 
and  prolonged  series  of  facts  which  often  constitute  the  phenomenon  con- 
noted by  a name.  But  where  it  is  seen  what  the  phenomenon  is,  there  is 
seldom  any  difficulty  in  seeing  that  the  assertion  conveyed  by  the  proposi- 
tion is,  the  co-existence  of  one  such  phenomenon  with  another ; or  the  suc- 
cession of  one  such  phenomenon  to  another:  so  that  where  the  one  is  found, 
we  may  calculate  on  finding  the  other,  though  perhaps  not  conversely. 

This,  however,  though  the  most  common,  is  not  the  only  meaning  which 
propositions  are  ever  intended  to  convey.  In  the  first  place,  sequences  and 
co-existences  are  not  only  asserted  respecting  Phenomena  ; we  make  propo- 
sitions also  respecting  those  hidden  causes  of  phenomena,  which  are  named 
substances  and  attributes.  A substance,  however,  being  to  us  nothing  but 
either  that  which  causes,  or  that  which  is  conscious  of,  phenomena;  and  the 
same  being  true,  mutatis  mutandis,  of  attributes;  no  assertion  can  be  made, 
at  least  with  a meaning,  concerning  these  unknown  and  unknowable  en- 
tities, except  in  virtue  of  the  Phenomena  by  which  alone  they  manifest 
themselves  to  our  faculties.  When  we  say  Socrates  was  contemporary  with 
the  Peloponnesian  war,  the  foundation  of  this  assertion,  as  of  all  assertions 
concerning  substances,  is  an  assertion  concerning  the  phenomena  which 
they  exhibit — namely,  that  the  series  of  facts  by  which  Socrates  manifested 
himself  to  mankind,  and  the  series  of  mental  states  which  constituted  his 
sentient  existence,  went  on  simultaneously  with  the  series  of  facts  known 
by  the  name  of  the  Peloponnesian  war.  Still,  the  proposition  as  commonly 
understood  does  not  assert  that  alone;  it  asserts  that  the  Thing  in  itself, 
the  noumenon  Socrates,  was  existing,  and  doing  or  experiencing  those  vari- 
ous facts  during  the  same  time.  Co-existence  and  sequence,  therefore,  may 
be  affirmed  or  denied  not  only  between  phenomena,  but  between  noumena, 
or  between  a noumenon  and  phenomena.  And  both  of  noumena  and  of 
phenomena  we  may  affirm  simple  existence.  But  what  is  a noumenon? 
An  unknown  cause.  In  affirming,  therefore,  the  existence  of  a noumenon, 
we  affirm  causation.  Here,  therefore,  are  two  additional  kinds  of  fact, 
capable  of  being  asserted  in  a proposition.  Besides  the  propositions  which 
assert  Sequence  or  Co-existence,  there  are  some  which  assert  simple  Exist- 
ence;* and  others  assert  Causation,  which,  subject  to  the  explanations 

* Professor  Bain,  in  his  Logic  (i.,  256),  excludes  Existence  from  the  list,  considering  it  as  a 
mere  name.  All  propositions,  he  says,  which  predicate  mere  existence  “are  more  or  less  ab- 
breviated, or  elliptical : when  fully  expressed  they  fall  under  either  co-existence  or  succession. 
When  we  say  there  exists  a conspiracy  for  a particular  purpose,  we  mean  that  at  the  present 
time  a body  of  men  have  formed  themselves  into  a society  for  a particular  object;  which  is  a 
complex  affirmation,  resolvable  into  propositions  of  co-existence  and  succession  (as  causation). 
The  assertion  that  the  dodo  does  not  exist,  points  to  the  fact  that  this  animal,  once  known  in 
a certain  place,  has  disappeared  or  become  extinct ; is  no  longer  associated  with  the  locality : 
all  which  may  be  better  stated  without  the  use  of  the  verb  ‘exist.’  There  is  a debated  ques- 
tion— Does  an  ether  exist?  but  the  concrete  form  would  be  this — ‘Are  heat  and  light  and 


IMPORT  OF  PROPOSITIONS. 


83 


which  will  follow  in  the  Third  Book,  must  be  considered  provisionally  as  a 
distinct  and  peculiar  kind  of  assertion. 

§ 6.  To  these  four  kinds  of  matter-of-fact  or  assertion,  must  be  added 
a fifth,  Resemblance.  This  was  a sjrecies  of  attribute  which  we  found  it 
impossible  to  analyze ; for  which  no  fundamentum,  distinct  from  the  ob- 
jects themselves,  could  be  assigned.  Besides  propositions  which  assert  a 
sequence  or  co-existence  between  two  phenomena,  there  are  therefore  also 
propositions  which  assert  resemblance  between  them ; as,  This  color  is  like 
that  color;  The  heat  of  to-day  is  equal  to  the  heat  of  yesterday.  It  is 
true  that  such  an  assertion  might  with  some  plausibility  be  brought  within 
the  description  of  an  affirmation  of  sequence,  by  considering  it  as  an  asser- 
tion that  the  simultaneous  contemplation  of  the  two  colors  is  followed  by 
a specific  feeling  termed  the  feeling  of  resemblance.  But  there  would  be 
nothing  gained  by  incumbering  ourselves,  especially  in  this  place,  rvith  a 
generalization  which  may  be  looked  upon  as  strained.  Logic  does  not  un- 
dertake to  analyze  mental  facts  into  their  ultimate  elements.  Resemblance 
between  two  phenomena  is  more  intelligible  in  itself  than  any  explanation 
could  make  it,  and  under  any  classification  must  remain  specifically  distinct 
from  the  ordinary  cases  of  sequence  and  co-existence. 

It  is  sometimes  said,  that  all  propositions  whatever,  of  which  the  pred- 
icate is  a general  name,  do,  in  point  of  fact,  affirm  or  deny  resemblance.  All 
snch  propositions  affirm  that  a thing  belongs  to  a class ; but  things  being 
classed  together  according  to  their  resemblance,  every  thing  is  of  course 
classed  with  the  things  which  it  is  supposed  to  resemble  most ; and  thence, 
it  may  be  said,  when  we  affirm  that  Gold  is  a metal,  or  that  Socrates  is  a 
man,  the  affirmation  intended  is,  that  gold  resembles  other  metals,  and  Soc- 

other  radiant  influences  propagated  bv  an  ethereal  medium  diffused  in  space which  is  a prop- 
osition of  causation.  In  like  manner  the  question  of  the  Existence  of  a Deity  can  not  be  dis- 
cussed in  that  form.  It  is  properly  a question  as  to  the  First  Cause  of  the  Universe,  and  as  to 
the  continued  exertion  of  that  Cause  in  providential  superintendence.”  (i. , 407.) 

Mr.  Bain  thinks  it  “fictitious  and  unmeaning  language”  to  carry  up  the  classification  of 
Nature  to  one  summum  genus,  Being,  or  that  which  Exists  ; since  nothing  can  he  perceived  or 
apprehended  but  by  way  of  contrast  with  something  else  (of  which  important  truth,  under  the 
name  of  Law  of  Relativity,  he  has  been  in  our  time  the  principal  expounder  and  champion), 
and  we  have  no  other  class  to  oppose  to  Being,  or  fact  to  contrast  with  Existence. 

I accept  fully  Mr.  Bain’s  Law  of  Relativity,  but  I do  not  understand  by  it  that  to  enable  us 
to  apprehend  or  be  conscious  of  any  fact,  it  is  necessary  that  we  should  contrast  it  with  some 
other  positive  fact.  The  antithesis  necessary  to  consciousness  need  not,  I conceive,  be  an  an- 
tithesis between  two  positives  ; it  may  be  between  one  positive  and  its  negative.  Hobbes  was 
undoubtedly  right  when  lie  said  that  a single  sensation  indefinitely  prolonged  would  cease  to  be 
felt  at  all ; but  simple  intermission,  without  other  change,  would  restore  it  to  consciousness. 
In  order  to  be  conscious  of  heat,  it  is  not  necessaiy  that  we  should  pass  to  it  from  cold ; it 
suffices  that  we  should  pass  to  it  from  a state  of  no  sensation,  or  from  a sensation  of  some  other 
kind.  The  relative  opposite  of  Being,  considered  as  a summum  genus,  is  Nonentity,  or 
Nothing ; and  we  have,  now  and  then,  occasion  to  consider  and  discuss  things  merely  in  con- 
trast with  Nonentity. 

I grant  that  the  decision  of  questions  of  Existence  usually  if  not  always  depends  on  a pre- 
vious question  of  either  Causation  or  Co-existence.  But  Existence  is  nevertheless  a different 
thing  from  Causation  or  Co-existence,  and  can  be  predicated  apart  from  them.  The  meaning 
of  the  abstract  name  Existence,  and  the  connotation  of  the  concrete  name  Being,  consist,  like 
the  meaning  of  all  other  names,  in  sensations  or  states  of  consciousness  : their  peculiarity  is 
that  to  exist,  is  to  excite,  or  be  capable  of  exciting,  any  sensations  or  states  of  consciousness : 
no  matter- what,  but  it  is  indispensable  that  there  should  be  some.  It  was  from  overlooking 
this  that  Hegel,  finding  that  Being  is  an  abstraction  reached  by  thinking  away  all  particular 
attributes,  arrived  at  the  self-contradictory  proposition  on  which  he  founded  all  his  philosophy, 
that  Being  is  the  same  as  Nothing.  It  is  really  the  name  of  Something,  taken  in  the  most 
comprehensive  sense  of  the  word. 


S4 


NAMES  AND  PROPOSITIONS. 


rates  other  men,  more  nearly  than  they  resemble  the  objects  contained  in 
any  other  of  the  classes  co-ordinate  with  these. 

There  is  some  slight  degree  of  foundation  for  this  remark,  but  no  more 
than  a slight  degree.  The  arrangement  of  things  into  classes,  such  as  the 
class  metal,  or  the  class  man,  is  grounded  indeed  on  a resemblance  among 
the  things  which  are  placed  in  the  same  class,  but  not  on  a mere  general 
resemblance : the  resemblance  it  is  grounded  on  consists  in  the  possession 
by  all  those  things,  of  certain  common  peculiarities;  and  those  peculiarities 
it  is  which  the  terms  connote,  and  which  the  propositions  consequently  as- 
sert; not  the  resemblance.  For  though  when  I say,  Gold  is  a metal,  I say 
by  implication  that  if  there  be  any  other  metals  it  must  resemble  them,  yet 
if  there  were  no  other  metals  I might  still  assert  the  proposition  with  the 
same  meaning  as  at  present,  namely,  that  gold  has  the  various  properties 
implied  in  the  word  metal;  just  as  it  might  be  said, Christians  are  men, 
even  if  there  were  no  men  who  were  not  Christians.  Propositions,  there- 
fore, in  which  objects  are  referred  to  a class  because  they  possess  the  attri- 
butes constituting  the  class,  are  so  far  from  asserting  nothing  but  resem- 
blance, that  they  do  not,  properly  speaking,  assert  resemblance  at  all. 

But  we  remarked  some  time  ago  (and  the  reasons  of  the  remark  will  be 
more  fully  entered  into  in  a subsequent  Book*)  that  there  is  sometimes  a 
convenience  in  extending  the  boundaries  of  a class  so  as  to  include  things 
which  possess  in  a very  inferior  degree,  if  in  any,  some  of  the  characteris- 
tic properties  of  the  class — provided  they  resemble  that  class  more  than 
any  other,  insomuch  that  the  general  propositions  which  are  true  of  the 
class,  will  be  nearer  to  being  true  of  those  things  than  any  other  equally 
general  propositions.  For  instance,  there  are  substances  called  metals 
which  have  very  few  of  the  properties  by  which  metals  are  commonly  rec- 
ognized ; and  almost  every  great  family  of  plants  or  animals  has  a few  anom- 
alous genera  or  species  on  its  borders,  which  are  admitted  into  it  by  a sort 
of  courtesy,  and  concerning  which  it  has  been  matter  of  discussion  to  what 
family  they  properly  belonged.  Now  when  the  class-name  is  predicated  of 
any  object  of  this  description,  we  do,  by  so  predicating  it,  affirm  resem- 
blance and  nothing  more.  And  in  order  to  be  scrupulously  correct  it  ought 
to  be  said,  that  in  every  case  in  which  we  predicate  a general  name,  we  af- 
firm, not  absolutely  that  the  object  possesses  the  properties  designated  by 
the  name,  but  that  it  either  possesses  those  properties,  or  if  it  does  not,  at 
any  rate  resembles  the  things  which  do  so,  more  than  it  resembles  any  oth- 
er things.  In  most  cases,  however,  it  is  unnecessary  to  suppose  any  such 
alternative,  the  latter  of  the  two  grounds  being  very  seldom  that  on  which 
the  assertion  is  made:  and  when  it  is,  there  is  generally  some  slight  differ- 
ence in  the  form  of  the  expression,  as,  This  species  (or  genus)  is  consider- 
ed, or  m,ay  he  ranked,  as  belonging  to  such  and  such  a family : we  should 
hardly  say  positively  that  it  does  belong  to  it,  unless  it  possessed  unequiv- 
ocally the  properties  of  which  the  class-name  is  scientifically  significant. 

There  is  still  another  exceptional  case,  in  which,  though  the  predicate  is 
the  name  of  a class,  yet  in  predicating  it  we  affirm  nothing  but  resemblance, 
the  class  being  founded  not  on  resemblance  in  any  given  particular,  but  on 
general  unanalyzable  resemblance.  The  classes  in  question  are  those  into 
which  our  simple  sensations,  or  other  simple  feelings,  are  divided.  Sensa- 
tions of  white,  for  instance,  are  classed  together,  not  because  we  can  take 
them  to  pieces,  and  say  they  are  alike  in  this,  and  not  alike  in  that,  but  be- 


* Book  iv.,  chap.  vii. 


IMPORT  OF  PROPOSITIONS. 


85 


cause  we  feel  them  to  be  alike  altogether,  though  in  different  degrees. 
When,  therefore,  I say,  The  color  I saw  yesterday  was  a white  color,  or, 
The  sensation  I feel  is  one  of  tightness,  in  both  cases  the  attribute  I affirm 
of  the  color  or  of  the  other  sensation  is  mere  resemblance — simple  likeness 
to  sensations  which  I have  had  before,  and  which  have  had  those  names  be- 
stowed upon  them.  The  names  of  feelings,  like  other  concrete  general 
names,  are  connotative;  but  they  connote  a mere  resemblance.  When 
predicated  of  any  individual  feeling,  the  information  they  convey  is  that  of 
its  likeness  to  the  other  feelings  which  we  have  been  accustomed  to  call  by 
the  same  name.  Thus  much  may  suffice  in  illustration  of  the  kind  of  prop- 
ositions in  which  the  matter-of-fact  asserted  (or  denied)  is  simple  Resem- 
blance. 

Existence,  Co-existence,  Sequence,  Causation,  Resemblance : one  or  other 
of  these  is  asserted  (or  denied)  in  every  proposition  which  is  not  merely 
verbal.  This  five-fold  division  is  an  exhaustive  classification  of  matters-of- 
fact;  of  all  things  that  can  be  believed,  or  tendered  for  belief;  of  all  ques- 
tions that  can  be  propounded,  and  all  answers  that  can  be  returned  to  them. 

Professor  Bain*  distinguishes  two  kinds  of  Propositions  of  Co-existence. 
“ In  the  one  kind,  account  is  taken  of  Place ; they  may  be  described,  as 
propositions  of  Order  in  Place.”  In  the  other  kind,  the  co-existence  which 
is  predicated  is  termed  by  Mr.  Bain  Co-inherence  of  Attributes.  “ This  is  a 
distinct  variety  of  Propositions  of  Co-existence.  Instead  of  an  arrangement 
in  place  with  numerical  intervals,  we  have  the  concurrence  of  two  or  more 
attributes  or  powers  in  the  same  part  or  locality.  A mass  of  gold  contains, 
in  every  atom,  the  concurring  attributes  that  mark  the  substance — weight, 
hardness,  color,  lustre,  incorrosibility,  etc.  An  animal,  besides  having  parts 
situated  in  place,  has  co-inhering  functions  in  the  same  parts,  exerted  by 
the  very  same  masses  and  molecules  of  its  substance.  . . . The  Mind, 
which  affords  no  Propositions  of  Order  in  Place,  has  co-inhering  fnnctions. 
Wo  affirm  mind  to  contain  Feeling,  Will,  and  Thought,  not  in  local  separa- 
tion, but  in  commingling  exercise.  The  concurring  properties  of  minerals, 
of  plants,  and  of  the  bodily  and  the  mental  structure  of  animals,  are  united 
in  affirmations  of  co-inherence.” 

The  distinction  is  real  and  important.  But,  as  has  been  seen,  an  Attri- 
bute, when  it  is  any  thing  but  a simple  unanalysable  Resemblance  between 
the  subject  and  some  other  things,  consists  in  causing  impressions  of  some 
sort  on  consciousness.  Consequently,  the  co-inherence  of  two  attributes 
is  but  the  co-existence  of  the  two  states  of  consciousness  implied  in  their 
meaning  : with  the  difference,  however,  that  this  co-existence  is  sometimes 
potential  only,  the  attribute  being  considered  as  in  existence,  though  the 
fact  on  which  it  is  grounded  may  not  be  actually,  but  only  potentially  pres- 
ent. Snow,  for  instance,  is,  with  great  convenience,  said  to  be  white  even 
in  a state  of  total  darkness,  because,  though  we  are  not  now  conscious  of 
the  color,  we  shall  be  conscious  of  it  as  soon  as  morning  breaks.  Co-in- 
herence of  attributes  is  therefore  still  a case,  though  a complex  one,  of 
co-existence  of  states  of  consciousness ; a totally  different  thing,  however, 
from  Order  in  Place.  Being  a part  of  simultaneity,  it  belongs  not  to  Place 
but  to  Time. 

We  may  therefore  (and  we  shall  sometimes  find  it  a convenience)  instead 
of  Co-existence  and  Sequence,  say,  for  greater  particularity,  Order  in  Place 
and  Order  in  Time : Order  in  Place  being  a specific  mode  of  co-existence, 


Logic,  i.,  103-105. 


86 


NAMES  AND  PROPOSITIONS. 


not  necessary  to  be  more  particularly  analyzed  here;  while  the  mere  fact  of 
co-existence,  whether  between  actual  sensations,  or  between  the  potentiali- 
ties of  causing  them,  known  by  the  name  of  attributes,  may  be  classed,  to- 
gether with  Sequence,  under  the  head  of  Order  in  Time. 

§ 7.  In  the  foregoing  inquiry  into  the  import  of  propositions,  we  have 
thought  it  necessary  to  analyze  directly  those  alone,  in  which  the  terms  of 
the  proposition  (or  the  predicate  at  least)  are  concrete  terms.  But,  in  do- 
ing so,  we  have  indirectly  analyzed  those  in  which  the  terms  are  abstract. 
The  distinction  between  an  abstract  term  and  its  corresponding  concrete, 
does  not  turn  upon  any  difference  in  what  they  are  appointed  to  signify; 
for  the  real  signification  of  a concrete  general  name  is,  as  we  have  so  often 
said,  its  connotation;  and  what  the  concrete  term  connotes,  forms  the  en- 
tire meaning  of  the  abstract  name.  Since  there  is  nothing  in  the  import 
of  an  abstract  name  which  is  not  in  the  import  of  the  corresponding  con- 
crete, it  is  natural  to  suppose  that  neither  can  there  be  any  thing  in  the  im- 
port of  a proposition  of  which  the  terms  are  abstract,  but  what  there  is  in 
some  proposition  which  can  be  framed  of  concrete  terms. 

And  this  presumption  a closer  examination  will  confirm.  An  abstract 
name  is  the  name  of  an  attribute,  or  combination  of  attributes.  The  cor- 
responding concrete  is  a name  given  to  things,  because  of,  and  in  order  to 
express,  their  possessing  that  attribute,  or  that  combination  of  attributes. 
When,  therefore,  we  predicate  of  any  thing  a concrete  name,  the  attribute 
is  what  we  in  reality  predicate  of  it.  But  it  has  now  been  shown  that  in 
all  propositions  of  which  the  predicate  is  a concrete  name,  what  is  really 
predicated  is  one  of  five  things : Existence,  Co-existence,  Causation,  Se- 
quence, or  Resemblance.  An  attribute,  therefore,  is  necessarily  either  an 
existence,  a co-existence,  a causation,  a sequence,  or  a resemblance.  When 
a proposition  consists  of  a subject  and  predicate  which  are  abstract  terms, 
it  consists  of  terms  which  must  necessarily  signify  one  or  other  of  these 
things.  When  we  predicate  of  any  thing  an  abstract  name,  we  affirm 
of  the  thing  that  it  is  one  or  other  of  these  five  things  ; that  it  is  a case  of 
Existence,  or  of  Co-existence,  or  of  Causation,  or  of  Sequence,  or  of  Re- 
semblance. 

It  is  impossible  to  imagine  any  proposition  expressed  in  abstract  terms, 
which  can  not  be  transformed  into  a precisely  equivalent  proposition  in 
which  the  terms  are  concrete ; namely,  either  the  concrete  names  which 
connote  the  attributes  themselves,  or  the  names  of  the  fundamenta  of  those 
attributes;  the  facts  or  phenomena  on  which  they  are  grounded.  To  il- 
lustrate the  latter  case,  let  us  take  this  proposition,  of  which  the  subject 
only  is  an  abstract  name,  “ Thoughtlessness  is  dangerous.”  Thoughtless- 
ness is  an  attribute,  grounded  on  the  facts  which  we  call  thoughtless  ac- 
tions; and  the  proposition  is  equivalent  to  this,  Thoughtless  actions  are 
dangerous.  In  the  next  example  the  predicate  as  well  as  the  subject  are 
abstract  names : “ Whiteness  is  a color  ;”  or  “ The  color  of  snow  is  a white- 
ness.” These  attributes  being  grounded  on  sensations,  the  equivalent  prop- 
ositions in  the  concrete  would  be,  The  sensation  of  white  is  one  of  the  sen- 
sations called  those  of  color — The  sensation  of  sight,  caused  by  looking  at 
snow,  is  one  of  the  sensations  called  sensations  of  white.  In  these  proposi- 
tions, as  we  have  before  seen,  the  matter-of-fact  asserted  is  a Resemblance. 
In  the  following  examples,  the  concrete  terms  are  those  which  directly  cor- 
respond to  the  abstract  names  ; connoting  the  attribute  which  these  de- 
note. “ Prudence  is  a virtue :”  this  may  be  rendered,  “ All  prudent  per- 


IMPORT  OE  PROPOSITIONS. 


87 


sons,  in  so  far  as  prudent,  are  virtuous “ Courage  is  deserving  of  hon- 
orthus, “All  courageous  persons  are  deserving  of  honor  in  so  far  as  they 
are  courageous:”  which  is  equivalent  to  this  — “All  courageous  persons 
deserve  an  addition  to  the  honor,  or  a diminution  of  the  disgrace,  which 
would  attach  to  them  on  other  grounds.” 

In  order  to  throw  still  further  light  upon  the  import  of  propositions  of 
which  the  terms  are  abstract,  we  will  subject  one  of  the  examples  given 
above  to  a minuter  analysis.  The  proposition  we  shall  select  is  the  follow- 
ing : “ Prudence  is  a virtue.”  Let  us  substitute  for  the  word  virtue  an 
equivalent  but  more  definite  expression,  such  as  “ a mental  quality  beneficial 
to  society,”  or  “ a mental  quality  pleasing  to  God,”  or  whatever  else  we 
adopt  as  the  definition  of  virtue.  What  the  proposition  asserts  is  a se- 
quence, accompanied  with  causation ; namely,  that  benefit  to  society,  or 
that  the  approval  of  God,  is  consequent  on,  and  caused  by,  prudence.  Here 
is  a sequence;  but  between  what?  We  understand  the  consequent  of  the 
sequence,  but  we  have  yet  to  analyze  the  antecedent.  Prudence  is  an  at- 
tribute; and,  in  connection  with  it,  two  things  besides  itself  are  to  be  con- 
sidered ; prudent  persons,  who  are  the  subjects  of  the  attribute,  and  pru- 
dential conduct,  which  may  be  called  the  foundation  of  it.  How  is  either 
of  these  the  antecedent?  and,  first,  is  it  meant,  that  the  approval  of  God, 
or  benefit  to  society,  is  attendant  upon  all  prudent  persons  ? Ho;  except 
in  so  far  as  they  are  prudent;  for  prudent  persons  who  are  scoundrels  can 
seldom,  on  the  whole,  be  beneficial  to  society,  nor  can  they  be  acceptable  to 
a good  being.  Is  it  upon  prudential  conduct , then,  that  divine  approbation 
and  benefit  to  mankind  are  supposed  to  be  invariably  consequent?  Heither 
is  this  the  assertion  meant,  when  it  is  said  that  prudence  is  a virtue ; ex- 
cept with  the  same  reservation  as  before,  and  for  the  same  reason,  namely, 
that  prudential  conduct,  although  in  so  far  as  it  is  prudential  it  is  benefi- 
cial to  society,  may  yet,  by  reason  of  some  other  of  its  qualities,  be  produc- 
tive of  an  injury  outweighing  the  benefit,  and  deserve  a displeasure  exceed- 
ing the  approbation  which  would  be  due  to  the  prudence.  Heither  the 
substance,  therefore  (viz.,  the  person),  nor  the  phenomenon  (the  conduct), 
is  an  antecedent  on  which  the  other  term  of  the  sequence  is  universally 
consequent.  But  the  proposition,  “ Prudence  is  a virtue,”  is  a universal 
proposition.  What  is  it,  then,  upon  which  the  proposition  affirms  the  ef- 
fects in  question  to  be  universally  consequent?  Upon  that  in  the  person, 
and  in  the  conduct,  which  causes  them  to  be  called  prudent,  and  which  is 
equally  in  them  when  the  action,  though  prudent,  is  wicked ; namely,  a cor- 
rect foresight  of  consequences,  a just  estimation  of  their  importance  to  the 
object  in  view,  and  repression  of  any  unreflecting  impulse  at  variance  with 
the  deliberate  purpose.  These,  which  are  states  of  the  person’s  mind,  are 
the  real  antecedent  in  the  sequence,  the  real  cause  in  the  causation,  asserted 
by  the  proposition.  But  these  are  also  the  real  ground,  or  foundation,  of 
the  attribute  Prudence ; since  wherever  these  states  of  mind  exist  we  may 
predicate  prudence,  even  before  we  know  whether  any  conduct  has  fol- 
lowed. And  in  this  manner  every  assertion  respecting  an  attribute,  may 
be  transformed  into  an  assertion  exactly  equivalent  respecting  the  fact  or 
phenomenon  which  is  the  ground  of  the  attribute.  And  no  case  can  be 
assigned,  where  that  which  is  predicated  of  the  fact  or  phenomenon,  does 
not  belong  to  one  or  other  of  the  five  species  formerly  enumerated:  it  is 
either  simple  Existence,  or  it  is  some  Sequence,  Co-existence,  Causation,  or 
Resemblance. 

And  as  these  five  are  the  only  things  which  can  be  affirmed,  so  are  they 


ss 


NAMES  AND  PROPOSITIONS. 


t lie  onlv  tilings  which  can  be  denied.  “No  horses  are  web-footed”  denies 
that  the  attributes  of  a horse  ever  co-exist  with  web-feet.  It  is  scarcely 
necessary  to  apply  the  same  analysis  to  Particular  affirmations  and  nega- 
tions. “Some  birds  are  web-footed,”  affirms  that,  with  the  attributes  con- 
noted bv  bird,  the  phenomenon  web-feet  is  sometimes  co-existent:  “Some 
birds  are  not  web-footed,”  asserts  that  there  are  other  instances  in  which 
this  co-existence  does  not  have  place.  Any  further  explanation  of  a thing 
which,  if  the  previous  exposition  has  been  assented  to,  is  so  obvious,  may 
here  be  spared. 


CHAPTER  VI. 

OF  PROPOSITIONS  51ERELY  VERBAL. 

§ 1.  As  a preparation  for  the  inquiry  which  is  the  proper  object  of 
Logic,  namely,  in  what  manner  propositions  are  to  be  proved,  we  have 
found  it  necessary  to  inquire  what  they  contain  which  requires,  or  is  sus- 
ceptible of,  proof ; or  (which  is  the  same  thing)  what  they  assert.  In  the 
course  of  this  preliminary  investigation  into  the  import  of  Propositions, 
we  examined  the  opinion  of  the  Conceptualists,  that  a proposition  is  the 
expression  of  a relation  between  two  ideas ; and  the  doctrine  of  the  ex- 
treme Nominalists,  that  it  is  the  expression  of  an  agreement  or  disagree- 
ment between  the  meanings  of  two  names.  We  decided  that,  as  general 
theories,  both  of  these  are  erroneous ; and  that,  though  propositions  may 
be  made  both  respecting  names  and  respecting  ideas,  neither  the  one  nor 
the  other  are  the  subject-matter  of  Propositions  considered  generally.  We 
then  examined  the  different  kinds  of  Propositions,  and  found  that,  with  the 
exception  of  those  which  are  merely  verbal,  they  assert  live  different  kinds 
of  matters  of  fact,  namely,  Existence,  Order  in  Place,  Order  in  Time,  Causa- 
tion, and  Resemblance ; that  in  every  proposition  one  of  these  five  is  either 
affirmed,  or  denied,  of  some  fact  or  phenomenon,  or  of  some  object  the  un- 
known source  of  a fact  or  phenomenon. 

In  distinguishing,  however,  the  different  kinds  of  matters  of  fact  asserted 
in  propositions,  we  reserved  one  class  of  propositions,  which  do  not  relate 
to  any  matter  of  fact,  in  the  proper  sense  of  the  term  at  all,  but  to  the 
meaning  of  names.  Since  names  and  their  signification  are  entirely  arbi- 
trary, such  propositions  are  not,  strictly  speaking,  susceptible  of  truth  or 
falsity,  but  only  of  conformity  or  disconformity  to  usage  or  convention; 
and  all  the  proof  they  are  capable  of,  is  proof  of  usage;  proof  that  the 
words  have  been  employed  by  others  in  the  acceptation  in  which  the  speak- 
er or  writer  desires  to  use  them.  These  propositions  occupy,  however,  a 
conspicuous  place  in  philosophy;  and  their  nature  and  characteristics  are 
of  as  much  importance  in  logic,  as  those  of  any  of  the  other  classes  of  prop- 
ositions previously  adverted  to. 

If  all  propositions  respecting  the  signification  of  words  were  as  simple 
and  unimportant  as  those  which  served  us  for  examples  when  examining 
Hobbes’s  theory  of  predication,  viz.,  those  of  which  the  subject  and  predi- 
cate are  proper  names,  and  which  assert  only  that  those  names  have,  or 
that  they  have  not,  been  conventionally  assigned  to  the  same  individual, 
there  would  be  little  to  attract  to  such  propositions  the  attention  of  phi- 
losophers. But  the  class  of  merely  verbal  propositions  embraces  not  only 
much  more  than  these,  but  much  more  than  any  propositions  which  at  first 


VERBAL  AND  REAL  PROPOSITIONS. 


89 


sight  present  themselves  as  verbal ; comprehending  a kind  of  assertions 
which  have  been  regarded  not  only  as  relating  to  things,  bnt  as  having 
actually  a more  intimate  relation  with  them  than  any  other  propositions 
whatever.  The  student  in  philosophy  will  perceive  that  I allude  to  the 
distinction  on  which  so  much  stress  was  laid  by  the  schoolmen,  and  which 
has  been  retained  either  under  the  same  or  under  other  names  by  most 
metaphysicians  to  the  present  day,  viz.,  between  what  were  called  essential , 
and  what  were  called  accidental , propositions,  and  between  essential  and 
accidental  properties  or  attributes. 

§ 2.  Almost  all  metaphysicians  prior  to  Locke,  as  well  as  many  since  his 
time,  have  made  a great  mystery  of  Essential  Predication,  and  of  predi- 
cates which  are  said  to  be  of  the  essence  of  the  subject.  The  essence  of  a 
tiling,  they  said,  was  that  without  which  the  thing  could  neither  be,  nor 
be  conceived  to  be.  Thus,  rationality  was  of  the  essence  of  man,  because 
without  rationality,  man  could  not  be  conceived  to  exist.  The  different 
attributes  which  made  up  the  essence  of  the  thing  were  called  its  essential 
properties ; and  a proposition  in  which  any  of  these  were  predicated  of  it 
was  called  an  Essential  Proposition,  and  was  considered  to  go  deeper  into 
the  nature  of  the  thing,  and  to  convey  more  important  information  respect- 
ing it,  than  any  other  proposition  could  do.  All  properties,  not  of  the  es- 
sence of  the  thing,  were  called  its  accidents;  were  supposed  to  have  noth- 
ing at  all,  or  nothing  comparatively,  to  do  with  its  inmost  nature ; and  the 
propositions  in  which  any  of  these  were  predicated  of  it  were  called  Acci- 
dental Propositions.  A connection  may  be  traced  between  this  distinction, 
which  originated  with  the  schoolmen,  and  the  well-known  dogmas  of  sub- 
stantiae secundce  or  general  substances,  and  substanticd  forms,  doctrines 
which  under  varieties  of  language  pervaded  alike  the  Aristotelian  and  the 
Platonic  schools,  and  of  which  more  of  the  spirit  has  come  down  to  mod- 
ern times  than  might  be  conjectured  from  the  disuse  of  the  phraseology. 
The  false  views  of  the  nature  of  classification  and  generalization  which  pre- 
vailed among  the  schoolmen,  and  of  which  these  dogmas  were  the  technical 
expression,  afford  the  only  explanation  which  can  be  given  of  their  having 
misunderstood  the  real  nature  of  those  Essences  which  held  so  conspicuous 
a place  in  their  philosophy.  They  said,  truly,  that  man  can  not  be  con- 
ceived without  rationality.  But  though  man  can  not,  a being  may  be  con- 
ceived exactly  like  a man  in  all  points  except  that  one  quality,  and  those 
others  which  are  the  conditions  or  consequences  of  it.  All,  therefore,  which 
is  really  true  in  the  assertion  that  man  can  not  be  conceived  without  ration- 
ality, is  only,  that  if  he  had  not  rationality,  he  would  not  be  reputed  a man. 
There  is  no  impossibility  in  conceiving  the  thing,  nor,  for  aught  we  know, 
in  its  existing : the  impossibility  is  in  the  conventions  of  language,  which 
will  not  allow  the  thing,  even  if  it  exist,  to  be  called  by  the  name  which  is 
reserved  for  rational  beings.  Rationality,  in  short,  is  involved  in  the  mean- 
ing of  the  word  man  : is  one  of  the  attributes  connoted  by  the  name.  The 
essence  of  man,  simply  means  the  whole  of  the  attributes  connoted  by  the 
word  ; and  any  one  of  those  attributes  taken  singly,  is  an  essential  property 
of  man. 

But  these  reflections,  so  easy  to  us,  would  have  been  difficult  to  persons 
who  thought,  as  most  of  the  later  Aristotelians  did,  that  objects  were  made 
what  they  were  called,  that  gold  (for  instance)  was  made  gold,  not  by  the 
possession  of  certain  properties  to  which  mankind  have  chosen  to  attach 
that  name,  but  by  participation  in  the  nature  of  a general  substance,  called 


90 


NAMES  AND  PROPOSITIONS. 


gold  in  general,  which  substance,  together  with  all  the  properties  that  be- 
longed to  it,  inhered  in  every  individual  piece  of  gold.*  As  they  did  not 
consider  these  universal  substances  to  be  attached  to  all  general  names,  but 
only  to  some,  they  thought  that  an  object  borrowed  only  a part  of  its  prop- 
erties from  a universal  substance,  and  that  the  rest  belonged  to  it  individu- 
ally  : the  former  they  called  its  essence,  and  the  latter  its  accidents.  The 
scholastic  doctrine  of  essences  long  survived  the  theory  on  which  it  rested, 
that  of  the  existence  of  real  entities  corresponding  to  general  terms;  and  it 
was  reserved  for  Locke,  at  the  end  of  the  seventeenth  century,  to  convince 
philosophers  that  the  supposed  essences  of  classes  were  merely  the  signifi- 
cation of  their  names;  nor,  among  the  signal  services  which  his  writings 
rendered  to  philosophy,  was  there  one  more  needful  or  more  valuable. 

Now,  as  the  most  familiar  of  the  general  names  by  which  an  object  is 
designated  usually  connotes  not  one  only,  but  several  attributes  of  the  ob- 
ject, each  of  which  attributes  separately  forms  also  the  bond  of  union  of 
some  class,  and  the  meaning  of  some  general  name;  we  may  predicate  of  a 
name  which  connotes  a variety  of  attributes,  another  name  which  connotes 
only  one  of  these  attributes,  or  some  smaller  number  of  them  than  all.  In 
such  cases,  the  universal  affirmative  proposition  will  be  true;  since  what- 
ever possesses  the  whole  of  any  set  of  attributes,  must  possess  any  part  of 
that  same  set.  A proposition  of  this  sort,  however,  conveys  no  informa- 
tion to  any  one  who  previously  understood  the  whole  meaning  of  the  terms. 
The  propositions,  Every  man  is  a corporeal  being,  Every  man  is  a living 
creature,  Every  man  is  rational,  convey  no  knowledge  to  any  one  who  rvas 
already  aware  of  the  entire  meaning  of  the  word  man,  for  the  meaning  of 
the  word  includes  all  this : and  that  every  man  has  the  attributes  connoted 
by  all  these  predicates,  is  already  asserted  when  he  is  called  a man.  Now, 
of  this  nature  are  all  the  propositions  which  have  been  called  essential. 
They  are,  in  fact,  identical  propositions. 

It  is  true  that  a proposition  which  predicates  any  attribute,  even  though 
it  be  one  implied  in  the  name,  is  in  most  cases  understood  to  involve  a tacit 
assertion  that  there  exists  a thing  corresponding  to  the  name,  arid  possess- 
ing the  attributes  connoted  by  it ; and  this  implied  assertion  may  convey 
information,  even  to  those  who  understood  the  meaning  of  the  name.  But 
all  information  of  this  sort,  conveyed  by  all  the  essential  propositions  of 
which  man  can  be  made  the  subject,  is  included  in  the  assertion,  Men  exist, 
And  this  assumption  of  real  existence  is,  after  all,  the  result  of  an  imper- 
fection of  language.  It  arises  from  the  ambiguity  of  the  copula,  which,  in 
addition  to  its  proper  office  of  a mark  to  show  that  an  assertion  is  made,  is 
also,  as  formerly  remarked,  a concrete  word  connoting  existence.  The  act- 
ual  existence  of  the  subject  of  the  proposition  is  therefore  only  apparently, 
not  really,  implied  in  the  predication,  if  an  essential  one:  we  may  say,  A 
ghost  is  a disembodied  spirit,  without  believing  in  ghosts.  But  an  acci- 
dental, or  non-essential,  affirmation,  does  imply  the  real  existence  of  the 
subject,  because  in  the  case  of  a non-existent  subject  there  is  nothing  for 
the  proposition  to  assert.  Such  a proposition  as,  The  ghost  of  a murdered 
person  haunts  the  couch  of  the  murderer,  can  only  have  a meaning  if  un- 
derstood as  implying  a belief  in  ghosts;  for  since  the  signification  of  the 

* The  doctrines  which  prevented  the  real  meaning  of  Essences  from  being  understood,  had 
not  assumed  so  settled  a shape  in  the  time  of  Aristotle  and  his  immediate  followers,  as  was 
afterward  given  to  them  by  the  Realists  of  the  Middle  Ages.  Aristotle  himself  (in  his  Trea- 
tise on  the  Categories)  expressly  denies  that  the  devregai  oucicu,  or  Substantia;  Secundai,  in- 
here in  a subject.  They  are  only,  he  says,  predicated  of  it. 


VERBAL  AND  REAL  PROPOSITIONS. 


91 


word  ghost  implies  nothing  of  the  kind,  the  speaker  either  means  nothing, 
or  means  to  assert  a thing  which  he  wishes  to  be  believed  to  have  really 
taken  place. 

It  will  be  hereafter  seen  that  when  any  important  consequences  seem  to 
follow,  as  in  mathematics,  from  an  essential  proposition,  or,  in  other  words, 
from  a proposition  involved  in  the  meaning  of  a name,  what  they  really 
flow  from  is  the  tacit  assumption  of  the  real  existence  of  the  objects  so 
named.  Apart  from  this  assumption  of  real  existence,  the  class  of  proposi- 
tions in  which  the  predicate  is  of  the  essence  of  the  subject  (that  is,  in 
which  the  predicate  connotes  the  whole  or  part  of  what  the  subject  con- 
notes, but  nothing  besides)  answer  no  purpose  but  that  of  unfolding  the 
whole  or  some  part  of  the  meaning  of  the  name,  to  those  who  did  not  pre- 
viously know  it.  Accordingly,  the  most  useful,  and  in  strictness  the  only 
useful  kind  of  essential  propositions,  are  Definitions:  which,  to  be  com- 
plete, should  unfold  the  whole  of  what  is  involved  in  the  meaning  of  the 
word  defined  ; that  is  (when  it  is  a connotative  word),  the  whole  of  what  it 
connotes.  In  defining  a name,  however,  it  is  not  usual  to  specify  its  entire 
connotation,  but  so  much  only  as  is  sufficient  to  mark  out  the  objects  usu- 
ally denoted  by  it  from  all  other  known  objects.  And  sometimes  a merely 
accidental  property,  not  involved  in  the  meaning  of  the  name,  answers  this 
purpose  equally  well.  The  various  kinds  of  definition  which  these  distinc- 
tions give  rise  to,  and  the  purposes  to  which  they  are  respectively  subserv- 
ient, will  be  minutely  considered  in  the  proper  place. 

§ 3.  According  to  the  above  view  of  essential  propositions,  no  proposi- 
tion can  be  reckoned  such  which  relates  to  an  individual  by  name,  that  is, 
in  which  the  subject  is  a proper  name.  Individuals  have  no  essences. 
When  the  schoolmen  talked  of  the  essence  of  an  individual,  they  did  not 
mean  the  properties  implied  in  its  name,  for  the  names  of  individuals  imply 
no  properties.  They  regarded  as  of  the  essence  of  an  individual,  whatever 
was  of  the  essence  of  the  species  in  which  they  were  accustomed  to  place 
that  individual ; i.  e.,  of  the  class  to  which  it  was  most  familiarly  referred, 
and  to  which,  therefore,  they  conceived  that  it  by  nature  belonged.  Thus, 
because  the  proposition  Man  is  a rational  being,  was  an  essential  proposi- 
tion, they  affirmed  the  same  thing  of  the  proposition,  Julius  Cassar  is  a 
rational  being.  This  followed  very  naturally  if  genera  and  species  were  to 
be  considered  as  entities,  distinct  from,  but  inhering  in,  the  individuals 
composing  them.  If  man  was  a substance  inhering  in  each  individual 
man,  the  essence  of  man  (whatever  that  might  mean)  was  naturally  sup- 
posed to  accompany  it;  to  inhere  in  John  Thompson,  and  to  form  the 
common  essence  of  Thompson  and  Julius  Caesar.  It  might  then  be  fairly 
said,  that  rationality,  being  of  the  essence  of  Man,  was  of  the  essence  also 
of  Thompson.  But  if  Man  altogether  be  only  the  individual  men  and  a 
name  bestowed  upon  them  in  consequence  of  certain  common  properties, 
what  becomes  of  John  Thompson’s  essence? 

A fundamental  error  is  seldom  expelled  from  philosophy  by  a single  vic- 
tory. It  retreats  slowly,  defends  every  inch  of  ground,  and  often,  after  it 
has  been  driven  from  the  open  country,  retains  a footing  in  some  remote 
fastness.  The  essences  of  individuals  were  an  unmeaning  figment  arising 
from  a misapprehension  of  the  essences  of  classes,  yet  even  Locke,  when  he 
extirpated  the  parent  error,  could  not  shake  himself  free  from  that  which 
was  its  fruit.  He  distinguished  two  sorts  of  essences,  Real  and  Nominal. 
His  nominal  essences  were  the  essences  of  classes,  explained  nearly  as  we 


92 


NAMES  AND  PROPOSITIONS. 


have  now  explained  them.  Nor  is  any  thing  wanting  to  render  the  third 
book  of  Locke’s  Essay  a nearly  unexceptional  treatise  on  the  connotation 
of  names,  except  to  free  its  language  from  the  assumption  of  what  are 
called  Abstract  Ideas,  which  unfortunately  is  involved  in  the  phraseology, 
though  not  necessarily  connected  with  the  thoughts  contained  in  that  im- 
mortal Third  Book.*  But  besides  nominal  essences,  he  admitted  real  es- 
sences, or  essences  of  individual  objects,  which  he  supposed  to  be  the  causes 
of  the  sensible  properties  of  those  objects.  We  know  not  (said  he)  what 
these  are  (and  this  acknowledgment  rendered  the  fiction  comparatively  in- 
nocuous) ; but  if  we  did,  we  could,  from  them  alone,  demonstrate  the  sen- 
sible properties  of  the  object,  as  the  properties  of  the  triangle  are  demon- 
strated from  the  definition  of  the  triangle.  I shall  have  occasion  to  revert 
to  this  theory  in  treating  of  Demonstration,  and  of  the  conditions  under 
which  one  property  of  a thing  admits  of  being  demonstrated  from  another 
property.  It  is  enough  here  to  remark  that,  according  to  this  definition, 
the  real  essence  of  an  object  has,  in  the  progress  of  physics,  come  to  be 
conceived  as  nearly  equivalent,  in  the  case  of  bodies,  to  their  corpuscular 
structure:  what  it  is  now  supposed  to  mean  in  the  case  of  any  other  en- 
tities, I would  not  take  upon  myself  to  define. 

§ 4.  An  essential  proposition,  then,  is  one  which  is  purely  verbal ; which 
asserts  of  a thing  under  a particular  name,  only  what  is  asserted  of  it  in 
the  fact  of  calling  it  by  that  name;  and  which,  therefore,  either  gives  no 
information,  or  gives  it  respecting  the  name,  not  the  thing.  Non-essential, 
or  accidental  propositions,  on  the  contrary,  may  be  called  Real  Proposi- 
tions, in  opposition  to  Verbal.  They  predicate  of  a thing  some  fact  not 
involved  in  the  signification  of  the  name  by  which  the  proposition  speaks 
of  it;  some  attribute  not  connoted  by  that  name.  Such  are  all  proposi- 
tions concerning  things  individually  designated,  and  all  general  or  partic- 
ular propositions  in  which  the  predicate  connotes  any  attribute  not  con- 
noted by  the  subject.  All  these,  if  true,  add  to  our  knowledge:  they  con- 
vey information,  not  already  involved  in  the  names  employed.  When  I 
am  told  that  all,  or  even  that  some  objects,  which  have  certain  qualities,  or 
which  stand  in  certain  relations,  have  also  certain  other  qualities,  or  stand 
in  certain  other  relations,  I learn  from  this  proposition  a new  fact ; a fact 
not  included  in  my  knowledge  of  the  meaning  of  the  words,  nor  even  of 
the  existence  of  Things  answering  to  the  signification  of  those  words.  It 
is  this  class  of  propositions  only  which  are  in  themselves  instructive,  or 
from  which  any  instructive  propositions  can  be  inferred. f 

Nothing  has  probably  contributed  more  to  the  opinion  so  long  prevalent 
of  the  futility  of  the  school  logic,  than  the  circumstance  that  almost  all  the 
examples  used  in  the  common  school  books  to  illustrate  the  doctrine  of 

* The  always  acute  and  often  profound  author  of  An  Outline  of  Sematology  (Mr.  B.  II. 
Smart)  justly  says,  “Locke  will  be  much  more  intelligible,  if,  in  the  majority  of  places,  we 
substitute  ‘the  knowledge  of’  for  what  he  calls  ‘the  Idea  of’”  (p.  10).  Among  the  many 
criticisms  on  Locke’s  use  of  the  word  Idea,  this  is  the  one  which,  as  it  appears  to  me,  most 
nearly  hits  the  mark ; and  I quote  it  for  the  additional  reason  that  it  precisely  expresses  the 
point  of  difference  respecting  the  import  of  Propositions,  between  my  view  and  what  I have 
spoken  of  as  the  Conceptualist  view  of  them.  Where  a Conceptualist  says  that  a name  or  a 
proposition  expresses  our  Idea  of  a thing,  I should  generally  say  (instead  of  our  Idea)  our 
Knowledge,  or  Belief,  concerning  the  thing  itself. 

f This  distinction  corresponds  to  that  which  is  drawn  by  Kant  and  other  metaphysicians 
between  what  they  term  analytic  and  synthetic , judgments ; the  former  being  those  which  can 
be  evolved  from  the  meaning  of  the  terms  used. 


VERBAL  AND  REAL  PROPOSITIONS. 


93 


predication  and  that  of  the  syllogism,  consist  of  essential  propositions. 
They  were  usually  taken  either  from  the  branches  or  from  the  main  trunk 
of  the  Predicamental  Tree,  which  included  nothing  but  what  was  of  the  es- 
sence of  the  species : Omne  corpus  est  substantia , Omne  animal  est  corpus , 
Omnis  homo  est  corpus,  Omnis  homo  est  animal,  Omnis  homo  est  rationalis, 
and  so  forth.  It  is  far  from  wonderful  that  the  syllogistic  art  should  have 
been  thought  to  be  of  no  use  in  assisting  correct  reasoning,  when  almost 
the  only  propositions  which,  in  the  hands  of  its  professed  teachers,  it  was 
employed  to  prove,  were  such  as  every  one  assented  to  without  proof  the 
moment  he  comprehended  the  meaning  of  the  words;  and  stood  exactly 
on  a level,  in  point  of  evidence,  with  the  premises  from  which  they  were 
drawn.  I have,  therefore,  throughout  this  work,  avoided  the  employment 
of  essential  propositions  as  examples,  except  where  the  nature  of  the  prin- 
ciple to  be  illustrated  specifically  required  them. 

§ 5.  With  respect  to  propositions  which  do  convey  information — which 
assert  something  of  a Thing,  under  a name  that  does  not  already  presup- 
pose what  is  about  to  be  asserted ; there  are  two  different  aspects  in  which 
these,  or  rather  such  of  them  as  are  general  propositions,  may  be  consid- 
ered: we  may  either  look  at  them  as  portions  of  speculative  truth,  or  as 
memoranda  for  practical  use.  According  as  we  consider  propositions  in 
one  or  the  other  of  these  lights,  their  import  may  be  conveniently  expressed 
in  one  or  in  the  other  of  two  formulas. 

According  to  the  formula  which  we  have  hitherto  employed,  and  which 
is  best  adapted  to  express  the  import  of  the  proposition  as  a portion  of 
our  theoretical  knowledge,  All  men  are  mortal,  means  that  the  attributes 
of  man  are  always  accompanied  by  the  attribute  mortality:  No  men  are 
gods,  means  that  the  attributes  of  man  are  never  accompanied  by  the  at- 
tributes, or  at  least  never  by  all  the  attributes,  signified  by  the  word  god. 
But  when  the  proposition  is  considered  as  a memorandum  for  practical  use, 
we  shall  find  a different  mode  of  expressing  the  same  meaning  better  adapt- 
ed to  indicate  the  office  which  the  proposition  performs.  The  practical  use 
of  a proposition  is,  to  apprise  or  remind  us  what  we  have  to  expect,  in  any 
individual  case  which  comes  within  the  assertion  contained  in  the  proposi- 
tion. In  reference  to  this  purpose,  the  proposition,  All  men  are  mortal, 
means  that  the  attributes  of  man  are  evidence  of,  are  a mark  of,  mortality ; 
an  indication  by  which  the  presence  of  that  attribute  is  made  manifest. 
No  men  are  gods,  means  that  the  attributes  of  man  are  a mark  or  evidence 
that  some  or  all  of  the  attributes  understood  to  belong  to  a god  are  not 
there ; that  where  the  former  are,  we  need  not  expect  to  find  the  latter. 

These  two  forms  of  expression  are  at  bottom  equivalent;  but  the  one 
points  the  attention  more  directly  to  what  a proposition  means,  the  latter 
to  the  manner  in  which  it  is  to  be  used. 

Now  it  is  to  be  observed  that  Reasoning  (the  subject  to  which  we  are 
next  to  proceed)  is  a process  into  which  propositions  enter  not  as  ultimate 
results,  but  as  means  to  the  establishment  of  other  propositions.  We  may 
expect,  therefore,  that  the  mode  of  exhibiting  the  import  of  a general  prop- 
osition which  shows  it  in  its  application  to  practical  use,  will  best  express 
the  function  which  propositions  perform  in  Reasoning.  And  accordingly, 
in  the  theory  of  Reasoning,  the  mode  of  viewing  the  subject  which  consid- 
ers a Proposition  as  asserting  that  one  fact  or  phenomenon  is  a mark  or  ev- 
idence of  another  fact  or  phenomenon,  will  be  found  almost  indispensable. 
For  the  purposes  of  that  Theory,  the  best  mode  of  defining  the  import  of 


04 


NAMES  AND  PKOPOSITIONS. 


a proposition  is  not  the  mode  which  shows  most  clearly  what  it  is  in  itself, 
but  that  which  most  distinctly  suggests  the  manner  in  which  it  may  be 
made  available  for  advancing  from  it  to  other  propositions. 


CHAPTER  VII. 

OP  THE  NATURE  OF  CLASSIFICATION,  AND  THE  FIVE  PREDICABLES. 

§ 1.  In  examining  into  the  nature  of  general  propositions,  we  have  ad- 
verted much  less  than  is  usual  with  logicians  to  the  ideas  of  a Class,  and 
Classification  ; ideas  which,  since  the  Realist  doctrine  of  General  Substances 
went  out  of  vogue,  have  formed  the  basis  of  almost  every  attempt  at  a 
philosophical  theory  of  general  terms  and  general  propositions.  We  have 
considered  general  names  as  having  a meaning,  quite  independently  of  their 
being  the  names  of  classes.  That  circumstance  is  in  truth  accidental,  it 
being  wholly  immaterial  to  the  signification  of  the  name  whether  there  are 
many  objects,  or  only  one,  to  which  it  happens  to  be  applicable,  or  whether 
there  be  any  at  all.  God  is  as  much  a general  term  to  the  Christian  or 
Jew  as  to  the  Polytheist;  and  dragon,  hippogriff,  chimera,  mermaid,  ghost, 
are  as  much  so  as  if  real  objects  existed,  corresponding  to  those  names. 
Every  name  the  signification  of  which  is  constituted  by  attributes,  is  po- 
tentially a name  of  an  indefinite  number  of  objects;  but  it  needs  not  be 
actually  the  name  of  any ; and  if  of  any,  it  may  be  the  name  of  only  one. 
As  soon  as  we  employ  a name  to  connote  attributes,  the  things,  be  they 
more  or  fewer,  which  happen  to  possess  those  attributes,  are  constituted 
ip  so  facto  a class.  But  in  predicating  the  name  we  predicate  only  the  at- 
tributes ; and  the  fact  of  belonging  to  a class  does  not,  in  many  cases,  come 
into  view  at  all. 

Although,  however,  Predication  does  not  presuppose  Classification,  and 
though  the  theory  of  Names  and  of  Propositions  is  not  cleared  up,  but  only 
encumbered,  by  intruding  the  idea  of  classification  into  it,  there  is  never- 
theless a close  connection  between  Classification  and  the  employment  of 
General  Names.  By  every  general  name  which  we  introduce,  we  create  a 
class,  if  there  be  any  things,  real  or  imaginary,  to  compose  it;  that  is,  any 
Things  corresponding  to  the  signification  of  the  name.  Classes,  therefore, 
mostly  owe  their  existence  to  general  language.  But  general  language, 
also,  though  that  is  not  the  most  common  case,  sometimes  owes  its  exist- 
ence to  classes.  A general,  which  is  as  much  as  to  say  a significant,  name, 
is  indeed  mostly  introduced  because  we  have  a signification  to  express  by 
it ; because  wTe  need  a word  by  means  of  which  to  predicate  the  attributes 
which  it  connotes.  But  it  is  also  true  that  a name  is  sometimes  introduced 
because  we  have  found  it  convenient  to  create  a class;  because  we  have 
thought  it  useful  for  the  regulation  of  our  mental  operations,  that  a certain 
group  of  objects  should  be  thought  of  together.  A naturalist,  for  purposes 
connected  with  his  particular  science,  sees  reason  to  distribute  the  animal 
or  vegetable  creation  into  certain  groups  rather  than  into  any  others,  and 
he  requires  a name  to  bind,  as  it  were,  each  of  his  groups  together.  It 
must  not,  however,  be  supposed  that  such  names,  when  introduced,  differ 
in  any  respect,  as  to  their  mode  of  signification,  from  other  connotative 
names.  The  classes  which  they  denote  are,  as  much  as  any  other  classes, 
constituted  by  certain  common  attributes,  and  their  names  are  significant 
of  those  attributes,  and  of  nothing  else.  The  names  of  Cuvier’s  classes  and 


CLASSIFICATION  AND  THE  PREDICABLES. 


95 


orders,  Plantigrades,  Digitigrades,  etc.,  are  as  much  the  expression  of  at- 
tributes as  if  those  names  had  preceded,  instead  of  grown  out  of,  his  clas- 
sification of  animals.  The  only  peculiarity  of  the  case  is,  that  the  conven- 
ience of  classification  was  here  the  primary  motive  for  introducing  the 
names;  while  in  other  cases  the  name  is  introduced  as  a means  of  predica- 
tion, and  the  formation  of  a class  denoted  by  it  is  only  an  indirect  conse- 
quence. 

The  principles  which  ought  to  regulate  Classification,  as  a logical  process 
subservient  to  the  investigation  of  truth,  can  not  be  discussed  to  any  pur- 
pose until  a much  later  stage  of  our  inquiry.  But,  of  Classification  as  re- 
sulting from,  and  implied  in,  the  fact  of  employing  general  language,  we 
can  not  forbear  to  treat  here,  without  leaving  the  theory  of  general  names, 
and  of  their  employment  in  predication,  mutilated  and  formless. 

§ 2.  This  portion  of  the  theory  of  general  language  is  the  subject  of 
what  is  termed  the  doctrine  of  the  Predicables ; a set  of  distinctions  hand- 
ed down  from  Aristotle,  and  his  follower  Porphyry,  many  of  which  have 
taken  a firm  root  in  scientific,  and  some  of  them  even  in  popular,  phraseolo- 
gy. The  predicables  are  a fivefold  division  of  General  Names,  not  ground- 
ed as  usual  on  a difference  in  their  meaning,  that  is,  in  the  attribute  which 
they  connote,  but  on  a difference  in  the  kind  of  class  which  they  denote. 
We  may  predicate  of  a thing  five  different  varieties  of  class-name : 


It  is  to  be  remarked  of  these  distinctions,  that  they  express,  not  what  the 
predicate  is  in  its  own  meaning,  but  what  relation  it  bears  to  the  subject 
of  which  it  happens  on  the  particular  occasion  to  be  predicated.  There 
are  not  some  names  which  are  exclusively  genera,  and  others  which  are  ex- 
clusively species,  or  differentiae;  but  the  same  name  is  referred  to  one  or 
another  predicable,  according  to  the  subject  of  which  it  is  predicated  on 
the  particular  occasion.  Animal , for  instance,  is  a genus  with  respect  to 
man,  or  John;  a species  with  respect  to  Substance,  or  Being.  Rectangu- 
lar is  one  of  the  Differentiae  of  a geometrical  square ; it  is  merely  one  of 
the  Accidentia  of  the  table  at  which  I am  writing.  The  words  genus,  spe- 
cies, etc.,  are  therefore  relative  terms;  they  are  names  applied  to  certain 
predicates,  to  express  the  relation  between  them  and  some  given  subject : a 
relation  grounded,  as  we  shall  see,  not  on  what  the  predicate  connotes,  but 
on  the  class  which  it  denotes,  and  on  the  place  which,  in  some  given  classi- 
fication, that  class  occupies  relatively  to  the  particular  subject. 

§ 3.  Of  these  five  names,  two,  Genus  and  Species,  are  not  only  nsed  by 
naturalists  in  a technical  acceptation  not  precisely  agreeing  with  their  phil- 
osophical meaning,  but  have  also  acquired  a popular  acceptation,  much 
more  general  than  either.  In  this  popular  sense  any  two  classes,  one  of 
which  includes  the  whole  of  the  other  and  more,  may  be  called  a Genus 
and  a Species.  Such,  for  instance,  are  Animal  and  Man  ; Man  and  Mathe- 
matician. Animal  is  a Genus;  Man  and  Brute  are  its  two  species;  or  we 
may  divide  it  into  a greater  number  of  species,  as  man,  horse,  dog,  etc. 
Biped,,  or  two-footed  animal , may  also  be  considered  a genus,  of  which 


A genus  of  the  thin: 
A species 


»S 


A differentia 
A proprium 
An  accidens 


(diaipopa). 

(iSior). 

(<7Vju/3£/3>;«!c). 


96 


NAMES  AND  PROPOSITIONS. 


man  and  bird  arc  two  species.  Taste  is  a genus,  of  which  sweet  taste,  sour 
taste,  salt  taste,  etc.,  are  species.  Virtue  is  a genus;  justice,  prudence, 
courage,  fortitude,  generosity,  etc.,  are  its  species. 

The  same  class  which  is  a genus  with  reference  to  the  sub-classes  or 
species  included  in  it,  may  be  itself  a species  with  reference  to  a more 
comprehensive,  or,  as  it  is  often  called,  a superior  genus.  Man  is  a species 
with  reference  to  animal,  but  a genus  with  reference  to  the  species  Mathe- 
matician. Animal  is  a genus, divided  into  two  species,  man  and  brute;  but 
animal  is  also  a species,  which,  with  another  species,  vegetable,  makes  up 
the  genus,  organized  being.  Biped  is  a genus  with  reference  to  man  and 
bird,  but  a species  with  respect  to  the  superior  genus,  animal.  Taste  is  a 
genus  divided  into  species,  but  also  a species  of  the  genus  sensation.  Vir 
tue,  a genus  with  reference  to  justice,  temperance,  etc.,  is  one  of  the  species 
of  the  genus,  mental  quality. 

In  this  popular  sense  the  words  Genus  and  Species  have  passed  into 
common  discourse.  And  it  should  be  observed  that  in  ordinary  parlance, 
not  the  name  of  the  class,  but  the  class  itself,  is  said  to  be  the  genus  or 
species;  not,  of  course,  the  class  in  the  sense  of  each  individual  of  the 
class,  but  the  individuals  collectively,  considered  as  an  aggregate  whole ; 
the  name  by  which  the  class  is  designated  being  then  called  not  the  genus 
or  species,  but  the  generic  or  specific  name.  And  this  is  an  admissible 
form  of  expression  ; nor  is  it  of  any  importance  which  of  the  two  modes 
of  speaking  we  adopt,  provided  the  rest  of  our  language  is  consistent  with 
it ; but,  if  we  call  the  class  itself  the  genus,  we  must  not  talk  of  predica- 
ting the  genus.  We  predicate  of  man  the  name  mortal;  and  by  predica- 
ting the  name,  we  may  be  said,  in  an  intelligible  sense,  to  predicate  what 
the  name  expresses,  the  attribute  mortality ; but  in  no  allowable  sense  of 
the  word  predication  do  we  predicate  of  man  the  class  mortal.  We  predi- 
cate of  him  the  fact  of  belonging  to  the  class. 

By  the  Aristotelian  logicians,  the  terms  genus  and  species  were  used  in 
a more  restricted  sense.  They  did  not  admit  every  class  which  could  be 
divided  into  other  classes  to  be  a genus,  or  every  class  which  could  be  in- 
cluded in  a larger  class  to  be  a species.  Animal  was  by  them  considered 
a genus  ; man  and  brute  co-ordinate  species  under  that  genus:  biped , how- 
ever, would  not  have  been  admitted  to  be  a genus  with  reference  to  man, 
but  a proprium  or  accidens  only.  It  was  requisite,  according  to  their 
theory,  that  genus  and  species  should  be  of  the  essence  of  the  subject. 
Animal  was  of  the  essence  of  man ; biped  was  not.  And  in  every  classi- 
fication they  considered  some  one  class  as  the  lowest  or  infima  species. 
Man,  for  instance,  was  a lowest  species.  Any  further  divisions  into  which 
the  class  might  be  capable  of  being  broken  down,  as  man  into  white,  black, 
and  red  man,  or  into  priest  and  layman,  they  did  not  admit  to  be  species. 

It  has  been  seen,  however,  in  the  preceding  chapter,  that  the  distinction 
between  the  essence  of  a class,  and  the  attributes  or  properties  which  are 
not  of  its  essence — a distinction  which  has  given  occasion  to  so  much  ab- 
struse speculation,  and  to  which  so  mysterious  a character  was  formerly, 
and  by  many  writers  is  still,  attached — amounts  to  nothing  more  than  the 
difference  between  those  attributes  of  the  class  which  are,  and  those  which 
are  not,  involved  in  the  signification  of  the  class-name.  As  applied  to  in- 
dividuals, the  word  Essence,  we  found,  has  no  meaning,  except  in  connec- 
tion with  the  exploded  tenets  of  the  Realists;  and  what  the  schoolmen 
chose  to  call  the  essence  of  an  individual,  was  simply  the  essence  of  the 
class  to  which  that  individual  was  most  familiarly  referred. 


CLASSIFICATION  AND  THE  PEEDICABLES. 


97 


Is  there  no  difference,  then,  save  this  merely  verbal  one,  between  the 
classes  which  the  schoolmen  admitted  to  be  genera  or  species,  and  those  to 
which  they  refused  the  title?  Is  it  an  error  to  regard  some  of  the  differ- 
ences which  exist  among  objects  as  differences  in  kind  ( gcnere  or  specie), 
and  others  only  as  differences  in  the  accidents  ? Were  the  schoolmen  right 
or  wrong  in  giving  to  some  of  the  classes  into  which  things  may  be  divided, 
the  name  of  kinds,  and  considering  others  as  secondary  divisions,  ground- 
ed on  differences  of  a comparatively  superficial  nature?  Examination  will 
show  that  the  Aristotelians  did  mean  something  by  this  distinction,  and 
something  important;  but  which,  being  but  indistinctly  conceived,  was  in- 
adequately expressed  by  the  phraseology  of  essences,  and  the  various  other 
modes  of  speech  to  which  they  had  recourse. 

§ 4.  It  is  a fundamental  principle  in  logic,  that  the  power  of  framing 
classes  is  unlimited,  as  long  as  there  is  any  (even  the  smallest)  difference  to 
found  a distinction  upon.  Take  any  attribute  whatever,  and  if  some  things 
have  it,  and  others  have  not,  we  may  ground  on  the  attribute  a division  of 
all  things  into  two  classes ; and  we  actually  do  so,  the  moment  we  create  a 
name  which  connotes  the  attribute.  The  number  of  possible  classes,  there- 
fore, is  boundless ; and  there  are  as  many  actual  classes  (either  of  real  or 
of  imaginary  things)  as  there  are  general  names,  positive  and  negative  to- 
gether. 

But  if  we  contemplate  any  one  of  the  classes  so  formed,  such  as  the  class 
animal  or  plant,  or  the  class  sulphur  or  phosphorus,  or  the  class  white  or 
red,  and  consider  in  what  particulars  the  individuals  included  in  the  class 
differ  from  those  which  do  not  come  within  it,  we  find  a very  remarkable 
diversity  in  this  respect  between  some  classes  and  others.  There  are  some 
classes,  the  things  contained  in  which  differ  from  other  things  only  in  cer- 
tain particulars  which  may  be  numbered,  while  others  differ  in  more  than 
can  be  numbered,  more  even  than  we  need  ever  expect  to  know.  Some 
classes  have  little  or  nothing  in  common  to  characterize  them  by,  except 
precisely  what  is  connoted  by  the  name : white  things,  for  example,  are  not 
distinguished  by  any  common  properties  except  whiteness ; or  if  they  are, 
it  is  only  by  such  as  are  in  some  way  dependent  on,  or  connected  with, 
whiteness.  But  a hundred  generations  have  not  exhausted  the  common 
properties  of  animals  or  of  plants,  of  sulphur  or  of  phosphorus ; nor  do  we 
suppose  them  to  be  exhaustible,  but  proceed  to  new  observations  and  ex- 
periments, in  the  full  confidence  of  discovering  new  properties  which  were 
by  no  means  implied  in  those  we  previously  knew.  While,  if  any  one  were 
to  propose  for  investigation  the  common  properties  of  all  things  which  are 
of  the  same  color,  the  same  shape,  or  the  same  specific  gravity,  the  absurd- 
ity would  be  palpable.  We  have  no  ground  to  believe  that  any  such  com- 
mon properties  exist,  except  such  as  may  be  shown  to  be  involved  in  the 
supposition  itself,  or  to  be  derivable  from  it  by  some  law  of  causation.  It 
appears,  therefore,  that  the  properties,  on  which  wre  ground  our  classes, 
sometimes  exhaust  all  that  the  class  has  in  common,  or  contain  it  all  by 
some  mode  of  implication ; but  in  other  instances  we  make  a selection  of  a 
few  properties  from  among  not  only  a greater  number,  but  a number  inex- 
haustible by  us,  and  to  which  as  we  know  no  bounds,  they  may,  so  far  as 
we  are  concerned,  be  regarded  as  infinite. 

There  is  no  impropriety  in  saying  that,  of  these  two  classifications,  the 
one  answers  to  a much  more  radical  distinction  in  the  things  themselves, 
than  the  other  does.  And  if  any  one  even  chooses  to  say  that  the  one  clas- 

7 


98 


NAMES  AND  PROPOSITIONS. 


sification  is  made  by  nature,  the  other  by  us  for  our  convenience,  he  will  be 
right ; provided  he  means  no  more  than  this : Where  a certain  apparent 
difference  between  things  (though  perhaps  in  itself  of  little  moment)  an- 
swers to  we  know  not  what  number  of  other  differences,  pervading  not 
only  their  known  properties,  but  properties  yet  undiscovered,  it  is  not  op- 
tional but  imperative  to  recognize  this  difference  as  the  foundation  of  a 
specific  distinction  ; while,  on  the  contrary,  differences  that  are  merely  finite 
and  determinate,  like  those  designated  by  the  words  white,  black,  or  red, 
may  be  disregarded  if  the  purpose  for  which  the  classification  is  made  does 
not  require  attention  to  those  particular  properties.  The  differences,  how- 
ever, are  made  by  nature,  in  both  cases;  while  the  recognition  of  those  dif- 
ferences as  grounds  of  classification  and  of  naming,  is,  equally  in  both  cases, 
the  act  of  man  : only  in  the  one  case,  the  ends  of  language  and  of  classifica- 
tion would  be  subverted  if  no  notice  were  taken  of  the  difference,  while  in 
the  other  case,  the  necessity  of  taking  notice  of  it  depends  on  the  impor- 
tance or  unimportance  of  the  particular  qualities  in  which  the  difference 
happens  to  consist. 

Now,  th'ese  classes,  distinguished  by  unknown  multitudes  of  properties, 
and  not  solely  by  a few  determinate  ones — which  are  parted  off  from  one 
another  by  an  unfathomable  chasm,  instead  of  a mere  ordinary  ditch  with 
a visible  bottom — are  the  only  classes  which,  by  the  Aristotelian  logicians, 
were  considered  as  genera  or  species.  Differences  which  extended  only  to 
a certain  property  or  properties,  and  there  terminated,  they  considered  as 
differences  only  in  the  accidents  of  things ; but  where  any  class  differed 
from  other  things  by  an  infinite  series  of  differences,  known  and  unknown, 
they  considered  the  distinction  as  one  of  kind,  and  spoke  of  it  as  being  an 
essential  difference,  which  is  also  one  of  the  current  meanings  of  that  vague 
expression  at  the  present  day. 

Conceiving  the  schoolmen  to  have  been  justified  in  drawing  a broad  line 
of  separation  between  these  two  kinds  of  classes  and  of  class-distinctions,  I 
shall  not  only  retain  the  division  itself,  but  continue  to  express  it  in  their 
language.  According  to  that  language,  the  proximate  (or  lowest)  Kind  to 
which  any  individual  is  referrible,  is  called  its  species.  Conformably  to 
this,  Isaac  Newton  would  be  said  to  be  of  the  species  man.  There  are 
indeed  numerous  sub-classes  included  in  the  class  man,  to  which  Newton 
also  belongs ; for  example,  Christian,  and  Englishman,  and  Mathematician. 
But  these,  though  distinct  classes,  are  not,  in  our  sense  of  the  term,  distinct 
Kinds  of  men.  A Christian,  for  example,  differs  from  other  human  be- 
ings; but  he  differs  only  in  the  attribute  which  the  word  expresses,  namely, 
belief  in  Christianity,  and  whatever  else  that  implies,  either  as  involved  in 
the  fact  itself,  or  connected  with  it  through  some  law  of  cause  and  effect. 
We  should  never  think  of  inquiring  what  properties,  unconnected  with 
Christianity,  either  as  cause  or  effect,  are  common  to  all  Christians  and  pe- 
culiar to  them ; while  in  regard  to  all  Men,  physiologists  are  perpetually 
carrying  on  such  an  inquiry ; nor  is  the  answer  ever  likely  to  be  completed. 
Man,  therefore,  we  may  call  a species ; Christian,  or  Mathematician,  we 
can  not. 

Note  here,  that  it  is  by  no  means  intended  to  imply  that  there  may  not 
be  different  Kinds,  or  logical  species,  of  man.  The  various  races  and  tem- 
peraments, the  two  sexes,  and  even  the  various  ages,  may  be  differences  of 
kind,  within  our  meaning  of  the  term.  I do  not  say  that  they  are  so.  For 
in  the  progress  of  physiology  it  may  almost  be  said  to  be  made  out,  that 
the  differences  which  really  exist  between  different  races,  sexes,  etc.,  follow 


CLASSIFICATION  AND  THE  PREDICABLES. 


99 


as  consequences,  under  laws  of  nature,  from  a small  number  of  primary 
differences  which  can  be  precisely  determined,  and  which,  as  the  phrase  is, 
account  for  all  the  rest.  If  this  be  so,  these  are  not  distinctions  in  kind; 
no  more  than  Christian,  Jew,  Mussulman,  and  Pagan,  a difference  which 
also  carries  many  consequences  along  with  it.  And  in  this  way  classes  are 
often  mistaken  for  real  Kinds,  which  are  afterward  proved  not  to  be  so. 
But  if  it  turned  out  that  the  differences  were  not  capable  of  being  thus  ac- 
counted for,  then  Caucasian,  Mongolian,  Negro,  etc.,  would  be  really  differ- 
ent Kinds  of  human  beings,  and  entitled  to  be  ranked  as  species  by  the 
logician;  though  not  by  the  naturalist.  For  (as  already  noticed)  the  word 
species  is  used  in  a different  signification  in  logic  and  in  natural  history. 
By  the  naturalist,  organized  beings  are  not  usually  said  to  be  of  different 
species,  if  it  is  supposed  that  they  have  descended  from  the  same  stock. 
That,  however,  is  a sense  artificially  given  to  the  word,  for  the  technical 
purposes  of  a particular  science.  To  the  logician,  if  a negro  and  a white 
man  differ  in  the  same  manner  (however  less  in  degree)  as  a horse  and  a 
camel  do,  that  is,  if  their  differences  are  inexhaustible,  and  not  referrible  to 
any  common  cause,  they  are  different  species,  whether  they  are  descended 
from  common  ancestors  or  not.  But  if  their  differences  can  all  be  traced 
to  climate  and  habits,  or  to  some  one  or  a few  special  differences  in  struc- 
ture, they  are  not,  in  the  logician’s  view,  specifically  distinct. 

When  the  inflma  species,  or  proximate  Kind,  to  which  an  individual 
belongs,  has  been  ascertained,  the  properties  common  to  that  Kind  include 
necessarily  the  whole  of  the  common  properties  of  every  other  real  Kind 
to  which  the  individual  can  be  referrible.  Let  the  individual,  for  example, 
be  Socrates,  and  the  proximate  Kind,  man.  Animal,  or  living  creature,  is 
also  a real  kind,  and  includes  Socrates;  but,  since  it  likewise  includes  man, 
or  in  other  words,  since  all  men  are  animals,  the  properties  common  to  ani- 
mals form  a portion  of  the  common  properties  of  the  sub-class,  man.  And 
if  there  be  any  class  which  includes  Socrates  without  including  man,  that 
class  is  not  a real  Kind.  Let  the  class,  for  example,  be  flat-nosed ; that 
being  a class  which  includes  Socrates,  without  including  all  men.  To  de- 
termine whether  it  is  a real  Kind,  we  must  ask  ourselves  this  question : 
Have  all  flat-nosed  animals,  in  addition  to  whatever  is  implied  in  their  flat 
noses,  any  common  properties,  other  than  those  which  are  common  to  all 
animals  whatever  ? If  they  had ; if  a flat  nose  were  a mark  or  index  to  an 
indefinite  number  of  other  peculiarities,  not  deducible  from  the  former  by 
an  ascertainable  law,  then  out  of  the  class  man  we  might  cut  another  class, 
flat-nosed  man,  which,  according  to  our  definition,  would  be  a Kind.  But 
if  we  could  do  this,  man  would  not  be,  as  it  was  assumed  to  be,  the  proxi- 
mate Kind.  Therefore,  the  properties  of  the  proximate  Kind  do  compre- 
hend those  (whether  known  or  unknown)  of  all  other  Kinds  to  which  the 
individual  belongs;  which  was  the  point  we  undertook  to  prove.  And 
hence,  every  other  Kind  which  is  predicable  of  the  individual,  will  be  to 
the  proximate  Kind  in  the  relation  of  a genus,  according  to  even  the  popu- 
lar acceptation  of  the  terms  genus  and  species ; that  is,  it  will  be  a larger 
class,  including  it  and  more. 

We  are  now  able  to  fix  the  logical  meaning  of  these  terms.  Every  class 
which  is  a real  Kind,  that  is,  which  is  distinguished  from  all  other  classes 
by  an  indeterminate  multitude  of  properties  not  derivable  from  one  an- 
other, is  either  a genus  or  a species.  A Kind  which  is  not  divisible  into 
other  Kinds,  can  not  be  a genus,  because  it  has  no  species  under  it;  but  it 
is  itself  a species,  both  with  reference  to  the  individuals  below  and  to  the 


100 


NAMES  AND  PROPOSITIONS. 


genera  above  (Species  Pnedicabilis  and  Species  Subjicibilis).  But  every 
Kind  which  admits  of  division  into  real  Kinds  (as  animal  into  mammal, 
bird,  fish,  etc.,  or  bird  into  various  species  of  birds)  is  a genus  to  all  below 
it,  a species  to  all  genera  in  which  it  is  itself  included.  And  here  we  may 
close  this  part  of  the  discussion,  and  pass  to  the  three  remaining  predica- 
tes, Differentia,  Proprium,  and  Accidens. 

§ 5.  To  begin  with  Differentia.  This  word  is  correlative  with  the  words 
genus  and  species,  and  as  all  admit,  it  signifies  the  attribute  which  distin- 
guishes a given  species  from  every  other  species  of  the  same  genus.  This 
is  so  far  clear : but  we  may  still  ask,  which  of  the  distinguishing  attributes 
it  signifies.  For  we  have  seen  that  every  Kind  (and  a species  must  be  a 
Kind)  is  distinguished  from  other  Kinds,  not  by  any  one  attribute,  but  by 
an  indefinite  number.  Man,  for  instance,  is  a species  of  the  genus  animal : 
Rational  (or  rationality,  for  it  is  of  no  consequence  here  whether  we  use 
the  concrete  or  the  abstract  form)  is  generally  assigned  by  logicians  as  the 
Differentia  ; and  doubtless  this  attribute  serves  the  purpose  of  distinction  : 
but  it  has  also  been  remarked  of  man,  that  he  is  a cooking  animal ; the 
only  animal  that  dresses  its  food.  This,  therefore,  is  another  of  the  at- 
tributes by  which  the  species  man  is  distinguished  from  other  species  of 
the  same  genus:  would  this  attribute  serve  equally  well  for  a differentia? 
The  Aristotelians  say  No;  having  laid  it  down  that  the  differentia  must, 
like  the  genus  and  species,  be  of  the  essence  of  the  subject. 

And  here  we  lose  even  that  vestige  of  a meaning  grounded  in  the  nature 
of  the  things  themselves,  which  may  be  supposed  to  be  attached  to  the 
word  essence  when  it  is  said  that  genus  and  species  must  be  of  the  essence 
of  the  thing.  There  can  be  no  doubt  that  when  the  schoolmen  talked  of 
the  essences  of  things  as  opposed  to  their  accidents,  they  had  confusedly 
in  view  the  distinction  between  differences  of  kind,  and  the  differences 
which  are  not  of  kind ; they  meant  to  intimate  that  genera  and  species 
must  be  Kinds.  Their  notion  of  the  essence  of  a thing  was  a vague  notion 
of  a something  which  makes  it  what  it  is,  i.  e.,  which  makes  it  the  Kind  of 
thing  that  it  is — which  causes  it  to  have  all  that  variety  of  properties  which 
distinguish  its  Kind.  But  when  the  matter  came  to  be  looked  at  more 
closely,  nobody  could  discover  what  caused  the  thing  to  have  all  those  prop- 
erties, nor  even  that  there  was  any  thing  which  caused  it  to  have  them. 
Logicians,  however,  not  liking  to  admit  this,  and  being  unable  to  detect 
what  made  the  thing  to  be  what  it  was,  satisfied  themselves  with  what 
made  it  to  be  what  it  was  called.  Of  the  innumerable  properties,  known 
and  unknown,  that  are  common  to  the  class  man,  a portion  only,  and  of 
course  a very  small  portion,  are  connoted  by  its  name ; these  few,  however, 
will  naturally  have  been  thus  distinguished  from  the  rest  either  for  their 
greater  obviousness,  or  for  greater  supposed  importance.  These  prop- 
erties, then,  which  were  connoted  by  the  name,  logicians  seized  upon,  and 
called  them  the  essence  of  the  species;  and  not  stopping  there,  they  af- 
firmed them,  in  the  case  of  the  infima  species , to  be  the  essence  of  the  in- 
dividual too  ; for  it  was  their  maxim,  that  the  species  contained  the  “ whole 
essence’"  of  the  thing.  Metaphysics,  that  fertile  field  of  delusion  propa- 
gated by  language,  does  not  afford  a more  signal  instance  of  such  delusion. 
On  this  account  it  was  that  rationality,  being  connoted  by  the  name  man, 
was  allowed  to  be  a differentia  of  the  class;  but  the  peculiarity  of  cook- 
ing their  food,  not  being  connoted,  was  relegated  to  the  class  of  accidental 
properties. 


CLASSIFICATION  AND  THE  PREDICABLES. 


101 


The  distinction,  therefore,  between  Differentia,  Proprium,  and  Accidens, 
is  not  grounded  in  the  nature  of  things,  but  in  the  connotation  of  names ; 
and  we  must  seek  it  there,  if  we  wish  to  find  what  it  is. 

From  the  fact  that  the  genus  includes  the  species,  in  other  words  denotes 
more  than  the  species,  or  is  predicable  of  a greater  number  of  individuals, 
it  follows  that  the  species  must  connote  more  than  the  genus.  It  must 
connote  all  the  attributes  which  the  genus  connotes,  or  there  would  be 
nothing  to  prevent  it  from  denoting  individuals  not  included  in  the  genus. 
And  it  must  connote  something  besides,  otherwise  it  would  include  the 
whole  genus.  Animal  denotes  all  the  individuals  denoted  by  man,  and 
many  more.  Man,  therefore,  must  connote  all  that  animal  connotes,  other- 
wise there  might  be  men  who  are  not  animals;  and  it  must  connote  some- 
thing more  than  animal  connotes,  otherwise  all  animals  would  be  men. 
This  surplus  of  connotation — this  which  the  species  connotes  over  and 
above  the  connotation  of  the  genus — is  the  Differentia,  or  specific  differ- 
ence ; or,  to  state  the  same  proposition  in  other  words,  the  Differentia  is 
that  which  must  be  added  to  the  connotation  of  the  genus,  to  complete  the 
connotation  of  the  species.  * 

The  word  man,  for  instance,  exclusively  of  what  it  conuotes  in  common 
with  animal,  also  connotes  rationality,  and  at  least  some  approximation  to 
that  external  form  which  we  all  know,  but  which  as  we  have  no  name  for 
it  considered  in  itself,  we  are  content  to  call  the  human.  The  Differentia, 
or  specific  difference,  therefore,  of  man,  as  referred  to  the  genus  animal,  is 
that  outward  form  and  the  possession  of  reason.  The  Aristotelians  said, 
the  possession  of  reason,  without  the  outward  form.  But  if  they  adhered 
to  this,  they  would  have  been  obliged  to  call  the  Houyhnhnms  men.  The 
question  never  arose,  and  they  were  never  called  upon  to  decide  how  such 
a case  would  have  affected  their  notion  of  essentiality.  However  this  may 
be,  they  were  satisfied  with  taking  such  a portion  of  the  differentia  as  suf- 
ficed to  distinguish  the  species  from  all  other  existing  things,  though  by  so 
doing  they  might  not  exhaust  the  connotation  of  the  name. 

§ 6.  And  here,  to  prevent  the  notion  of  differentia  from  being  restricted 
within  too  narrow  limits,  it  is  necessary  to  remark,  that  a species,  even  as 
referred  to  the  same  genus,  will  not  always  have  the  same  differentia,  but 
a different  one,  according  to  the  principle  and  purpose  which  preside  over 
the  particular  classification.  For  example,  a naturalist  surveys  the  various 
kinds  of  animals,  and  looks  out  for  the  classification  of  them  most  in  ac- 
cordance with  the  order  in  which,  for  zoological  purposes,  he  considers  it 
desirable  that  we  should  think  of  them.  With  this  view  he  finds  it  advisa- 
ble that  one  of  his  fundamental  divisions  should  be  into  warm-blooded  and 
cold-blooded  animals ; or  into  animals  which  breathe  with  lungs  and  those 
which  breathe  with  gills  ; or  into  carnivorous,  and  frugivorous  or  graminiv- 
orous ; or  into  those  which  walk  on  the  flat  part  and  those  which  walk  on 
the  extremity  of  the  foot,  a distinction  on  which  two  of  Cuvier’s  families  are 
founded.  In  doing  this,  the  naturalist  creates  as  many  new  classes ; which 
are  by  no  means  those  to  which  the  individual  animal  is  familiarly  and  spon- 
taneously referred ; nor  should  we  ever  think  of  assigning  to  them  so  prom- 
inent a position  in  our  arrangement  of  the  animal  kingdom,  unless  for  a pre- 
conceived purpose  of  scientific  convenience.  And  to  the  liberty  of  doing 
this  there  is  no  limit.  In  the  examples  we  have  given,  most  of  the  classes 
are  real  Kinds,  since  each  of  the  peculiarities  is  an  index  to  a multitude 
of  properties  belonging  to  the  class  which  it  characterizes : but  even  if  the 


102 


NAMES  AND  PROPOSITIONS. 


case  were  otherwise — if  the  other  properties  of  those  classes  could  all  be 
derived,  by  any  process  known  to  us,  from  the  one  peculiarity  on  which  the 
class  is  founded — even  then,  if  these  derivative  properties  were  of  primary 
importance  for  the  purposes  of  the  naturalist,  he  would  be  warranted  in 
founding  his  primary  divisions  on  them. 

If,  however,  practical  convenience  is  a sufficient  warrant  for  making  the 
main  demarkations  in  our  arrangement  of  objects  run  in  lines  not  coin- 
ciding with  any  distinction  of  Kind,  and  so  creating  genera  and  species  in 
the  popular  sense  which  are  not  genera  or  species  in  the  rigorous  sense  at 
all ; d fortiori  must  we  be  warranted,  when  our  genera  and  species  are  real 
genera  and  species,  in  marking  the  distinction  between  them  by  those  of 
their  properties  which  considerations  of  practical  convenience  most  strong- 
ly recommend.  If  we  cut  a species  out  of  a given  genus — the  species  man, 
for  instance,  out  of  the  genus  animal— with  an  intention  on  our  part  that 
the  peculiarity  by  which  we  are  to  be  guided  in  the  application  of  the 
name  man  should  be  rationality,  then  rationality  is  the  differentia  of  the 
species  man.  Suppose,  however,  that  being  naturalists,  we,  for  the  pur- 
poses of  our  particular  study,  cut  out  of  the  genus  animal  the  same  species 
man,  but  with  an  intention  that  the  distinction  between  man  and  all  other 
species  of  animal  should  be,  not  rationality,  but  the  possession  of  “ four 
incisors  in  each  jaw,  tusks  solitary,  and  erect  posture.”  It  is  evident  that 
the  word  man,  when  used  by  us  as  naturalists,  no  longer  connotes  rational- 
ity, but  connotes  the  three  other  properties  specified;  for  that  which  we 
have  expressly  in  view  when  we  impose  a name,  assuredly  forms  part  of 
the  meaning  of  that  name.  We  may,  therefore,  lay  it  down  as  a maxim, 
that  wherever  there  is  a Genus,  and  a Species  marked  out  from  that  genus 
by  an  assignable  differentia,  the  name  of  the  species  must  be  connotative, 
and  must  connote  the  differentia ; but  the  connotation  may  be  special — not 
involved  in  the  signification  of  the  term  as  ordinarily  used,  but  given  to  it 
when  employed  as  a term  of  art  or  science.  The  word  Man  in  common 
use,  connotes  rationality  and  a certain  form,  but  does  not  connote  the  num- 
ber or  character  of  the  teeth ; in  the  Linnasan  system  it  connotes  the  num- 
ber of  incisor  and  canine  teeth,  but  does  not  connote  rationality  nor  any 
particular  form.  The  word  man  has,  therefore,  two  different  meanings; 
though  not  commonly  considered  as  ambiguous,  because  it  happens  in  both 
cases  to  denote  the  same  individual  objects.  But  a case  is  conceivable  in 
which  the  ambiguity  would  become  evident : we  have  only  to  imagine  that 
some  new  kind  of  animal  were  discovered,  having  Linnaeus’s  three  char- 
acteristics of  humanity,  but  not  rational,  or  not  of  the  human  form.  In 
ordinary  parlance,  these  animals  would  not  be  called  men ; but  in  natural 
history  they  must  still  be  called  so  by  those,  if  any  there  should  be,  who 
adhere  to  the  Linnsean  classification  ; and  the  question  would  arise,  whether 
the  word  should  continue  to  be  used  in  two  senses,  or  the  classification  be 
given  up,  and  the  technical  sense  of  the  term  be  abandoned  along  with  it. 

Words  not  otherwise  connotative  may,  in  the  mode  just  adverted  to, 
acquire  a special  or  technical  connotation.  Thus  the  word  whiteness,  as 
we  have  so  often  remarked,  connotes  nothing;  it  merely  denotes  the  at- 
tribute corresponding  to  a certain  sensation : but  if  we  are  making  a clas- 
sification of  colors,  and  desire  to  justify,  or  even  merely  to  point  out,  the 
particular  place  assigned  to  whiteness  in  our  arrangement,  we  may  define 
it  “the  color  produced  by  the  mixture  of  all  the  simple  rays;”  and  this 
fact,  though  by  no  means  implied  in  the  meaning  of  the  word  whiteness 
as  ordinarily  used,  but  only  known  by  subsequent  scientific  investigation, 


CLASSIFICATION  AND  THE  PREDICABLES. 


103 


is  part  of  its  meaning  in  the  particular  essay  or  treatise,  and  becomes  the 
differentia  of  the  species.* 

The  differentia,  therefore,  of  a species  may  be  defined  to  be,  that  part  of 
the  connotation  of  the  specific  name,  whether  ordinary  or  special  and  tech- 
nical, which  distinguishes  the  species  in  question  from  all  other  species  of 
the  genus  to  which  on  the  particular  occasion  we  are  referring  it. 

§ 7.  Having  disposed  of  Genus,  Species,  and  Differentia,  we  shall  not  find 
much  difficulty  in  attaining  a clear  conception  of  the  distinction  between 
the  other  two  predicables,  as  well  as  between  them  and  the  first  three. 

In  the  Aristotelian  phraseology,  Genus  and  Differentia  are  of  the  essence 
of  the  subject;  by  which,  as  we  have  seen,  is  really  meant  that  the  proper- 
ties signified  by  the  genus  and  those  signified  by  the  differentia,  form  part 
of  the  connotation  of  the  name  denoting  the  sj^ecies.  Proprium  and  Ae- 
cidens,  on  the  other  hand,  form  no  part  of  the  essence,  but  are  predicated 
of  the  species  only  accidentally.  Both  are  Accidents,  in  the  wider  sense  in 
which  the  accidents  of  a thing  are  opposed  to  its  essence ; though,  in  the 
doctrine  of  the  Predicables,  Accidens  is  used  for  one  sort  of  accident  only, 
Proprium  being  another  sort.  Proprium,  continue  the  schoolmen,  is  pred- 
icated accidentally , indeed,  but  necessarily ; or,  as  they  further  explain  it, 
signifies  an  attribute  which  is  not  indeed  part  of  the  essence,  but  which 
flows  from,  or  is  a consequence  of,  the  essence,  and  is,  therefore,  inseparably 
attached  to  the  species ; e.  g.,  the  various  properties  of  a triangle,  which, 
though  no  part  of  its  definition,  must  necessarily  be  possessed  by  whatever 
comes  under  that  definition.  Accidens,  on  the  contrary,  has  no  connection 
whatever  with  the  essence,  but  may  come  and  go,  and  the  species  still  re- 
main what  it  was  before.  If  a species  could  exist  without  its  Propria,  it 
must  be  capable  of  existing  without  that  on  which  its  Propria  are  neces- 
sarily consequent,  and  therefore  without  its  essence,  without  that  which  con- 
stitutes it  a species.  But  an  Accidens,  whether  separable  or  inseparable 
from  the  species  in  actual  experience,  may  be  supposed  separated,  without 
the  necessity  of  supposing  any  other  alteration ; or  at  least,  without  sup- 
posing any  of  the  essential  properties  of  the  species  to  be  altered,  since 
with  them  an  Accidens  has  no  connection. 

A Proprium,  therefore,  of  the  species,  may  be  defined,  any  attribute  which 
belongs  to  all  the  individuals  included  in  the  species,  and  which,  though 
not  connoted  by  the  specific  name  (either  ordinarily  if  the  classification  we 
are  considering  be  for  ordinary  purposes,  or  specially  if  it  be  for  a special 
purpose),  yet  follows  from  some  attribute  which  the  name  either  ordinarily 
or  specially  connotes. 

One  attribute  may  follow  from  another  in  two  ways ; and  there  are  con- 
sequently two  kinds  of  Proprium.  It  may  follow  as  a conclusion  follows 
premises,  or  it  may  follow  as  an  effect  follows  a cause.  Thus,  the  attribute 
of  having  the  opposite  sides  equal,  which  is  not  one  of  those  connoted  by 
the  word  Parallelogram,  nevertheless  follows  from  those  connoted  by  it, 
namely,  from  having  the  opposite  sides  straight  lines  and  parallel,  and  the 
number  of  sides  four.  The  attribute,  therefore,  of  having  the  opposite 
sides  equal,  is  a Proprium  of  the  class  parallelogram;  and  a Proprium  of 
the  first  kind,  which  follows  from  the  connoted  attributes  by  way  of  dem- 

* If  we  allow  a differentia  to  what  is  not  really  a species.  For  the  distinction  of  Kinds, 
in  the  sense  explained  by  us,  not  being  in  any  way  applicable  to  attributes,  it  of  course  follows 
that  although  attributes  may  be  put  into  classes,  those  classes  can  be  admitted  to  be  genera 
or  species  only  by  courtesy. 


104 


NAMES  AND  PROPOSITIONS. 


onstration.  The  attribute  of  being  capable  of  understanding  language,  is 
a Proprium  of  the  species  man,  since  without  being  connoted  by  the  word, 
it  follows  from  an  attribute  which  the  word  does  connote,  viz.,  from  the 
attribute  of  rationality.  But  this  is  a Proprium  of  the  second  kind,  which 
follows  by  way  of  causation.  How  it  is  that  one  property  of  a thing  fol- 
lows, or  can  be  inferred,  from  another ; under  what  conditions  this  is  pos- 
sible, and  what  is  the  exact  meaning  of  the  phrase ; are  among  the  ques- 
tions which  will  occupy  us  in  the  two  succeeding  Books.  At  present  it 
needs  only  be  said,  that  whether  a Proprium  follows  by  demonstration  or 
by  causation,  it  follows  necessarily ; that  is  to  say,  its  not  following  would 
be  inconsistent  with  some  law  which  we  regard  as  a part  of  the  constitu- 
tion either  of  our  thinking  faculty  or  of  the  universe. 

§ 8.  Under  the  remaining  predicable,  Accidens,  are  included  all  attri- 
butes of  a thing  which  are  neither  involved  in  the  signification  of  the  name 
(whether  ordinarily  or  as  a term  of  art),  nor  have,  so  far  as  we  know, 
any  necessary  connection  with  attributes  which  are  so  involved.  They  are 
commonly  divided  into  Separable  and  Inseparable  Accidents.  Inseparable 
accidents  are  those  which — although  we  know  of  no  connection  between 
them  and  the  attributes  constitutive  of  the  species,  and  although,  therefore, 
so  far  as  we  are  aware,  they  might  be  absent  without  making  the  namo  in- 
applicable and  the  species  a different  species — are  yet  never  in  fact  known 
to  be  absent.  A concise  mode  of  expressing  the  same  meaning  is,  that  in- 
separable accidents  are  properties  which  are  universal  to  the  species,  but 
not  necessary  to  it.  Thus,  blackness  is  an  attribute  of  a crow,  and,  as  far 
as  we  know,  a universal  one.  But  if  we  were  to  discover  a race  of  white 
birds,  in  other  respects  resembling  crows,  we  should  not  say,  These  are 
not  crows ; we  should  say,  These  are  white  crows.  Crow,  therefore,  does 
not  connote  blackness;  nor,  from  any  of  the  attributes  which  it  does  con- 
note, whether  as  a word  in  popular  use  or  as  a term  of  art,  could  blackness 
be  inferred.  Not  only,  therefore,  can  we  conceive  a white  crow,  but  we 
know  of  no  reason  why  such  an  animal  should  not  exist.  Since,  how- 
ever, none  but  black  crows  are  known  to  exist,  blackness,  in  the  present 
state  of  our  knowledge,  ranks  as  an  accident,  but  an  inseparable  accident, 
of  the  species  crow. 

Separable  Accidents  are  those  which  are  found,  in  point  of  fact,  to  be 
sometimes  absent  from  the  species;  which  are  not  only  not  necessary,  but 
not  even  universal.  They  are  such  as  do  not  belong  to  every  individual 
of  the  species,  but  only  to  some  individuals ; or  if  to  all,  not  at  all  times. 
Thus  the  color  of  a European  is  one  of  the  separable  accidents  of  the  spe- 
cies man,  because  it  is  not  an  attribute  of  all  human  creatures.  Being- 
born,  is  also  (speaking  in  the  logical  sense)  a separable  accident  of  the  spe- 
cies man,  because,  though  an  attribute  of  all  human  beings,  it  is  so  only  at 
one  particular  time.  A fortiori  those  attributes  which  are  not  constant 
even  in  the  same  individual,  as,  to  be  in  one  or  in  another  place,  to  be  hot 
or  cold,  sitting  or  walking,  must  be  ranked  as  separable  accidents. 


DEFINITION. 


105 


CHAPTER  VIII. 

OF  DEFINITION. 

§ 1.  One  necessary  part  of  the  theory  of  Names  and  of  Propositions  re- 
mains to  be  treated  of  in  this  place : the  theory  of  Definitions.  As  being 
the  most  important  of  the  class  of  propositions  which  we  have  character- 
ized as  purely  verbal,  they  have  already  received  some  notice  in  the  chapter 
preceding  the  last.  But  their  fuller  treatment  was  at  that  time  postponed, 
because  definition  is  so  closely  connected  with  classification,  that,  until  the 
nature  of  the  latter  process  is  in  some  measure  understood,  the  former  can 
not  be  discussed  to  much  purpose. 

The  simplest  and  most  correct  notion  of  a Definition  is,  a proposition 
declaratory  of  the  meaning  of  a word ; namely,  either  the  meaning  which 
it  bears  in  common  acceptation,  or  that  which  the  speaker  or  writer,  for 
the  particular  purposes  of  his  discourse,  intends  to  annex  to  it. 

The  definition  of  a word  being  the  proposition  which  enunciates  its 
meaning,  words  which  have  no  meaning  are  unsusceptible  of  definition. 
Proper  names,  therefore,  can  not  be  defined.  A proper  name  being  a mere 
mark  put  upon  an  individual,  and  of  which  it  is  the  characteristic  property 
to  be  destitute  of  meaning,  its  meaning  can  not  of  course  be  declared ; 
though  we  may  indicate  by  language,  as  we  might  indicate  still  more  con- 
veniently by  pointing  with  the  finger,  upon  what  individual  that  particular 
mark  has  been,  or  is  intended  to  be,  put.  It  is  no  definition  of  “John 
Thomson”  to  say  he  is  “the  son  of  General  Thomson for  the  name  John 
Thomson  does  not  express  this.  Neither  is  it  any  definition  of  “John 
Thomson  ” to  say  he  is  “ the  man  now  crossing  the  street.”  These  propo- 
sitions may  serve  to  make  known  who  is  the  particular  man  to  whom  the 
name  belongs,  but  that  may  be  done  still  more  unambiguously  by  pointing 
to  him,  which,  however,  has  not  been  esteemed  one  of  the  modes  of  defi- 
nition. 

In  the  case  of  connotative  names,  the  meaning,  as  has  been  so  often  ob- 
served, is  the  connotation ; and  the  definition  of  a connotative  name,  is  the 
proposition  which  declares  its  connotation.  This  might  be  done  either  di- 
rectly or  indirectly.  The  direct  mode  would  be  by  a proposition  in  this 
form:  “Man”  (or  whatsoever  the  word  may  be)  “is  a name  connoting  such 
and  such  attributes,”  or  “ is  a name  which,  when  predicated  of  any  thing, 
signifies  the  possession  of  such  and  such  attributes  by  that  thing.”  Or 
thus : Man  is  every  thing  which  possesses  such  and  such  attributes : Man 
is'  every  thing  which  possesses  corporeity,  organization,  life,  rationality,  and 
certain  peculiarities  of  external  form. 

This  form  of  definition  is  the  most  precise  and  least  equivocal  of  any ; 
but  it  is  not  brief  enough,  and  is  besides  too  technical  for  common  discourse. 
The  more  usual  mode  of  declaring  the  connotation  of  a name,  is  to  predi- 
cate of  it  another  name  or  names  of  known  signification,  which  connote  the 
same  aggregation  of  attributes.  This  may  be  done  either  by  predicating 
of  the  name  intended  to  be  defined,  another  connotative  name  exactly  syn- 
onymous, as,  “ Man  is  a human  being,”  which  is  not  commonly  accounted  a 


106 


NAMES  AND  PROPOSITIONS. 


definition  at  all;  or  by  predicating  two  or  more  connotative  names,  which 
make  up  among  them  the  whole  connotation  of  the  name  to  be  defined.  In 
this  last  case,  again,  we  may  either  compose  our  definition  of  as  many  con- 
notativc  names  as  there  are  attributes,  each  attribute  being  connoted  by 
one,  as,  Man  is  a corporeal,  organized,  animated,  rational  being,  shaped  so 
and  so ; or  we  employ  names  which  connote  sevei’al  of  the  attributes  at 
once,  as,  Man  is  a rational  animal,  shaped  so  and  so. 

The  definition  of  a name,  according  to  this  view  of  it,  is  the  sum  total 
of  all  the  essential  propositions  which  can  be  framed  with  that  name  for 
their  subject.  All  propositions  the  truth  of  which  is  implied  in  the  name, 
all  those  which  we  are  made  aware  of  by  merely  hearing  the  name,  are  in- 
cluded in  the  definition,  if  complete,  and  may  be  evolved  from  it  without 
the  aid  of  any  other  premises ; whether  the  definition  expresses  them  in 
two  or  three  words,  or  in  a larger  number.  It  is,  therefore,  not  without 
reason  that  Condillac  and  other  writers  have  affirmed  a definition  to  be  an 
analysis.  To  resolve  any  complex  whole  into  the  elements  of  which  it  is 
compounded,  is  the  meaning  of  analysis : and  this  we  do  when  we  replace 
one  word  which  connotes  a set  of  attributes  collectively,  by  two  or  more 
which  connote  the  same  attributes  singly,  or  in  smaller  groups. 

§ 2.  From  this,  however,  the  question  naturally  arises,  in  what  manner 
are  we  to  define  a name  which  connotes  only  a single  attribute : for  in- 
stance, “ white,”  which  connotes  nothing  but  whiteness ; “ rational,”  which 
connotes  nothing  but  the  possession  of  reason.  It  might  seem  that  the 
meaning  of  such  names  could  only  be  declared  in  two  ways ; by  a synony- 
mous term,  if  any  such  can  be  found ; or  in  the  direct  way  already  alluded 
to  : “ White  is  a name  connoting  the  attribute  whiteness.”  Let  us  see, 
however,  whether  the  analysis  of  the  meaning  of  the  name,  that  is,  the 
breaking  down  of  that  meaning  into  several  parts,  admits  of  being  carried 
farther.  Without  at  present  deciding  this  question  as  to  the  word  white, 
it  is  obvious  that  in  the  case  of  rational  some  further  explanation  may  be 
given  of  its  meaning  than  is  contained  in  the  proposition,  “Rational is  that 
which  possesses  the  attribute  of  reason ;”  since  the  attribute  reason  itself 
admits  of  being  defined.  And  here  we  must  turn  our  attention  to  the  def- 
initions of  attributes,  or  rather  of  the  names  of  attributes,  that  is,  of  ab- 
stract names. 

In  regard  to  such  names  of  attributes  as  are  connotative,  and  express 
attributes  of  those  attributes,  there  is  no  difficulty : like  other  connotative 
names,  they  are  defined  by  declaring  their  connotation.  Thus  the  word 
fault  may  be  defined,  “ a quality  productive  of  evil  or  inconvenience.” 
Sometimes,  again,  the  attribute  to  be  defined  is  not  one  attribute,  but  a 
union  of  several : we  have  only,  therefore,  to  put  together  the  names  of  all 
the  attributes  taken  separately,  and  we  obtain  the  definition  of  the  name 
which  belongs  to  them  all  taken  together ; a definition  which  will  corre- 
spond exactly  to  that  of  the  corresponding  concrete  name.  For,  as  we  de- 
fine a concrete  name  by  enumerating  the  attributes  which  it  connotes,  and 
as  the  attributes  connoted  by  a concrete  name  form  the  entire  signification 
of  the  corresponding  abstract  name,  the  same  enumeration  will  serve  for 
the  definition  of  both.  Thus,  if  the  definition  of  a human  being  be  this, 
“ a being,  corporeal,  animated,  rational,  shaped  so  and  so,”  the  definition  of 
humanity  will  be  corporeity  and  animal  life,  combined  with  rationality, 
and  with  such  and  such  a shape. 

When,  on  the  other  hand,  the  abstract  name  does  not  express  a compli- 


DEFINITION. 


107 


cation  of  attributes,  but  a single  attribute,  we  must  remember  that  every 
attribute  is  grounded  on  some  fact  or  phenomenon,  from  which,  and  which 
alone,  it  derives  its  meaning.  To  that  fact  or  phenomenon,  called  in  a for- 
mer chapter  the  foundation  of  the  attribute,  we  must,  therefore,  have  re- 
course for  its  definition.  Now,  the  foundation  of  the  attribute  may  be 
a phenomenon  of  any  degree  of  complexity,  consisting  of  many  different 
parts,  either  co-existent  or  in  succession.  To  obtain  a definition  of  the  attri- 
bute, we  must  analyze  the  phenomenon  into  these  parts.  Eloquence,  for 
example,  is  the  name  of  one  attribute  only ; but  this  attribute  is  grounded 
on  external  effects  of  a complicated  nature,  flowing  from  acts  of  the  person 
to  whom  we  ascribe  the  attribute ; and  by  resolving  this  phenomenon  of 
causation  into  its  two  parts,  the  cause  and  the  effect,  we  obtain  a definition 
of  eloquence,  viz.  the  power  of  influencing  the  feelings  by  speech  or  writing. 

A name,  therefore,  whether  concrete  or  abstract,  admits  of  definition, 
provided  we  are  able  to  analyze,  that  is,  to  distinguish  into  parts,  the  attri- 
bute or  set  of  attributes  which  constitute  the  meaning  both  of  the  concrete 
name  and  of  the  corresponding  abstract : if  a set  of  attributes,  by  enumer- 
ating them ; if  a single  attribute,  by  dissecting  the  fact  or  phenomenon 
(whether  of  perception  or  of  internal  consciousness)  which  is  the  foundation 
of  the  attribute.  But,  further,  even  when  the  fact  is  one  of  our  simple 
feelings  or  states  of  consciousness,  and  therefore  unsusceptible  of  analy- 
sis, the  names  both  of  the  object  and  of  the  attribute  still  admit  of  defini- 
tion ; or  rather,  would  do  so  if  all  our  simple  feelings  had  names.  White- 
ness may  be  defined,  the  property  or  power  of  exciting  the  sensation  of 
white.  A white  object  may  be  defined,  an  object  which  excites  the  sensation 
of  white.  The  only  names  which  are  unsusceptible  of  definition,  because 
their  meaning  is  unsusceptible  of  analysis,  are  the  names  of  the  simple  feel- 
ings themselves.  These  are  in  the  same  condition  as  proper  names.  They 
are  not  indeed,  like  proper  names,  unmeaning ; for  the  words  sensation 
of  white  signify,  that  the  sensation  which  I so  denominate  resembles  other 
sensations  which  I remember  to  have  had  before,  and  to  have  called  by  that 
name.  But  as  we  have  no  words  by  which  to  recall  those  former  sensations, 
except  the  very  word  which  we  seek  to  define,  or  some  other  which,  being 
exactly  synonymous  with  it,  requires  definition  as  much,  words  can  not  un- 
fold the  signification  of  this  class  of  names ; and  we  are  obliged  to  make  a 
direct  appeal  to  the  personal  experience  of  the  individual  whom  we  address. 

§ 3.  Having  stated  what  seems  to  be  the  true  idea  of  a Definition,  I pro- 
ceed to  examine  some  opinions  of  philosophers,  and  some  popular  concep- 
tions on  the  subject,  which  conflict  more  or  less  with  that  idea. 

The  only  adequate  definition  of  a name  is,  as  already  remarked,  one  which 
declares  the  facts,  and  the  whole  of  the  facts,  which  the  name  involves  in 
its  signification.  But  with  most  persons  the  object  of  a definition  does  not 
embrace  so  much  ; they  look  for  nothing  more,  in  a definition,  than  a guide 
to  the  correct  use  of  the  term — a protection  against  applying  -it  in  a man- 
ner inconsistent  with  custom  and  convention.  Any  thing,  therefore,  is  to 
them  a sufficient  definition  of  a term,  which  will  serve  as  a correct  index 
to  what  the  term  c/enotes ; though  not  embracing  the  whole,  and  some- 
times, perhaps,  not  even  any  part,  of  what  it  connotes.  This  gives  rise  to 
two  sorts  of  imperfect,  or  unscientific  definition ; Essential  but  incomplete 
Definitions,  and  Accidental  Definitions,  or  Descriptions.  In  the  former,  a 
connotative  name  is  defined  by  a part  only  of  its  connotation ; in  the  latter, 
by  something  which  forms  no  part  of  the  counotatiou  at  all. 


108 


NAMES  AND  PROPOSITIONS. 


An  example  of  the  first  kind  of  imperfect  definitions  is  the  following : 
Man  is  a rational  animal.  It  is  impossible  to  consider  this  as  a complete 
definition  of  the  word  Man,  since  (as  before  remarked)  if  we  adhered  to  it 
we  should  be  obliged  to  call  the  Houyhnhnms  men  ; but  as  there  happen  to 
be  no  Houyhnhnms,  this  imperfect  definition  is  sufficient  to  mark  out  and 
distinguish  from  all  other  things,  the  objects  at  present  denoted  by  “ man 
all  the  beings  actually  known  to  exist,  of  whom  the  name  is  predicable. 
Though  the  word  is  defined  by  some  only  among  the  attributes  which  it 
connotes,  not  by  all,  it  happens  that  all  known  objects  which  possess  the 
enumerated  attributes,  possess  also  those  which  are  omitted ; so  that  the 
field  of  predication  which  the  word  covers,  and  the  employment  of  it  which 
is  conformable  to  usage,  are  as  well  indicated  by  the  inadequate  definition 
as  by  an  adequate  one.  Such  definitions,  however,  are  always  liable  to  be 
overthrown  by  the  discovery  of  new  objects  in  nature. 

Definitions  of  this  kind  are  what  logicians  have  had  in  view,  when  they 
laid  down  the  rule,  that  the  definition  of  a species  should  be  per  genus  et 
differ entiam.  Differentia  being  seldom  taken  to  mean  the  whole  of  the 
peculiarities  constitutive  of  the  species,  but  some  one  of  those  peculiarities 
only,  a complete  definition  would  be  per  genus  et  dfferentias,  rather  than 
dfferentiam.  It  would  include,  with  the  name  of  the  superior  genus,  not 
merely  some  attribute  which  distinguishes  the  species  intended  to  be  de- 
fined from  all  other  species  of  the  same  genus,  but  all  the  attributes  im- 
plied in  the  name  of  the  species,  which  the  name  of  the  superior  genus 
has  not  already  implied.  The  assertion,  however,  that  a definition' must 
of  necessity  consist  of  a genus  and  differentite,  is  not  tenable.  It  was  early 
remarked  by  logicians,  that  the  summum  genus  in  any  classification,  hav- 
ing no  genus  superior  to  itself,  could  not  be  defined  in  this  manner.  Yet 
we  have  seen  that  all  names,  except  those  of  our  elementary  feelings,  are 
susceptible  of  definition  in  the  strictest  sense ; by  setting  forth  in  words 
the  constituent  parts  of  the  fact  or  phenomenon,  of  which  the  connotation 
of  every  word  is  ultimately  composed. 

§ 4.  Although  the  first  kind  of  imperfect  definition  (which  defines  a con- 
notative  term  by  a part  only  of  what  it  connotes,  but  a part  sufficient  to 
mark  out  correctly  the  boundaries  of  its  denotation),  has  been  considered 
by  the  ancients,  and  by  logicians  in  general,  as  a complete  definition  ; it  has 
always  been  deemed  necessary  that  the  attributes  employed  should  really 
form  part  of  the  connotation ; for  the  rule  was  that  the  definition  must  be 
drawn  from  the  essence  of  the  class ; and  this  would  not  have  been  the  case 
if  it  had  been  in  any  degree  made  up  of  attributes  not  connoted  by  the 
name.  The  second  kind  of  imperfect  definition,  therefore,  in  which  the 
name  of  a class  is  defined  by  any  of  its  accidents — that  is,  by  attributes 
which  are  not  included  in  its  connotation — has  been  rejected  from  the  rank 
of  genuine  Definition  by  all  logicians,  and  has  been  termed  Description. 

This  kind  of  imperfect  definition,  however,  takes  its  rise  from  the  same 
cause  as  the  other,  namely,  the  willingness  to  accept  as  a definition  any  thing 
which,  whether  it  expounds  the  meaning  of  the  name  .or  not,  enables  us  to 
discriminate  the  things  denoted  by  the  name  from  all  other  things,  and  con- 
sequently to  employ  the  term  in  predication  without  deviating  from  estab- 
lished usage.  This  purpose  is  duly  answered  by  stating  any  (no  matter 
what)  of  the  attributes  which  are  common  to  the  whole  of  the  class,  and 
peculiar  to  it ; or  any  combination  of  attributes  which  happens  to  be  pe- 
culiar to  it,  though  separately  each  of  those  attributes  may  be  common  to 


DEFINITION. 


109 


it  with  some  other  things.  It  is  only  necessary  that  the  definition  (or  de- 
scription) thus  formed,  should  be  convertible  with  the  name  which  it  pro- 
fesses to  define ; that  is,  should  be  exactly  co-extensive  with  it,  being  pred- 
icable of  every  thing  of  which  it  is  predicable,  and  of  nothing  of  which  it 
is  not  predicable ; though  the  attributes  specified  may  have  no  connection 
with  those  which  mankind  had  in  view  when  they  formed  or  recognized  the 
class,  and  gave  it  a name.  The  following  are  correct  definitions  of  Man, 
according  to  this  test:  Man  is  a mammiferous  animal,  having  (by  nature) 
two  hands  (for  the  human  species  answers  to  this  description,  and  no  other 
animal  does) : Man  is  an  animal  who  cooks  his  food : Man  is  a featherless 
biped. 

What  would  otherwise  be  a mere  description,  may  be  raised  to  the  rank 
of  a real  definition  by  the  peculiar  purpose  which  the  speaker  or  writer 
has  in  view.  As  was  seen  in  the  preceding  chapter,  it  may,  for  the  ends 
of  a particular  art  or  science,  or  for  the  more  convenient  statement  of  an 
author’s  particular  doctrines,  be  advisable  to  give  to  some  general  name, 
without  altering  its  denotation,  a special  connotation,  different  from  its  or- 
dinary one.  When  this  is  done,  a definition  of  the  name  by  means  of  the 
attributes  which  make  up  the  special  connotation,  though  in  general  a mere 
accidental  definition  or  description,  becomes  on  the  particular  occasion  and 
for  the  particular  purpose  a complete  and  genuine  definition.  This  actual- 
ly occurs  with  respect  to  one  of  the  preceding  examples,  “Man  is  a mam- 
miferous animal  having  two  hands,”  which  is  the  scientific  definition  of 
man,  considered  as  one  of  the  species  in  Cuvier’s  distribution  of  the  animal 
kingdom. 

In  cases  of  this  sort,  though  the  definition  is  still  a declaration  of  the 
meaning  which  in  the  particular  instance  the  name  is  appointed  to  convey, 
it  can  not  be  said  that  to  state  the  meaning  of  the  wore!  is  the  purpose  of 
the  definition.  The  purpose  is  not  to  expound  a name,  but  a classification. 
The  special  meaning  which  Cuvier  assigned  to  the  word  Man  (quite  foreign 
to  its  ordinary  meaning,  though  involving  no  change  in  the  denotation  of 
the  word),  was  incidental  to  a plan  of  arranging  animals  into  classes  on  a 
certain  principle,  that  is,  according  to  a certain  set  of  distinctions.  And 
since  the  definition  of  Man  according  to  the  ordinary  connotation  of  the 
word,  though  it  would  have  answered  every  other  purpose  of  a definition, 
would  not  have  pointed  out  the  place  which  the  species  ought  to  occupy 
in  that  particular  classification ; he  gave  the  word  a special  connotation, 
that  he  might  be  able  to  define  it  by  the  kind  of  attributes  on  which,  for 
reasons  of  scientific  convenience,  he  had  resolved  to  found  his  division  of 
animated  nature. 

Scientific  definitions,  whether  they  are  definitions  of  scientific  terms,  or 
of  common  terms  used  in  a scientific  sense,  are  almost  always  of  the  kind 
last  spoken  of:  their  main  purpose  is  to  serve  as  the  landmarks  of  scien- 
tific classification.  And  since  the  classifications  in  any  science  are  con- 
tinually modified  as  scientific  knowledge  advances,  the  definitions  in  the 
sciences  are  also  constantly  varying.  A striking  instance  is  afforded  by 
the  words  Acid  and  Alkali,  especially  the  former.  As  experimental  dis- 
covery advanced,  the  substances  classed  with  acids  have  been  constantly 
multiplying,  and  by  a natural  consequence  the  attributes  connoted  by  the 
word  have  receded  and  become  fewer.  At  first  it  connoted  the  attributes, 
of  combining  with  an  alkali  to  form  a neutral  substance  (called  a salt) ; 
being  compounded  of  a base  and  oxygen ; causticity  to  the  taste  and  touch  ; 
fluidity,  etc.  The  true  analysis  of  muriatic  acid,  into  chlorine  and  hydro- 


110 


NAMES  AND  PROPOSITIONS. 


gen,  caused  the  second  property,  composition  from  a base  and  oxygen,  to 
be  excluded  from  the  connotation.  The  same  discovery  fixed  the  attention 
of  chemists  upon  hydrogen  as  an  important  element  in  acids;  and  more 
recent  discoveries  having  led  to  the  recognition  of  its  presence  in  sulphuric, 
nitric,  and  many  other  acids,  where  its  existence  was  not  previously  sus- 
pected, there  is  now  a tendency  to  include  the  presence  of  this  element  in 
the  connotation  of  the  word.  But  carbonic  acid,  silica,  sulphurous  acid, 
have  no  hydrogen  in  their  composition ; that  property  can  not,  therefore, 
be  connoted  by  the  term,  unless  those  substances  are  no  longer  to  be  con- 
sidered acids.  Causticity  and  fluidity  have  long  since  been  excluded  from 
the  characteristics  of  the  class,  by  the  inclusion  of  silica  and  many  other 
substances  in  it;  and  the  formation  of  neutral  bodies  by  combination  with 
alkalis,  together  with  such  electro-chemical  peculiarities  as  this  is  supposed 
to  imply,  are  now  the  only  differentiae  which  form  the  fixed  connotation  of 
the  word  Acid,  as  a term  of  chemical  science. 

What  is  true  of  the  definition  of  any  term  of  science,  is  of  course  true  of 
the  definition  of  a science  itself ; and  accordingly  (as  observed  in  the  In- 
troductory Chapter  of  this  work),  the  definition  of  a science  must  neces- 
sarily be  progressive  and  provisional.  Any  extension  of  knowledge  or  al- 
teration in  the  current  opinions  respecting  the  subject-matter,  may  lead  to 
a change  more  or  less  extensive  in  the  particulars  included  in  the  science ; 
and  its  composition  being  thus  altered,  it  may  easily  happen  that  a different 
set  of  characteristics  will  be  found  better  adapted  as  differentiae  for  defin- 
ing its  name. 

In  the  same  manner  in  which  a special  or  technical  definition  has  for  its 
object  to  expound  the  artificial  classification  out  of  which  it  grows;  the 
Aristotelian  logicians  seem  to  have  imagined  that  it  was  also  the  business 
of  ordinary  definition  to  expound  the  ordinary,  and  what  they  deemed  the 
natural,  classification  of  things,  namely,  the  division  of  them  into  Kinds ; 
and  to  show  the  place  which  each  Kind  occupies,  as  superior,  collateral,  or 
subordinate,  among  other  Kinds.  This  notion  would  account  for  the  rule 
that  all  definition  must  necessarily  be  per  genus  et  dfferentiam,  and  would 
also  explain  why  a single  differentia  was  deemed  sufficient.  But  to  ex- 
pound, or  express  in  words,  a distinction  of  Kind,  has  already  been  shown 
to  be  an  impossibility : the  very  meaning  of  a Kind  is,  that  the  properties 
which  distinguish  it  do  not  grow  out  of  one  another,  and  can  not  therefore 
be  set  forth  in  words,  even  by  implication,  otherwise  than  by  enumerating 
them  all : and  all  are  not  known,  nor  are  ever  likely  to  be  so.  It  is  idle, 
therefore,  to  look  to  this  as  one  of  the  purposes  of  a definition : while,  if  it 
be  only  required  that  the  definition  of  a Kind  should  indicate  what  kinds 
include  it  or  are  included  by  it,  any  definitions  which  expound  the  connota- 
tion of  the  names  will  do  this : for  the  name  of  each  class  must  necessarily 
connote  enough  of  its  properties  to  fix  the  boundaries  of  the  class.  If  the 
definition,  therefore,  be  a full  statement  of  the  connotation,  it  is  all  that  a 
definition  can  be  required  to  be.* 

* Professor  Bain,  in  his  Logic,  takes  a peculiar  view  of  Definition.  He  holds  (i.,  71)  with 
the  present  work,  that  “the  definition  in  its  full  import,  is  the  sum  of  all  the  properties  con- 
noted by  the  name;  it  exhausts  the  meaning  of  a word.”  But  he  regards  the  meaning  of  a 
general  name  as  including,  not  indeed  all  the  common  properties  of  the  class  named,  but  all 
of  them  that  are  ultimate  properties,  not  resolvable  into  one  another.  “The  enumeration  of 
the  attributes  of  oxygen,  of  gold,  of  man,  should  be  an  enumeration  of  the  final  (so  far  as  can 
be  made  out),  the  underivable,  powers  or  functions  of  each,”  and  nothing  less  than  this  is  a 
complete  Definition  (i.,  75).  An  independent  property,  not  derivable  frpm  other  properties, 
even  if  previously  unknown,  yet  as  soon  as  discovered  becomes,  according  to  him,  part  of  the 


DEFINITION. 


Ill 


§ 5.  Of  the  two  incomplete  and  popular  modes  of  definition,  and  in  what 
they  differ  from  the  complete  or  philosophical  mode,  enough  has  now  been 
said.  We  shall  next  examine  an  ancient  doctrine,  once  generally  prevalent 
and  still  by  no  means  exploded,  which  I regard  as  the  source  of  a great  part 
of  the  obscurity  hanging  over  some  of  the  most  important  processes  of  the 
understanding  in  the  pursuit  of  truth.  According  to  this,  the  definitions 
of  which  we  have  now  treated  are  only  one  of  two  sorts  into  which  defini- 
tions may  be  divided,  viz.,  definitions  of  names,  and  definitions  of  things. 
The  former  are  intended  to  explain  the  meaning  of  a term ; the  latter,  the 
nature  of  a thing;  the  last  being  incomparably  the  most  important. 

This  opinion  was  held  by  the  ancient  philosophers,  and  by  their  follow- 
ers, with  the  exception  of  the  Nominalists;  but  as  the  spirit  of  modern 
metaphysics,  until  a recent  period,  has  been  on  the  whole  a Nominalist 
spirit,  the  notion  of  definitions  of  things  has  been  to  a certain  extent  in 
abeyance,  still  continuing,  however,  to  breed  confusion  in  logic,  by  its  con- 
sequences indeed  rather  than  by  itself.  Yet  the  doctrine  in  its  own  proper 
form  now  and  then  breaks  out,  and  has  appeared  (among  other  places) 
where  it  was  scarcely  to  be  expected,  in  a justly  admired  word,  Archbishop 
Whately’s Logic*  In  a review  of  that  work  published  by  me  in  the  TVest- 

meaning  of  the  term,  and  should  he  included  in  the  definition.  “When  we  are  told  that  dia- 
mond, which  we  know  to  be  a transparent,  glittering,  hard,  and  high-priced  substance,  is  com- 
posed of  carbon,  and  is  combustible,  we  must  put  these  additional  properties  on  the  same  level 
as  the  rest;  to  us  they  are  henceforth  connoted  by  the  name”(i.,  73).  Consequently  the 
propositions  that  diamond  is  composed  of  carbon,  and  that  it  is  combustible,  are  regarded  by 
Mr.  Bain  as  merely  verbal  propositions.  He  carries  this  doctrine  so  far  as  to  say  that  unless 
mortality  can  be  shown  to  be  a consequence  of  the  ultimate  laws  of  animal  organization,  mor- 
tality is  connoted  by  man,  and  “ Man  is  Mortal  ” is  a merely  verbal  proposition.  And  one  of 
the  peculiarities  (I  think  a disadvantageous  peculiarity)  of  his  able  and  valuable  treatise,  is 
the  large  number  of  propositions  requiring  proof,  and  learned  by  experience,  which,  in  con- 
formity with  this  doctrine,  he  considers  as  not  real,  but  verbal,  propositions. 

The  objection  I have  to  this  language  is  that  it  confounds,  or  at  least  confuses,  a much 
more  important  distinction  than  that  which  it  draws.  The  only  reason  for  dividing  Proposi- 
tions into  real  and  verbal,  is  in  order  to  discriminate  propositions  which  convey  information 
about  facts,  from  those  which  do  not.  A proposition  which  affirms  that  an  object  has  a given 
attribute,  while  designating  the  object  by  a name  which  already  signifies  the  attribute,  adds 
no  information  to  that  which  was  already  possessed  by  all  who  understood  the  name.  But 
when  this  is  said,  it  is  implied  that,  by  the  signification  of  a name,  is  meant  the  signification 
attached  to  it  in  the  common  usage  of  life.  I can  not  think  we  ought  to  say  that  the  meaning 
of  a word  includes  matters  of  fact  which  are  unknown  to  every  person  who  uses  the  word  un- 
less he  has  learned  them  by  special  study  of  a particular  department  of  Nature  ; or  that  because 
a few  persons  are  aware  of  these  matters  of  fact,  the  affirmation  of  them  is  a proposition  con- 
veying no  information.  I hold  that  (special  scientific  connotation  apart)  a name  means,  or 
connotes,  only  the  properties  which  it  is  a mark  of  in  the  general  mind ; and  that  in  the  case 
of  any  additional  properties,  however  uniformly  found  to  accompany  these,  it  remains  possible 
that  a thing  which  did  not  possess  the  properties  might  still  be  thought  entitled  to  the  name. 
Ruminant,  according  to  Mr.  Bain’s  use  of  language,  connotes  cloven-hoofed,  since  the  two 
properties  are  always  found  together,  and  no  connection  has  ever  been  discovered  between 
them : but  ruminant  does  not  mean  cloven-hoofed ; and  were  an  animal  to  be  discovered 
which  chews  the  cud,  but  has  its  feet  undivided,  I venture  to  say  that  it  would  still  be  called 
ruminant. 

* In  the  fuller  discussion  which  Archbishop  Whately  has  given  to  this  subject  in  his  later 
editions,  he  almost  ceases  to  regard  the  definitions  of  names  and  those  of  things  as,  in  any  im- 
portant sense,  distinct.  He  seems  (9th  ed.,  p.  145)  to  limit  the  notion  of  a Real  Definition  to 
one  which  “explains  any  thing  more  of  the  nature  of  the  thing  than  is  implied  in  the  name 
(including  under  the  word  “implied,”  not  only  what  the  name  connotes,  but  every  thing  which 
can  be  deduced  by  reasoning  from  the  attributes  connoted).  Even  this,  as  he  adds,  is  usually 
called  not  a Definition,  but  a Description  ; and  (ns  it  seems  to  me)  rightly  so  called.  A De- 
scription, I conceive,  can  only  be  ranked  among  Definitions,  when  taken  (as  in  the  case  of  the 
zoological  definition  of  man)  to  fulfill  the  true  office  of  a Definition,  by  declaring  the  connota- 
tion given  to  a word  in  some  special  use,  as  a term  of  science  or  art : which  special  conno- 


112 


NAMES  AND  PROPOSITIONS. 


minster  Review  for  January,  1S28,  and  containing  some  opinions  which  I 
no  longer  entertain,  I find  the  following  observations  on  the  question  now 
before  us ; observations  with  which  my  present  view  of  that  question  is 
still  sufficiently  in  accordance. 

“The  distinction  between  nominal  and  real  definitions,  between  defini- 
tions of  words  and  what  are  called  definitions  of  things,  though  conforma- 
ble to  the  ideas  of  most  of  the  Aristotelian  logicians,  can  not,  as  it  appears 
to  us,  be  maintained.  We  apprehend  that  no  definition  is  ever  intended  to 
4 explain  and  unfold  the  nature  of  a thing.’  It  is  some  confirmation  of  our 
opinion,  that  none  of  those  writers  who  have  thought  that  there  were  defini- 
tions of  things,  have  ever  succeeded  in  discovering  any  criterion  by  which 
the  definition  of  a thing  can  be  distinguished  from  any  other  proposition 
relating  to  the  thing.  The  definition,  they  say,  unfolds  the  nature  of  the 
thing:  but  no  definition  can  unfold  its  whole  nature;  and  every  proposi- 
tion in  which  any  quality  whatever  is  predicated  of  the  thing,  unfolds  some 
part  of  its  nature.  The  true  state  of  the  case  we  take  to  be  this.  All 
definitions  are  of  names,  and  of  names  only ; but,  in  some  definitions,  it  is 
clearly  apparent,  that  nothing  is  intended  except  to  explain  the  meaning  of 
the  word ; while  in  others,  besides  explaining  the  meaning  of  the  word,  it 
is  intended  to  be  implied  that  there  exists  a thing,  corresponding  to  the 
word.  Whether  this  be  or  be  not  implied  in  any  given  case,  can  not  be 
collected  from  the  mere  form  of  the  expression.  4 A centaur  is  an  animal 
with  the  upper  parts  of  a man  and  the  lower  parts  of  a horse,’  and  4 A tri- 
angle is  a rectilineal  figure  with  three  sides,’  are,  in  form,  expressions  pre- 
cisely similar ; although  in  the  former  it  is  not  implied  that  any  thing,  con- 
formable to  the  term,  really  exists,  while  in  the  latter  it  is ; as  may  be  seen 
by  substituting  in  both  definitions,  the  word  means  for  is.  In  the  first 
expression,  4 A centaur  means  an  animal,’  etc.,  the  sense  would  remain  un- 
changed : in  the  second, 4 A triangle  means,’  etc.,  the  meaning  would  be  al- 
tered, since  it  would  be  obviously  impossible  to  deduce  any  of  the  truths 
of  geometry  from  a proposition  expressive  only  of  the  manner  in  which  we 
intend  to  employ  a particular  sign. 

“ There  are,  therefore,  expressions,  commonly  passing  for  definitions, 
which  include  in  themselves  more  than  the  mere  explanation  of  the  meaning 
of  a term.  But  it  is  not  correct  to  call  an  expression  of  this  sort  a peculiar 
kind  of  definition.  Its  difference  from  the  other  kind  consists  in  this,  that 
it  is  not  a definition,  but  a definition  and  something  more.  The  definition 
above  given  of  a triangle,  obviously  comprises  not  one,  but  two  proposi- 
tions, perfectly  distinguishable.  The  one  is,  4 There  may  exist  a figure, 
bounded  by  three  straight  lines ;’  the  other, 4 And  this  figure  may  be  termed 
a triangle.’  The  former  of  these  propositions  is  not  a definition  at  all:  the 

tation  of  course  would  not  be  expressed  by  the  proper  definition  of  the  word  in  its  ordinary 
employment. 

Mr.  De  Morgan,  exactly  reversing  the  doctrine  of  Archbishop  Whately,  understands  by  a 
Real  Definition  one  which  contains  less  than  the  Nominal  Definition,  provided  only  that  what 
it  contains  is  sufficient  for  distinction.  “By  real  definition  I mean  such  an  explanation  of 
the  word,  be  it  the  whole  of  the  meaning  or  only  part,  as  will  be  sufficient  to  separate  the 
things  contained  under  that  word  from  all  others.  Thus  the  following,  I believe,  is  a complete 
definition  of  an  elephant : An  animal  which  naturally  drinks  by  drawing  the  water  into  its 
nose,  and  then  spurting  it  into  its  mouth.” — Formal  Logic , p.  36.  Mr.  De  Morgan’s  gen- 
eral proposition  and  his  example  are  at  variance ; for  the  peculiar  mode  of  drinking  of  the 
elephant  certainly  forms  no  part  of  the  meaning  of  the  word  elephant.  It  could  not  be  said, 
because  a person  happened  to  be  ignorant  of  this  property,  that  he  did  not  know  what  an 
elephant  means. 


DEFINITION. 


113 


latter  is  a mere  nominal  definition,  or  explanation  of  the  use  and  applica- 
tion of  a term.  The  first  is  susceptible  of  truth  or  falsehood,  and  may 
therefore  be  made  the  foundation  of  a train  of  reasoning.  The  latter  can 
neither  be  true  nor  false;  the  only  character  it  is  susceptible  of  is  that  of 
conformity  or  disconformity  to  the  ordinary  usage  of  language.” 

There  is  a real  distinction,  then,  between  definitions  of  names,  and  what 
are  erroneously  called  definitions  of  things ; but  it  is,  that  the  latter,  along 
with  the  meaning  of  a name,  covertly  asserts  a matter  of  fact.  This  covert 
assertion  is  not  a definition,  but  a postulate.  The  definition  is  a mere  iden- 
tical proposition,  which  gives  information  only  about  the  use  of  language, 
and  from  which  no  conclusions  affecting  matters  of  fact  can  possibly  be 
drawn.  The  accompanying  postulate,  on  the  other  hand,  affirms  a fact, 
which  may  lead  to  consequences  of  every  degree  of  importance.  It  affirms 
the  actual  or  possible  existence  of  Things  possessing  the  combination  of 
attributes  set  forth  in  the  definition;  and  this,  if  true,  may  be  foundation 
sufficient  on  which  to  build  a whole  fabric  of  scientific  truth. 

We  have  already  made,  and  shall  often  have  to  repeat,  the  remark,  that 
the  philosophers  who  overthrew  Realism  by  no  means  got  rid  of  the  con- 
sequences of  Realism,  but  retained  long  afterward,  in  their  own  philosophy, 
numerous  propositions  which  could  only  have  a rational  meaning  as  part 
of  a Realistic  system.  It  had  been  handed  down  from  Aristotle,  and  prob- 
ably from  earlier  times,  as  an  obvious  truth,  that  the  science  of  Geometry 
is  deduced  from  definitions.  This,  so  long  as  a definition  was  considered 
to  be  a proposition  “ unfolding  the  nature  of  the  thing,”  did  well  enough. 
But  Hobbes  followed,  and  rejected  utterly  the  notion  that  a definition  de- 
clares the  nature  of  the  thing,  or  does  any  thing  but  state  the  meaning  of 
a name;  yet  he  continued  to  affirm  as  broadly  as  any  of  his  predecessors, 
that  the  dpyal,  principia,  or  original  premises  of  mathematics,  and  even  of 
all  science,  are  definitions ; producing  the  singular  paradox,  that  systems 
of  scientific  truth,  nay,  all  truths  whatever  at  which  we  arrive  by  reasoning, 
are  deduced  from  the  arbitrary  conventions  of  mankind  concerning  the  sig- 
nification of  words. 

To  save  the  credit  of  the  doctrine  that  definitions  are  the  premises  of 
scientific  knowledge,  the  proviso  is  sometimes  added,  that  they  are  so  only 
under  a certain  condition,  namely,  that  they  be  framed  conformably  to  the 
phenomena  of  nature;  that  is,  that  they  ascribe  such  meanings  to  terms  as 
shall  suit  objects  actually  existing.  But  this  is  only  an  instance  of  the  at- 
tempt so  often  made,  to  escape  from  the  necessity  of  abandoning  old  lan- 
guage after  the  ideas  which  it  expresses  have  been  exchanged  for  contrary 
ones.  From  the  meaning  of  a name  (we  are  told)  it  is  possible  to  infer 
physical  facts,  provided  the  name  has  corresponding  to  it  an  existing  thing. 
But  if  this  proviso  be  necessary,  from  which  of  the  two  is  the  inference 
really  drawn?  From  the  existence  of  a thing  having  the  properties,  or 
from  the  existence  of  a name  meaning  them? 

Take,  for  instance,  any  of  the  definitions  laid  down  as  premises  in  Euclid’s 
Elements;  the  definition,  let  us  say,  of  a circle.  This,  being  analyzed,  con- 
sists of  two  propositions ; the  one  an  assumption  with  respect  to  a matter 
of  fact,  the  other  a genuine  definition.  “ A figure  may  exist,  having  all  the 
points  in  the  line  which  bounds  it  equally  distant  from  a single  point  with- 
in it “ Any  figure  possessing  this  property  is  called  a circle.”  Let  us 
look  at  one  of  the  demonstrations  which  are  said  to  depend  on  this  defini- 
tion, and  observe  to  which  of  the  two  propositions  contained  in  it  the  dem- 
onstration really  appeals.  “ About  the  centre  A,  describe  the  circle  B C D.” 

8 


114 


NAMES  AND  PROPOSITIONS. 


Here  is  an  assumption  that  a figure,  such  as  the  definition  expresses,  may 
be  described;  which  is  no  other  than  the  postulate,  or  covert  assumption, 
involved  in  the  so-called  definition.  But  whether  that  figure  be  called  a 
circle  or  not  is  quite  immaterial.  The  purpose  would  be  as  well  answered, 
in  all  respects  except  brevity,  were  we  to  say,  “ Through  the  point  B,  draw 
a line  returning  into  itself,  of  which  every  point  shall  be  at  an  equal  dis- 
tance from  the  point  A.”  By  this  the  definition  of  a circle  would  be  got 
rid  of,  and  rendered  needless ; but  not  the  postulate  implied  in  it ; without 
that  the  demonstration  could  not  stand.  The  circle  being  now  described, 
let  us  proceed  to  the  consequence.  “ Since  B C D is  a circle,  the  radius 
B A is  equal  to  the  radius  C A.”  B A is  equal  to  C A,  not  because  BCD 
is  a circle,  but  because  B C D is  a figure  with  the  radii  equal.  Our  war- 
rant for  assuming  that  such  a figure  about  the  centre  A,  with  the  radius 
B A,  may  be  made  to  exist,  is  the  postulate.  Whether  the  admissibility 
of  these  postulates  rests  on  intuition,  or  on  proof,  may  be  a matter  of  dis- 
pute ; but  in  either  case  they  are  the  premises  on  which  the  theorems  de- 
pend ; and  while  these  are  retained  it  would  make  no  difference  in  the  cer- 
tainty of  geometrical  truths,  though  every  definition  in  Euclid,  and  every 
technical  term  therein  defined,  were  laid  aside. 

It  is,  perhaps,  superfluous  to  dwell  at  so  much  length  on  what  is  so  near- 
ly self-evident;  but  when  a distinction,  obvious  as  it  may  appear,  has  been 
confounded,  and  by  powerful  intellects,  it  is  better  to  say  too  much  than 
too  little  for  the  purpose  of  rendering  such  mistakes  impossible  in  future. 
I will,  therefore  detain  the  reader  while  I point  out  one  of  the  absurd  con- 
sequences flowing  from  the  supposition  that  definitions,  as  such,  are  the 
premises  in  any  of  our  reasonings,  except  such  as  relate  to  words  only.  If 
this  supposition  were  true,  we  might  argue  correctly  from  true  premises, 
and  arrive  at  a false  conclusion.  We  should  only  have  to  assume  as  a 
premise  the  definition  of  a nonentity;  or  rather  of  a name  which  has  no 
entity  corresponding  to  it.  Let  this,  for  instance,  be  our  definition  : 

A dragon  is  a serpent  breathing  flame. 

This  proposition,  considered  only  as  a definition,  is  indisputably  correct. 
A dragon  is  a serpent  breathing  flame : the  word  means  that.  The  tacit 
assumption,  indeed  (if  there  were  any  such  understood  assertion),  of  the  ex- 
istence of  an  object  with  properties  corresponding  to  the  definition,  would, 
in  the  present  instance,  be  false.  Out  of  this  definition  we  may  carve  the 
premises  of  the  following  syllogism : 

A dragon  is  a thing  which  breathes  flame: 

A dragon  is  a serpent : 

From  which  the  conclusion  is, 

Therefore  some  serpent  or  serpents  breathe  flame: 
an  unexceptionable  syllogism  in  the  first  mode  of  the  third  figure,  in  which 
both  premises  are  true  and  yet  the  conclusion  false;  which  every  logician 
knows  to  be  an  absurdity.  The  conclusion  being  false  and  the  syllogism 
correct,  the  premises  can  not  be  true.  But  the  premises,  considered  as 
parts  of  a definition,  are  true.  Therefore,  the  premises  considered  as  parts 
of  a definition  can  not  be  the  real  ones.  The  real  premises  must  be — 

A dragon  is  a really  existing  thing  which  breathes  flame: 

A dragon  is  a really  existing  serpent : 
which  implied  premises  being  false,  the  falsity  of  the  conclusion  presents 
no  absurdity. 

If  we  would  determine  what  conclusion  follows  from  the  same  ostensible 
premises  when  the  tacit  assumption  of  real  existence  is  left  out,  let  us,  ac- 


DEFINITION. 


115 


cording  to  the  recommendation  in  a previous  page,  substitute  means  for  is. 
We  then  have — 

Dragon  is  a word  meaning  a thing  which  breathes  flame : 

Dra  gon  is  a word  meaning  a serpent : 

From  which  the  conclusion  is, 

Some  word  or  words  which  mean  a serpent,  also  mean  a thing  which 
breathes  flame : 

where  the  conclusion  (as  well  as  the  premises)  is  true,  and  is  the  only  kind 
of  conclusion  which  can  ever  follow  from  a definition,  namely,  a proposition 
relating  to  the  meaning  of  words. 

There  is  still  another  shape  into  which  we  may  transform  this  syllogism. 
We  may  suppose  the  middle  term  to  be  the  designation  neither  of  a thing 
nor  of  a name,  but  of  an  idea.  We  then  have — 

The  idea  of  a dragon  is  an  idea  of  a thing  which  breathes  flame : 
The  idea  of  a dragon  is  an  idea  of  a serpent : 

Therefore,  there  is  an  idea  of  a serpent,  which  is  an  idea  of  a 
thing  breathing  flame. 

Here  the  conclusion  is  true,  and  also  the  premises ; but  the  premises  are 
not  definitions.  They  are  propositions  affirming  that  an  idea  existing  in 
the  mind,  includes  certain  ideal  elements.  The  truth  of  the  conclusion  fol- 
lows from  the  existence  of  the  psychological  phenomenon  called  the  idea  of 
a dragon  ; and  therefore  still  from  the  tacit  assumption  of  a matter  of  fact.* 

When,  as  in  this  last  syllogism,  the  conclusion  is  a proposition  respecting 
an  idea,  the  assumption  on  which  it  depends  may  be  merely  that  of  the  ex- 
istence of  an  idea.  But  when  the  conclusion  is  a proposition  concerning  a 
Thing,  the  postulate  involved  in  the  definition  which  stands  as  the  apparent 
premise,  is  the  existence  of  a thing  conformable  to  the  definition,  and  not 
merely  of  an  idea  conformable  to  it.  This  assumption  of  real  existence  we 
always  convey  the  impression  that  we  intend  to  make,  when  we  profess  to 
define  any  name  which  is  already  known  to  be  a name  of  really  existing 
objects.  On  this  account  it  is,  that  the  assumption  was  not  necessarily 
implied  in  the  definition  of  a dragon,  while  there  was  no  doubt  of  its  be- 
ing included  in  the  definition  of  a circle. 

* In  the  only  attempt  which,  so  far  as  I know,  has  been  made  to  refute  the  preceding  argu- 
mentation, it  is  maintained  that  in  the  first  form  of  the  syllogism, 

A dragon  is  a thing  which  breathes  flame, 

A dragon  is  a seipent, 

Therefore  some  serpent  or  serpents  breathe  flame, 

“there  is  just  as  much  truth  in  the  conclusion  as  there  is  in  the  premises,  or  rather,  no  more 
in  the  latter  than  in  the  former.  If  the  general  name  serpent  includes  both  real  and  imaginary 
5617)6013,  there  is  no  falsity  in  the  conclusion  ; if  not,  there  is  falsity  in  the  minor  premise.” 

Let  us,  then,  try  to  set  out  the  syllogism  on  the  hypothesis  that  the  name  serpent  includes 
imaginary  serpents.  We  shall  find  that  it  is  now  necessary  to  alter  the  predicates  ; for  it  can 
not  be  asserted  that  an  imaginary  creature  breathes  flame ; in  predicating  of  it  such  a fact,  we 
assert  by  the  most  positive  implication  that  it  is  real,  and  not  imaginary.  The  conclusion  must 
run  thus,  “Some  serpent  or  serpents  either  do  or  are  imagined  to  breathe  flame.”  And  to 
prove  this  conclusion  by  the  instance  of  dragons,  the  premises  must  be,  A dragon  is  imagined 
as  breathing  flame.  A dragon  is  a (real  or  imaginary)  serpent : from  which  it  undoubtedly 
follows,  that  there  are  serpents  which  are  imagined  to  breathe  flame ; but  the  major  premise 
is  not  a definition,  nor  part  of  a definition ; which  is  all  that  I am  concerned  to  prove. 

Let  us  now  examine  the  other  assertion — that  if  the  word  serpent  stands  for  none  but  real 
serpents,  the  minor  premise  (a  dragon  is  a serpent)  is  false.  This  is  exactly  what  I have  my- 
self said  of  the  premise,  considered  as  a statement  of  fact : but  it  is  not  false  as  part  of  the 
definition  of  a dragon ; and  since  the  premises,  or  one  of  them,  must  be  false  (the  conclusion 
being  so),  the  real  premise  can  not  be  the  definition,  which  is  true,  but  the  statement  of  fact, 
which  is  false. 


116 


NAMES  AND.  PROPOSITIONS. 


§ 6.  One  of  the  circumstances  which  have  contributed  to  keep  up  the 
notion,  that  demonstrative  truths  follow  from  definitions  rather  than  from 
the  postulates  implied  in  those  definitions,  is,  that  the  postulates,  even  in 
those  sciences  which  are  considered  to  surpass  all  others  in  demonstrative 
certainty,  are  not  always  exactly  true.  It  is  not  true  that  a circle  exists,  or 
can  be  described,  which  has  all  its  radii  exactly  equal.  Such  accuracy  is 
ideal  only;  it  is  not  found  in  nature,  still  less  can  it  be  realized  by  art. 
People  had  a difficulty,  therefore,  in  conceiving  that  the  most  certain  of  all 
conclusions  could  rest  on  premises  which,  instead  of  being  certainly  true, 
are  certainly  not  true  to  the  full  extent  asserted.  This  apparent  paradox 
will  be  examined  when  we  come  to  treat  of  Demonstration;  where  we  shall 
be  able  to  show  that  as  much  of  the  postulate  is  true,  as  is  required  to  sup- 
port as  much  as  is  true  of  the  conclusion.  Philosophers,  however,  to  whom 
this  view  had  not  occurred,  or  whom  it  did  not  satisfy,  have  thought  it  in- 
dispensable that  there  should  be  found  in  definitions  something  more  cer- 
tain, or  at  least  more  accurately  true,  than  the  implied  postulate  of  the  real 
existence  of  a corresponding  object.  And  this  something  they  flattered 
themselves  they  had  found,  when  they  laid  it  down  that  a definition  is  a 
statement  and  analysis  not  of  the  mere  meaning  of  a word,  nor  yet  of  the 
nature  of  a thing,  but  of  an  idea.  Thus,  the  proposition,  “A  circle  is  a 
plane  figure  bounded  by  a line  all  the  points  of  which  are  at  an  equal  dis- 
tance from  a given  point  within  it,”  was  considered  by  them,  not  as  an  as- 
sertion that  any  real  circle  has  that  property  (which  would  not  be  exactly 
true),  but  that  we  conceive  a circle  as  having  it ; that  our  abstract  idea  of 
a circle  is  an  idea  of  a figure  with  its  radii  exactly  equal. 

Conformably  to  this  it  is  said,  that  the  subject-matter  of  mathematics, 
and  of  every  other  demonstrative  science,  is  not  things  as  they  really  exist, 
but  abstractions  of  the  mind.  A geometrical  line  is  a line  without  breadth  ; 
but  no  such  line  exists  in  nature;  it  is  a notion  merely  suggested  to  the 
mind  by  its  experience  of  nature.  The  definition  (it  is  said)  is  a definition 
of  this  mental  line,  not  of  any  actual  line : and  it  is  only  of  the  mental  line, 
not  of  any  line  existing  in  nature,  that  the  theorems  of  geometry  are  ac- 
curately true. 

Allowing  this  doctrine  respecting  the  nature  of  demonstrative  truth  to 
be  correct  (which,  in  a subsequent  place,  I shall  endeavor  to  prove  that  it 
is  not) ; even  on  that  supposition,  the  conclusions  which  seem  to  follow 
from  a definition,  do  not  follow  from  the  definition  as  such,  but  from  an 
implied  postulate.  Even  if  it  be  true  that  there  is  no  object  in  nature  an- 
swering to  the  definition  of  a line,  and  that  the  geometrical  properties  of 
lines  are  not  true  of  any  lines  in  nature,  but  only  of  the  idea  of  a line;  the 
definition,  at  all  events,  postulates  the  real  existence  of  such  an  idea : it  as- 
sumes that  the  mind  can  frame,  or  rather  has  framed,  the  notion  of  length 
without  breadth,  and  without  any  other  sensible  property  whatever.  To 
me,  indeed,  it  appears  that  the  mind  can  not  form  any  such  notion ; it  can 
not  conceive  length  without  breadth;  it  can  only,  in  contemplating  objects, 
attend  to  their  length,  exclusively  of  their  other  sensible  qualities,  and  so 
determine  what  properties  may  be  predicated  of  them  in  virtue  of  their 
length  alone.  If  this  be  true,  the  postulate  involved  in  the  geometrical 
definition  of  a line,  is  the  real  existence,  not  of  length  without  breadth,  but 
merely  of  length,  that  is,  of  long  objects.  This  is  quite  enough  to  support 
all  the  truths  of  geometry,  since  every  property  of  a geometrical  line  is 
really  a property  of  all  physical  objects  in  so  far  as  possessing  length.  But 
even  what  I hold  to  be  the  false  doctrine  on  the  subject,  leaves  the  conclu- 


DEFINITION. 


117 


sion  that  our  reasonings  are  grounded  on  the  matters  of  fact  postulated  in 
definitions,  and  not  on  the  definitions  themselves,  entirely  unaffected;  and 
accordingly  this  conclusion  is  one  which  I have  in  common  with  Dr.  Whe- 
well,  in  his  Philosophy  of  the  Inductive  Sciences:  though,  on  the  nature 
of  demonstrative  truth,  Dr.  Whewell’s  opinions  are  greatly  at  variance  with 
mine.  And  here,  as  in  many  other  instances,  I gladly  acknowledge  that  his 
writings  are  eminently  serviceable  in  clearing  from  confusion  the  initial 
steps  in  the  analysis  of  the  mental  processes,  even  where  his  views  respect- 
ing the  ultimate  analysis  are  such  as  (though  with  unfeigned  respect)  I can 
not  but  regard  as  fundamentally  erroneous. 

§ 7.  Although,  according  to  the  opinion  here  presented,  Definitions  are 
properly  of  names  only,  and  not  of  things,  it  does  not  follow  from  this  that 
definitions  are  arbitrary.  How  to  define  a name,  may  not  only  be  an  in- 
quiry of  considerable  difficulty  and  intricacy,  but  may  involve  considera- 
tions going  deep  into  the  nature  of  the  things  which  are  denoted  by  the 
name.  Such,  for  instance,  are  the  inquiries  which  form  the  subjects  of  the 
most  important  of  Plato’s  Dialogues;  as,  “What  is  rhetoric?”  the  topic  of 
the  Gorgias,  or,  “What  is  justice?”  that  of  the  Republic.  Such,  also,  is 
the  question  scornfully  asked  by  Pilate,  “What  is  truth?”  and  the  funda- 
mental question  with  speculative  moralists  in  all  ages,  “ What  is  virtue?” 

It  would  be  a mistake  to  represent  these  difficult  and  noble  inquiries  as 
having  nothing  in  view  beyond  ascertaining  the  conventional  meaning  of 
a name.  They  are  inquiries  not  so  much  to  determine  what  is,  as  what 
should  be,  the  meaning  of  a name ; which,  like  other  practical  questions  of 
terminology,  requires  for  its  solution  that  we  should  enter,  and  sometimes 
enter  very  deeply,  into  the  properties  not  merely  of  names  but  of  the 
things  named. 

Although  the  meaning  of  every  concrete  general  name  resides  in  the  at- 
tributes which  it  connotes,  the  objects  were  named  before  the  attributes; 
as  appears  from  the  fact  that  in  all  languages,  abstract  names  are  mostly 
compounds  or  other  derivatives  of  the  concrete  names  which  correspond  to 
them.  Connotative  names,  therefore,  were,  after  proper  names,  the  first 
which  were  used  : and  in  the  simpler  cases,  no  doubt,  a distinct  connotation 
was  present  to  the  minds  of  those  who  first  used  the  name,  and  was  dis- 
tinctly intended  by  them  to  be  conveyed  by  it.  The  first  person  who  used 
the  word  white,  as  applied  to  snow  or  to  any  other  object,  knew,  no  doubt, 
very  well  what  quality  he  intended  to  predicate,  and  had  a perfectly  dis- 
tinct conception  in  his  mind  of  the  attribute  signified  by  the  name. 

But  where  the  resemblances  and  differences  on  which  our  classifications 
are  founded  are  not  of  this  palpable  and  easily  determinable  kind  ; especial- 
ly where  they  consist  not  in  any  one  quality  but  in  a number  of  qualities, 
the  effects  of  which,  being  blended  together,  are  not  very  easily  discrimi- 
nated, and  referred  each  to  its  true  source ; it  often  happens  that  names 
are  applied  to  namable  objects,  with  no  distinct  connotation  present  to  the 
minds  of  those  who  apply  them.  They  are  only  influenced  by  a general 
resemblance  between  the  new  object  and  all  or  some  .of  the  old  familiar 
objects  which  they  have  been  accustomed  to  call  by  that  name.  This,  as 
we  have  seen,  is  the  law  which  even  the  mind  of  the  philosopher  must  fol- 
low, in  giving  names  to  the  simple  elementary  feelings  of  our  nature : but, 
, where  the  things  to  be  named  are  complex  wholes,  a philosopher  is  not 
content  with  noticing  a general  resemblance;  he  examines  what  the  resem- 
blance consists  in : and  he  only  gives  the  same  name  to  things  which  re- 


118 


NAMES  AND  PKOPOSITIONS. 


semble  one  another  in  the  same  definite  particulars.  The  philosopher, 
therefore,  habitually  employs  his  general  names  with  a definite  connota- 
tion. But  language  was  not  made,  and  can  only  in  some  small  degree  be 
mended,  by  philosophers.  In  the  minds  of  the  real  arbiters  of  language, 
general  names,  especially  where  the  classes  they  denote  can  not  be  brought 
before  the  tribunal  of  the  outward  senses  to  be  identified  and  discriminated, 
connote  little  more  than  a vague  gross  resemblance  to  the  things  which 
they  were  earliest,  or  have  been  most,  accustomed  to  call  by  those  names. 
When,  for  instance,  ordinary  persons  predicate  the  words  just  or  unjust 
of  any  action,  noble  or  mean  of  any  sentiment,  expression,  or  demeanor, 
statesman  or  charlatan  of  any  personage  figuring  in  politics,  do  they  mean 
to  affirm  of  those  various  subjects  any  determinate  attributes,  of  whatever 
kind?  No:  they  merely  recognize,  as  they  think,  some  likeness,  more  or 
less  vague  and  loose,  between  these  and  some  other  things  which  they 
have  been  accustomed  to  denominate  or  to  hear  denominated  by  those  ap- 
pellations. 

Language,  as  Sir  James  Mackintosh  used  to  say  of  governments,  “ is  not 
made,  but  grows.”  A name  is  not  imposed  at  once  and  by  previous  pur- 
pose upon  a class  of  objects,  but  is  first  applied  to  one  thing,  and  then  ex- 
tended by  a series  of  transitions  to  another  and  another.  By  this  process 
(as  has  been  remarked  by  several  writers,  and  illustrated  with  great  force 
and  clearness  by  Dugald  Stewart  in  his  Philosophical  Essays)  a name  not 
unfrequently  passes  by  successive  links  of  resemblance  from  one  object  to 
another,  until  it  becomes  applied  to  things  having  nothing  in  common  with 
the  first  things  to  which  the  name  was  given;  which,  however,  do  not,  for 
that  reason,  drop  the  name;  so  that  it  at  last  denotes  a confused  huddle  of 
objects,  having  nothing  whatever  in  common;  and  connotes  nothing,  not 
even  a vague  and  general  resemblance.  When  a name  has  fallen  into  this 
state,  in  which  by  predicating  it  of  any  object  wTe  assert  literally  nothing 
about  the  object,  it  has  become  unfit  for  the  purposes  either  of  thought  or 
of  the  communication  of  thought;  and  can  only  be  made  serviceable  by 
stripping  it  of  some  part  of  its  multifarious  denotation,  and  confining  it  to 
objects  possessed  of  some  attributes  in  common,  which  it  may  be  made  to 
connote.  Such  are  the  inconveniences  of  a language  which  “is  not  made, 
but  grows.”  Like  the  governments  which  are  in  a similar  case,  it  may  be 
compared  to  a road  which  is  not  made  but  has  made  itself:  it  requires  con- 
tinual mending  in  order  to  be  passable. 

From  this  it  is  already  evident,  why  the  question  respecting  the  defini- 
tion of  an  abstract  name  is  often  one  of  so  much  difficulty.  The  question, 
What  is  justice?  is,  in  other  words,  What  is  the  attribute  which  mankind 
mean  to  predicate  when  they  call  an  action  just?  To  which  the  first  an- 
swer is,  that  having  come  to  no  precise  agreement  on  the  point,  they  do 
not  mean  to  predicate  distinctly  any  attribute  at  all.  Nevertheless,  all  be- 
lieve that  there  is  some  common  attribute  belonging  to  all  the  actions  which 
they  are  in  the  habit  of  calling  just.  The  question  then  must  be,  whether 
there  is  any  such  common  attribute?  and,  in  the  first  place,  whether  man- 
kind agree  sufficiently  with  one  another  as  to  the  particular  actions  which 
they  do  or  do  not  call  just,  to  render  the  inquiry,  what  quality  those  ac- 
tions have  in  common,  a possible  one : if  so,  whether  the  actions  really  have 
any  quality  in  common ; and  if  they  have,  what  it  is.  Of  these  three,  the 
first  alone  is  an  inquiry  into  usage  and  convention  ; the  other  two  are  inqui- 
ries into  matters  of  fact.  And  if  the  second  question  (whether  the  actions* 
form  a class  at  all)  has  been  answered  negatively,  there  remains  a fourth, 


DEFINITION. 


119 


often  more  arduous  than  all  the  rest,  namely,  how  best  to  form  a class  arti- 
ficially, which  the  name  may  denote. 

And  here  it  is  fitting  to  remark,  that  the  study  of  the  spontaneous  growth 
of  languages  is  of  the  utmost  importance  to  those  who  would  logically  re- 
model them.  The  classifications  rudely  made  by  established  language,  when 
retouched,  as  they  almost  all  require  to  be,  by  the  hands  of  the  logician, 
are  often  themselves  excellently  suited  to  his  purposes.  As  compared  with 
the  classifications  of  a philosopher,  they  are  like  the  customary  law  of  a 
country,  which  has  grown  up  as  it  were  spontaneously,  compared  with  laws 
methodized  and  digested  into  a code : the  former  are  a far  less  perfect  in- 
strument than  the  latter;  but  being  the  result  of  a long,  though  unscien- 
tific, course  of  experience,  they  contain  a mass  of  materials  which  may  be 
made  very  usefully  available  in  the  formation  of  the  systematic  body  of 
written  law.  In  like  manner,  the  established  grouping  of  objects  under  a 
common  name,  even  when  founded  only  on  a gross  and  general  resemblance, 
is  evidence,  in  the  first  place,  that  the  resemblance  is  obvious,  and  therefore 
considerable;  and,  in  the  next  place,  that  it  is  a resemblance  which  has 
struck  great  numbers  of  persons  during  a series  of  years  and  ages.  Even 
when  a name,  by  successive  extensions,  has  come  to  be  applied  to  things 
among  which  there  does  not  exist  this  gross  resemblance  common  to  them 
all,  still  at  every  step  in  its  progress  we  shall  find  such  a resemblance.  And 
these  transitions  of  the  meaning  of  words  are  often  an  index  to  real  con- 
nections between  the  things  denoted  by  them,  which  might  otherwise  escape 
the  notice  of  thinkers ; of  those  at  least  who,  from  using  a different  lan- 
guage, or  from  any  difference  in  their  habitual  associations,  have  fixed  their 
attention  in  preference  on  some  other  aspect  of  the  things.  The  history  of 
philosophy  abounds  in  examples  of  such  oversights,  committed  for  want  of 
perceiving  the  hidden  link  that  connected  together  the  seemingly  disparate 
meanings  of  some  ambiguous  word.* 

Whenever  the  inquiry  into  the  definition  of  the  name  of  any  real  object 
consists  of  any  thing  else  than  a mere  comparison  of  authorities,  we  tacit- 
ly assume  that  a meaning  must  be  found  for  the  name,  compatible  with  its 
continuing  to  denote,  if  possible  all,  but  at  any  rate  the  greater  or  the  more 
important  part,  of  the  things  of  which  it  is  commonly  predicated.  The  in- 
quiry, therefore,  into  the  definition,  is  an  inquiry  into  the  resemblances  and 
differences  among  those  things  : whether  there  be  any  resemblance  running 
through  them  all ; if  not,  through  what  portion  of  them  such  a general  re- 
semblance can  be  traced : and  finally,  what  are  the  common  attributes,  the 
possession  of  which  gives  to  them  all,  or  to  that  portion  of  them,  the  char- 
acter of  resemblance  which  has  led  to  their  being  classed  together.  When 
these  common  attributes  have  been  ascertained  and  specified,  the  name 
which  belongs  in  common  to  the  resembling  objects  acquires  a distinct  in- 

* “Fw  people”  (I  have  said  in  another  place)  “have  reflected  how  great  a knowledge 
of  Things  is  required  to  enable  a man  to  affirm  that  any  given  argument  turns  wholly  upon 
words.  There  is,  perhaps,  not  one  of  the  leading  terms  of  philosophy  which  is  not  used  in 
almost  innumerable  shades  of  meaning,  to  express  ideas  more  or  less  widely  different  from 
one  another.  Between  two  of  these  ideas  a sagacious  and  penetrating  mind  will  discern,  as 
it  were  intuitively,  an  unobvious  link  of  connection,  upon  which,  though  perhaps  unable  to 
give  a logical  account  of  it,  he  will  found  a perfectly  valid  argument,  which  his  critic,  not 
having  so  keen  an  insight  into  the  Things,  will  mistake  for  a fallacy  turning  on  the  double 
meaning  of  a term.  And  the  greater  the  genius  of  him  who  thus  safely  leaps  over  the  chasm, 
the  greater  will  probably  be  the  crowing  and  vainglory  of  the  mere  logician,  who,  hobbling 
after  him,  evinces  his  own  superior  wisdom  by  pausing  on  its  brink,  and  giving  up  as  desper- 
ate his  proper  business  of  bridging  it  over.” 


120 


NAMES  AND  PROPOSITIONS. 


stead  of  a vague  connotation  ; and  by  possessing  this  distinct  connotation, 
becomes  susceptible  of  definition. 

In  giving  a distinct  connotation  to  the  general  name,  the  philosopher  will 
endeavor  to  fix  upon  such  attributes  as,  while  they  are  common  to  all  the 
things  usually  denoted  by  the  name,  are  also  of  greatest  importance  in  them- 
selves ; either  directly,  or  from  the  number,  the  conspicuousness,  or  the  in- 
teresting character,  of  the  consequences  to  which  they  lead.  Pie  will  select, 
as  far  as  possible,  such  differential  as  lead  to  the  greatest  number  of  inter- 
esting propria,.  For  these,  rather  than  the  more  obscure  and  recondite 
qualities  on  which  they  often  depend,  give  that  general  character  and  as- 
pect to  a set  of  objects,  which  determine  the  groups  into  which  they  natu- 
rally fall.  But  to  penetrate  to  the  more  hidden  agreement  on  which  these 
obvious  and  superficial  agreements  depend,  is  often  one  of  the  most  diffi- 
cult of  scientific  problems.  As  it  is  among  the  most  difficult,  so  it  seldom 
fails  to  be  among  the  most  important.  And  since  upon  the  result  of  this 
inquiry  respecting  the  causes  of  the  properties  of  a class  of  things,  there  in- 
cidentally depends  the  question  what  shall  be  the  meaning  of  a word  ; some 
of  the  most  profound  and  most  valuable  investigations  which  philosophy 
presents  to  us,  have  been  introduced  by,  and  have  offered  themselves  under 
the  guise  of,  inquiries  into  the  definition  of  a name. 


BOOK  II. 

OF  REASONING. 


Aiuipiffpepoiv  Se  tovtiop  Asy topep  ySri,  Sia  riviov,  xai  ttote,  icai  7 rwg  ytPETai  7r ag  avAAoyiupog 
voTipop  Si  Ackteop  7T£ pi  diroSti^Eiog.  Tlporepop  yap  Trepi  (rvAAoyirrpov  Aeicteop,  i)  7 repi  di ToSei- 
Cid  to  KaOo Aou  paAAop  tipai  top  avAAoyiapop.  H pip  yap  diroSiiiig,  ovAAoywpog  Tig'  u 
avAAoytcrpog  Si  ov  Trap,  dtioSti^ig. — Arist.,  Analyt.  Prior.,  1.  i.,  cap.  4. 


CHAPTER  I. 

OP  INFERENCE,  OR  REASONING,  IN  GENERAL. 

§ 1.  In  the  preceding  Book,  we  have  been  occupied  not  with  the  nature 
of  Proof,  but  with  the  nature  of  Assertion  : the  import  conveyed  by  a Prop- 
osition, whether  that  Proposition  be  true  or  false ; not  the  means  by  which 
to  discriminate  true  from  false  Propositions.  The  proper  subject,  however, 
of  Logic  is  Proof.  Before  we  could  understand  what  Proof  is,  it  was  nec- 
essary to  understand  what  that  is  to  which  proof  is  applicable;  what  that 
is  which  can  be  a subject  of  belief  or  disbelief,  of  affirmation  or  denial; 
what,  in  short,  the  different  kinds  of  Propositions  assert. 

This  preliminary  inquiry  we  have  prosecuted  to  a definite  result.  Asser- 
tion, in  the  first  place,  relates  either  to  the  meaning  of  words,  or  to  some 
property  of  the  things  which  words  signify.  Assertions  respecting  the 
meaning  of  words,  among  which  definitions  are  the  most  important,  hold  a 
place,  and  an  indispensable  one,  in  philosophy ; but  as  the  meaning  of  words 
is  essentially  arbitrary,  this  class  of  assertions  are  not  susceptible  of  truth 
or  falsity,  nor  therefore  of  proof  or  disproof.  Assertions  respecting  Tilings, 
or  what  may  be  called  Real  Propositions,  in  contradistinction  to  verbal 
ones,  are  of  various  sorts.  We  have  analyzed  the  import  of  each  sort,  and 
have  ascertained  the  nature  of  the  things  they  relate  to,  and  the  nature  of 
what  they  severally  assert  respecting  those  things.  WTe  found  that  what- 
ever be  the  form  of  the  proposition,  and  whatever  its  nominal  subject  or 
predicate,  the  real  subject  of  every  jiroposition  is  some  one  or  more  facts 
or  phenomena  of  consciousness,  or  some  one  or  more  of  the  hidden  causes 
or  powers  to  which  we  ascribe  those  facts ; and  that  what  is  predicated  or 
asserted,  either  in  the  affirmative  or  negative,  of  those  phenomena  or  those 
powers,  is  always  either  Existence,  Order  in  Place,  Order  in  Time,  Causa- 
tion, or  Resemblance.  This,  then,  is  the  theory  of  the  Import  of  Proposi- 
tions, reduced  to  its  ultimate  elements : but  there  is  another  and  a less  ab- 
struse expression  for  it,  which,  though  stopping  short  in  an  earlier  stage  of 
the  analysis,  is  sufficiently  scientific  for  many  of  the  purposes  for  which 
such  a general  expression  is  required.  This  expression  recognizes  the  com- 
monly received  distinction  between  Subject  and  Attribute,  and  gives  the 
following  as  the  analysis  of  the  meaning  of  propositions: — Every  Proposi- 


122 


REASONING. 


tion  asserts,  that  some  given  subject  does  or  does  not  possess  some  attri- 
bute; or  that  some  attribute  is  or  is  not  (either  in  all  or  in  some  portion 
of  the  subjects  in  which  it  is  met  with)  conjoined  with  some  other  attri- 
bute. 

We  shall  now  for  the  present  take  our  leave  of  this  portion  of  our  in- 
quiry, and  proceed  to  the  peculiar  problem  of  the  Science  of  Logic,  name- 
ly, how  the  assertions,  of  which  we  have  analyzed  the  import,  are  proved 
or  disproved;  such  of  them,  at  least,  as,  not  being  amenable  to  direct  con- 
sciousness or  intuition,  are  appropriate  subjects  of  proof. 

We  say  of  a fact  or  statement,  that  it  is  proved,  when  we  believe  its  truth 
by  reason  of  some  other  fact  or  statement  from  which  it  is  said  to  follow. 
Most  of  the  propositions,  whether  affirmative  or  negative,  universal,  partic- 
ular, or  singular,  which  we  believe,  are  not  believed  on  their  own  evidence, 
but  on  the  ground  of  something  previously  assented  to,  from  which  they 
are  said  to  be  inferred.  To  infer  a proposition  from  a previous  proposi- 
tion or  propositions;  to  give  credence  to  it,  or  claim  credence  for  it,  as  a 
conclusion  from  something  else;  is  to  reason,  in  the  most  extensive  sense 
of  the  term.  There  is  a narrower  sense,  in  which  the  name  reasoning  is 
confined  to  the  form  of  inference  which  is  termed  ratiocination,  and  of 
which  the  syllogism  is  the  general  type.  The  reasons  for  not  conforming 
to  this  restricted  use  of  the  term  were  stated  in  an  earlier  stage  of  our  in- 
quiry, and  additional  motives  will  be  suggested  by  the  considerations  on 
which  we  are  now  about  to  enter. 

§ 2.  In  proceeding  to  take  into  consideration  the  cases  in  which  infer- 
ences can  legitimately  be  drawn,  we  shall  first  mention  some  cases  in  which 
the  inference  is  apparent,  not  real ; and  which  require  notice  chiefly  that 
they  may  not  be  confounded  with  cases  of  inference  properly  so  called. 
This  occurs  when  the  proposition  ostensibly  inferred  from  another,  appears 
on  analysis  to  be  merely  a repetition  of  the  same,  or  part  of  the  same,  as- 
sertion, which  was  contained  in  the  first.  All  the  cases  mentioned  in  books' 
of  Logic  as  examples  of  equipollency  or  equivalence  of  propositions,  are 
of  this  nature.  Thus,  if  we  were  to  argue,  No  man  is  incapable  of  reason, 
for  every  man  is  rational ; or,  All  men  are  mortal,  for  no  man  is  exempt 
from  death ; it  would  be  plain  that  we  were  not  proving  the  proposition, 
but  only  appealing  to  another  mode  of  wording  it,  which  may  or  may  not 
be  more  readily  comprehensible  by  the  hearer,  or  better  adapted  to  suggest 
the  real  proof,  but  which  contains  in  itself  no  shadow  of  proof. 

Another  case  is  where,  from  a universal  proposition,  we  affect  to  infer 
another  which  differs  from  it  only  in  being  particular:  as  All  A is  B, there- 
fore Some  A is  B : No  A is  B,  therefore  Some  A is  not  B.  This,  too,  is  not 
to  conclude  one  proposition  from  another,  but  to  repeat  a second  time  some- 
thing which  had  been  asserted  at  first;  with  the  difference,  that  we  do  not 
here  repeat  the  whole  of  the  previous  assertion,  but  only  an  indefinite  part 
of  it. 

A third  case  is  where,  the  antecedent  having  affirmed  a predicate  of  a 
given  subject,  the  consequent  affirms  of  the  same  subject  something  already 
connoted  by  the  former  predicate : as,  Socrates  is  a man,  therefore  Socrates 
is  a living  creature;  where  all  that  is  connoted  by  living  creature  was  af- 
firmed of  Socrates  when  he  was  asserted  to  be  a man.  If  the  propositions 
are  negative,  we  must  invert  their  order,  thus  : Socrates  is  not  a living  crea- 
ture, therefore  he  is  not  a man;  for  if  we  deny  the  less,  the  greater,  which 
includes  it,  is  already  denied  by  implication.  These,  therefore,  are  not  real- 


INFERENCE  IN  GENERAL. 


123 


ly  cases  of  inference ; and  yet  the  trivial  examples  by  which,  in  manuals  of 
Logic,  the  rules  of  the  syllogism  are  illustrated,  are  often  of  this  ill-chosen 
kind ; formal  demonstrations  of  conclusions  to  which  whoever  understands 
the  terms  used  in  the  statement  of  the  data,  has  already,  and  consciously, 
assented.* 

The  most  complex  case  of  this  sort  of  apparent  inference  is  what  is  called 
the  Conversion  of  propositions;  which  consists  in  turning  the  predicate 
into  a subject,  and  the  subject  into  a predicate,  and  framing  out  of  the  same 
terms  thus  reversed,  another  proposition,  which  must  be  true  if  the  former 
is  true.  Thus,  from  the  particular  affirmative  proposition,  Some  A is  B, 
we  may  infer  that  Some  is  A.  From  the  universal  negative,  No  A is  B, 
we  may  conclude  that  No  B is  A.  From  the  universal  affirmative  proposi- 
tion, All  A is  B,  it  can  not  be  inferred  that  all  B is  A ; though  all  water  is 
liquid,  it  is  not  implied  that  all  liquid  is  water;  but  it  is  implied  that  some 
liquid  is  so ; and  hence  the  proposition,  All  A is  B,  is  legitimately  convert- 
ible into  Some  B is  A.  This  process,  which  converts  a universal  propo- 
sition into  a particular,  is  termed  conversion  per  ciccidens.  From  the  prop- 
osition, Some  A is  not  B,  we  can  not  even  infer  that  some  B is  not  A ; 
though  some  men  are  not  Englishmen,  it  does  not  follow  that  some  English- 
men are  not  men.  The  only  mode  usually  recognized  of  converting  a par- 
ticular negative  proposition,  is  in  the  form,  Some  A is  not  B,  therefore 
something  which  is  not  B is  A;  and  this  is  termed  conversion  by  contra- 
position. In  this  case, .however,  the  predicate  and  subject  are  not  merely 
reversed,  but  one  of  them  is  changed.  Instead  of  [A]  and  [B],  the  terms 
of  the  new  proposition  are  [a  thing  which  is  not  B],  and  [A],  The  origi- 
nal proposition,  Some  A is  not  B,  is  first  changed  into  a proposition  equi- 
pollent with  it,  Some  A is  “ a thing  which  is  not  B ;”  and  the  proposition, 
being  now  no  longer  a particular  negative,  but  a particular  affirmative,  ad- 
mits of  conversion  in  the  first  mode,  or  as  it  is  called,  simple  conversion.! 

In  all  these  cases  there  is  not  really  any  inference ; there  is  in  the  con- 
clusion no  new  truth,  nothing  but  what  was  already  asserted  in  the  prem- 
ises, and  obvious  to  whoever  apprehends  them.  The  fact  asserted  in  the 
conclusion  is  either  the  very  same  fact,  or  part  of  the  fact,  asserted  in  the 
original  proposition.  This  follows  from  our  previous  analysis  of  the  Im- 
port of  Propositions.  When  we  say,  for  example,  that  some  lawful  sov- 
ereigns are  tyrants,  what  is  the  meaning  of  the  assertion  ? That  the  attri- 
butes connoted  by  the  term  “lawful  sovereign,”  and  the  attributes  connoted 
by  the  term  “ tyrant,”  sometimes  co-exist  in  the  same  individual.  Now  this 
is  also  precisely  what  we  mean,  when  we  say  that  some  tyrants  are  lawful 
sovereigns ; which,  therefore,  is  not  a second  proposition  inferred  from  the 
first,  any  more  than  the  English  translation  of  Euclid’s  Elements  is  a col- 
lection of  theorems  different  from  and  consequences  of,  those  contained  in 
the  Greek  original.  Again,  if  we  assert  that  no  great  general  is  a rash 
man,  we  mean  that  the  attributes  connoted  by  “ great  general,”  and  those 
connoted  by  “rash,”  never  co-exist  in  the  same  subject;  which  is  also  the 
exact  meaning  which  would  be  expressed  by  saying,  that  no  rash  man  is  a 

* The  different  cases  of  Equipollency,  or  “Equivalent  Propositional  Forms,”  are  set  forth 
with  some  fullness  in  Professor  Bain’s  Logic.  One  of  the  commonest  of  these  changes  of 
expression,  that  from  affirming  a proposition  to  denying  its  negative,  or  vice  versa,  Mr.  Bain 
designates,  very  happily,  by  the  name  Obversion. 

t As  Sir  William  Hamilton  has  pointed  out,  “Some  A is  not  B ” may  also  be  converted  in 
the  following  form  : “ No  B is  some  A.”  Some  men  are  not  negroes  ; therefore,  No  negroes 
are  some  men  ( e . g.,  Europeans). 


124 


REASONING. 


great  general.  When  we  say  that  all  quadrupeds  are  warm-blooded,  we 
assert,  not  only  that  the  attributes  connoted  by  “ quadruped  ” and  those 
connoted  by  “ warm-blooded  ” sometimes  co-exist,  but  that  the  former  nev- 
er exist  without  the  latter:  now  the  proposition,  Some  warm-blooded  crea- 
tures are  quadrupeds,  expresses  the  first  half  of  this  meaning,  dropping  the 
latter  half;  and  therefore  has  been  already  affirmed  in  the  antecedent  prop- 
osition, All  quadrupeds  are  warm-blooded.  But  that  all  warm-blooded 
creatures  are  quadrupeds,  or,  in  other  words,  that  the  attributes  connoted 
by  “ warm-blooded  ” never  exist  without  those  connoted  by  “ quadruped,” 
lias  not  been  asserted,  and  can  not  be  inferred.  In  order  to  re-assert,  in  an 
inverted  form,  the  whole  of  what  was  affirmed  in  the  proposition,  All  quad- 
rupeds are  warm-blooded,  we  must  convert  it  by  contraposition,  thus,  Noth- 
ing which  is  not  warm-blooded  is  a quadruped.  This  proposition,  and  the 
one  from  which  it  is  derived,  are  exactly  equivalent,  and  either  of  them  may 
be  substituted  for  the  other ; for,  to  say  that  when  the  attributes  of  a quad- 
ruped are  present,  those  of  a warm-blooded  creature  are  present,  is  to  say 
that  when  the  latter  are  absent  the  former  are  absent. 

In  a manual  for  young  students,  it  would  be  proper  to  dwell  at  greater 
length  on  the  conversion  and  equipollency  of  propositions.  For  though 
that  can  not  be  called  reasoning  or  inference  which  is  a mere  re-assertion  in 
different  words  of  what  had  been  asserted  before,  there  is  no  more  impor- 
tant intellectual  habit,  nor  any  the  cultivation  of  which  falls  more  strictly 
within  the  province  of  the  art  of  logic,  than  that  of  discerning  rapidly  and 
surely  the  identity  of  an  assertion  when  disguised  under  diversity  of  lan- 
guage. That  important  chapter  in  logical  treatises  which  relates  to  the  Op- 
position of  Propositions,  and  the  excellent  technical  language  which  logic 
provides  for  distinguishing  the  different  kinds  or  modes  of  opposition,  are 
of  use  chiefly  for  this  purpose.  Such  considerations  as  these,  that  contrary 
propositions  may  both  be  false,  but  can  not  both  be  true ; that  subcontrary 
propositions  may  botli  be  true,  but  can  not  both  be  false ; that  of  two  con- 
tradictory propositions  one  must  be  true  and  the  other  false ; that  of  two 
subalternate  propositions  the  truth  of  the  universal  proves  the  truth  of  the 
particular,  and  the  falsity  of  the  particular  proves  the  falsity  of  the  univer- 
sal, but  not  vied  versa/*  are  apt  to  appear,  at  first  sight,  very  technical  and 
mysterious,  but  when  explained,  seem  almost  too  obvious  to  require  so  form- 
al a statement,  since  the  same  amount  of  explanation  which  is  necessary 
to  make  the  principles  intelligible,  would  enable  the  truths  which  they  con- 
vey to  be  apprehended  in  any  particular  case  which  can  occur.  In  this 
respect,  however,  these  axioms  of  logic  are  on  a level  with  those  of  mathe- 
matics. That  things  which  are  equal  to  the  same  thing  are  equal  to  one 
another,  is  as  obvious  in  any  particular  case  as  it  is  in  the  general  state- 
ment : and  if  no  such  general  maxim  had  ever  been  laid  down,  the  demon- 
strations in  Euclid  would  never  have  halted  for  any  difficulty  in  stepping 
across  the  gap  which  this  axiom  at  present  serves  to  bridge  over.  Yet  no 


* All  A is  B)  , . 

■vr  . • T,  - contraries. 
No  A is  I!| 

Some  A is  B > 

Some  A is  not  Bj 
All  A is  B > 

Some  A is  not  Bf 
No  A is  B> 

Some  A is  B) 

All  A is  B > 


- subcontraries, 
contradictories. 


also  contradictories. 
No  A is  B 


and 


Some  A is  B)  ‘ Some  A is  not  B) 


l 


respectively  subalternate. 


INFERENCE  IN  GENERAL. 


125 


one  has  ever  censured  writers  on  geometry,  for  placing  a list  of  these  ele- 
mentary generalizations  at  the  head  of  their  treatises,  as  a first  exercise  to 
the  learner  of  the  faculty  which  will  be  required  in  him  at  every  step,  that 
of  apprehending  a general  truth.  And  the  student  of  logic,  in  the  discus- 
sion even  of  such  truths  as  we  have  cited  above,  acquires  habits  of  cir- 
cumspect interpretation  of  words,  and  of  exactly  measuring  the  length  and 
breadth  of  his  assertions,  which  are  among  the  most  indispensable  condi- 
tions of  any  considerable  mental  attainment,  and  which  it  is  one  of  the 
primary  objects  of  logical  discipline  to  cultivate. 

§ 3.  Having  noticed,  in  order  to  exclude  from  the  province  of  Reasoning 
or  Inference  properly  so  called,  the  cases  in  which  the  progression  from  one 
truth  to  another  is  only  apparent,  the  logical  consequent  being  a mere  rep- 
etition of  the  logical  antecedent ; we  now  pass  to  those  which  are  cases  of 
inference  in  the  proper  acceptation  of  the  term,  those  in  which  we  set  out 
from  known  truths,  to  arrive  at  others  really  distinct  from  them. 

Reasoning,  in  the  extended  sense  in  which  I use  the  term,  and  in  which 
it  is  synonymous  with  Inference,  is  popularly  said  to  be  of  two  kinds : rea- 
soning from  particulars  to  generals,  and  reasoning  from  generals  to  partic- 
ulars ; the  former  being  called  Induction,  the  latter  Ratiocination  or  Syllo- 
gism. It  will  presently  be  shown  that  there  is  a third  species  of  reasoning, 
which  falls  under  neither  of  these  descriptions,  and  which,  nevertheless,  is 
not  only  valid,  but  is  the  foundation  of  both  the  others. 

It  is  necessary  to  observe,  that  the  expressions,  reasoning  from  particu- 
lars to  generals,  and  reasoning  from  generals  to  particulars,  are  recom- 
mended by  brevity  rather  than  by  precision,  and  do  not  adequately  mark, 
without  the  aid  of  a commentary,  the  distinction  between  Induction  (in  the 
sense  now  adverted  to)  and  Ratiocination.  The  meaning  intended  by  these 
expressions  is,  that  Induction  is  inferring  a proposition  from  propositions 
less  general  than  itself,  and  Ratiocination  is  inferring  a proposition  from 
propositions  equally  or  more  general.  When,  from  the  observation  of  a 
number  of  individual  instances,  we  ascend  to  a general  proposition,  or  when, 
by  combining  a number  of  general  propositions,  we  conclude  from  them 
another  proposition  still  more  general,  the  process,  which  is  substantially 
the  same  in  both  instances,  is  called  Induction.  When  from  a general  prop- 
osition, not  alone  (for  from  a single  proposition  nothing  can  be  concluded 
which  is  not  involved  in  the  terms),  but  by  combining  it  with  other  propo- 
sitions, we  infer  a proposition  of  the  same  degree  of  generality  with  itself, 
or  a less  general  proposition,  or  a proposition  merely  individual,  the  process 
is  Ratiocination.  When,  in  short,  the  conclusion  is  more  general  than  the 
largest  of  the  premises,  the  argument  is  commonly  called  Induction;  when 
less  general,  or  equally  general,  it  is  Ratiocination. 

As  all  experience  begins  with  individual  cases,  and  proceeds  from  them 
to  generals,  it  might  seem  most  conformable  to  the  natural  order  of  thought 
that  Induction  should  be  treated  of  before  we  touch  upon  Ratiocination. 
It  will,  however,  be  advantageous,  in  a science  which  aims  at  tracing  our 
acquired  knowledge  to  its  sources,  that  the  inquirer  should  commence  with 
the  latter  rather  than  with  the  earlier  stages  of  the  process  of  constructing 
our  knowledge ; and  should  trace  derivative  truths  backward  to  the  truths 
from  which  they  are  deduced,  and  on  which  they  depend  for  their  evidence, 
before  attempting  to  point  out  the  original  spring  from  which  both  ulti- 
mately take  their  rise.  The  advantages  of  this  order  of  proceeding  in  the 
present  instance  will  manifest  themselves  as  we  advance,  in  a manner  su- 
perseding the  necessity  of  any  further  justification  or  explanation. 


I2G 


REASONING. 


Of  Induction,  therefore,  we  shall  say  no  more  at  present,  than  that  it  at 
least  is,  without  doubt,  a process’ of  real  inference.  The  conclusion  in  an 
induction  embraces  more  than  is  contained  in  the  premises.  The  principle 
or  law  collected  from  particular  instances,  the  general  proposition  in  which 
we  embody  the  result  of  our  experience,  covers  a much  larger  extent  of 
ground  than  the  individual  experiments  which  form  its  basis.  A principle 
ascertained  by  experience,  is  more  than  a mere  summing  up  of  what  has 
been  specifically  observed  in  the  individual  cases  which  have  been  exam- 
ined ; it  is  a generalization  grounded  on  those  cases,  and  expressive  of  our 
belief,  that  what  we  there  found  true  is  true  in  an  indefinite  number  of 
cases  which  we  have  not  examined,  and  are  never  likely  to  examine.  The 
nature  and  grounds  of  this  inference,  and  the  conditions  necessary  to  make 
it  legitimate,  will  be  the  subject  of  discussion  in  the  Third  Book:  but  that 
such  inference  really  takes  place  is  not  susceptible  of  question.  In  every 
induction  we  proceed  from  truths  which  we  knew,  to  truths  which  we  did 
not  know ; from  facts  certified  by  observation,  to  facts  which  we  have  not 
observed,  and  even  to  facts  not  capable  of  being  now  observed ; future 
facts,  for  example ; but  which  we  do  not  hesitate  to  believe  on  the  sole  evi- 
dence of  the  induction  itself. 

Induction,  then,  is  a real  process  of  Reasoning  or  Inference.  Whether, 
and  in  what  sense,  as  much  can  be  said  of  the  Syllogism,  remains  to  be  de- 
termined by  the  examination  into  which  we  are  about  to  enter. 


CHAPTER  II. 

OP  RATIOCINATION,  OR  SYLLOGISM. 

§ 1.  The  analysis  of  the  Syllogism  has  been  so  accurately  and  fully  per- 
formed in  the  common  manuals  of  Logic,  that  in  the  present  work,  which 
is  not  designed  as  a manual,  it  is  sufficient  to  recapitulate,  memoriae,  causd, 
the  leading  results  of  that  analysis,  as  a foundation  for  the  remarks  to  be 
afterward  made  on  the  functions  of  the  Syllogism,  and  the  place  which  it 
holds  in  science. 

To  a legitimate  syllogism  it  is  essential  that  there  should  be  three,  and 
no  more  than  three,  propositions,  namely,  the  conclusion,  or  proposition  to 
be  proved,  and  two  other  propositions  which  together  prove  it,  and  which 
are  called  the  premises.  It  is  essential  that  there  should  be  three,  and  no 
more  than  three,  terms,  namely,  the  subject  and  predicate  of  the  conclu- 
sion, and  another  called  the  middle  term,  which  must  be  found  in  both 
premises,  since  it  is  by  means  of  it  that  the  other  two  terms  are  to  be  con- 
nected together.  The  predicate  of  the  conclusion  is  called  the  major  term 
of  the  syllogism;  the  subject  of  the  conclusion  is  called  the  minor  term. 
As  there  can  be  but  three  terms,  the  major  and  minor  terms  must  each  be 
found  in  one,  and  only  one,  of  the  premises,  together  with  the  middle  term 
which  is  in  them  both.  The  premise  which  contains  the  middle  term  and 
the  major  term  is  called  the  major  premise;  that  which  contains  the  mid- 
dle term  and  the  minor  term  is  called  the  minor  premise. 

Syllogisms  are  divided  by  some  logicians  into  three  figures,  by  others 
into  four,  according  to  the  position  of  the  middle  term,  which  may  either 
be  the  subject  in  both  premises,  the  predicate  in  both,  or  the  subject  in 
one  and  the  predicate  in  the  other.  The  most  common  case  is  that  in  which 


RATIOCINATION,  OR  SYLLOGISM. 


127 


the  middle  term  is  the  subject  of  the  major  premise  and  the  predicate  of 
the  minor.  This  is  reckoned  as  the  first  figure.  When  the  middle  term  is 
the  predicate  in  both  premises,  the  syllogism  belongs  to  the  second  figure ; 
when  it  is  the  subject  in  both,  to  the  third.  In  the  fourth  figure  the  mid- 
dle term  is  the  subject  of  the  minor  premise  and  the  predicate  of  the  major. 
Those  writers  who  reckon  no  more  than  three  figures,  include  this  case  in 


the  first. 

Each  figure  is  divided  into  moods,  according  to  what  are  called  the  quan- 
tity and  quality  of  the  propositions,  that  is,  according  as  they  are  universal 
or  particular,  affirmative  or  negative.  The  following  are  examples  of  all 
the  legitimate  moods,  that  is,  all  those  in  which  the  conclusion  correctly 


dws  from  the 

premises.  A is  the 

minor  term,  C the 

major,  B the  mid- 

term. 

FIRST  FIGURE. 

All  B is  C 

No  B is  C 

All  B is  C 

No  B is  C 

All  A is  B 

All  A is  B 

Some  A is  B 

Some  A is  B 

therefore 

therefore 

therefore 

therefore 

All  A is  C 

No  A is  C 

Some  A is  C 

Some  A is  not  C 

SECOND 

FIGURE. 

No  C is  B 

All  C is  B 

No  C is  B 

All  C is  B 

All  A is  B 

No  A is  B 

Some  A is  B 

Some  A is  not  B 

therefore 

therefore 

therefore 

therefore 

No  A is  C 

No  A is  C 

Some  A is  not  C 

Some  A is  not  C 

All  B is  C 
All  B is  A 
therefore 
Some  A is  C 


No  B is  C 
All  B is  A 
therefore 
Some  A is  notC 


THIRD  FIGURE. 

Some  B is  C All  B is  C 
All  B is  A Some  B is  A 
therefore  therefore 
Some  A is  C Some  A is  C 


Some  B is  not  C 
All  B is  A 
therefore 
Some  A is  not  C 


No  B is  C 
Seme  B is  A 
therefore 
Some  A is  notC 


FOURTH  FIGURE. 


All  C is  B 
All  B is  A 
therefore 
Some  A is  C 


All  C is  B Some  C is  B 

No  B is  A All  B is  A 

therefore  therefore 

Some  A is  not  C Some  A is  C 


No  C is  B 
All  B is  A 
therefore 
Some  A is  not  C 


No  C is  B 
Some  B is  A 
therefore 
Some  A is  not  C 


In  these  exemplars,  or  blank  forms  for  making  syllogisms,  no  place  is 
assigned  to  singular  propositions;  not,  of  course,  because  such  proposi- 
tions are  not  used  in  ratiocination,  but  because,  their  predicate  being  af- 
firmed or  denied  of  the  whole  of  the  subject,  they  are  ranked,  for  the  pur- 
poses of  the  syllogism,  with  universal  propositions.  Thus,  these  two  syllo- 
gisms— 

All  men  are  mortal,  All  men  are  mortal, 

All  kings  are  men,  Socrates  is  a man, 

therefore  therefore 

All  kings  are  mortal,  Socrates  is  mortal, 

are  arguments  precisely  similar,  and  are  both  ranked  in  the  first  mood  of 
the  first  figure.* 

* Professor  Bain  denies  the  claim  of  Singular  Propositions  to  be  classed,  for  the  purposes 
of  ratiocination,  with  Universal ; though  they  come  within  the  designation  which  he  himself 
proposes  as  an  equivalent  for  Universal,  that  of  Total.  He  would  even,  to  use  his  own  ex- 
pression, banish  them  entirely  from  the  syllogism.  He  takes  as  an  example, 

Socrates  is  wise, 

Socrates  is  poor,  therefore 
Some  poor  men  are  wise, 

or  more  properly  (as  be  observes)  “one  poor  man  is  wise.”  “Now,  if  wise,  poor,  and  a 
man,  are  attributes  belonging  to  the  meaning  of  the  word  Socrates,  there  is  then  no  march  of 


12$ 


REASONING. 


The  reasons  why  syllogisms  in  any  of  the  above  forms  are  legitimate, 
that  is,  why,  if  the  premises  are  true,  the  conclusion  must  inevitably  be  so, 
and  why  this  is  not  the  case  in  any  other  possible  mood  (that  is,  in  any 
other  combination  of  universal  and  particular,  affirmative  and  negative 
propositions),  any  person  taking  interest  in  these  inquiries  may  be  pre- 
sumed to  have  either  learned  from  the  common-school  books  of  the  syllo- 
gistic logic,  or  to  be  capable  of  discovering  for  himself.  The  reader  may, 
however,  be  referred,  for  every  needful  explanation,  to  Archbishop  Whate- 
ly’s  Elements  of  Logic,  where  he  will  find  stated  with  philosophical  pre- 
cision, and  explained  with  remarkable  perspicuity,  the  whole  of  the  com- 
mon doctrine  of  the  syllogism. 

All  valid  ratiocination ; all  reasoning  by  which,  from  general  propositions 

reasoning  at  all.  AVe  have  given  in  Socrates,  inter  alia , the  facts  wise,  poor,  and  a man,  and 
we  merely  repeat  the  concurrence  which  is  selected  from  the  whole  aggregate  of  properties 
making  up  the  whole,  Socrates.  The  case  is  one  under  the  head  ‘Greater  and  Less  Connota- 
tion ’ in  Equivalent  Propositional  Forms,  or  Immediate  Inference. 

“But  the  example  in  this  form  does  not  do  justice  to  the  syllogism  of  singulars.  We  must 
suppose  both  propositions  to  be  real,  the  predicates  being  in  no  way  involved  in  the  subject. 
Thus 

Socrates  was  the  master  of  Plato, 

Socrates  fought  at  Delium, 

The  master  of  Plato  fought  at  Delium. 

“It  may  fairly  be  doubted  whether  the  transitions,  in  this  instance,  are  any  thing  more 
than  equivalent  forms.  For  the  proposition  ‘ Socrates  was  the  master  of  Plato  and  fought  at 
Delium,’  compounded  out  of  the  two  premises,  is  obviously  nothing  more  than  a grammatical 
abbreviation.  No  one  can  say  that  there  is  here  any  change  of  meaning,  or  any  thing  beyond 
a verbal  modification  of  the  original  form.  The  next  step  is,  ‘ The  master  of  Plato  fought  at 
Delium,’  which  is  the  previous  statement  cut  down  by  the  omission  of  Socrates.  It  contents 
itself  with  reproducing  a part  of  the  meaning,  or  saying  less  than  had  been  previously  said. 
The  full  equivalent  of  the  affirmation  is,  ‘ The  master  of  Plato  fought  at  Delium,  and  the 
master  of  Plato  was  Socrates:’  the  new  form  omits  the  last  piece  of  information,  and  gives 
only  the  first.  Now,  we  never  consider  that  we  have  made  a real  inference,  a step  in  advance, 
when  we  repeat  less  than  we  are  entitled  to  say,  or  drop  from  a complex  statement  some  por- 
tion not  desired  at  the  moment.  Such  an  operation  keeps  strictly  within  the  domain  of  equiv- 
alence, or  Immediate  Inference.  In  no  way,  therefore,  can  a syllogism  with  two  singular 
premises  be  viewed  as  a genuine  syllogistic  or  deductive  inference.”  {Logic,  i.,  159.) 

The  first  argument,  as  will  have  been  seen,  rests  upon  the  supposition  that  the  name  Soc- 
rates has  a meaning ; that  man,  wise,  and  poor,  are  parts  of  this  meaning ; and  that  by  predi- 
cating them  of  Socrates  we  convey  no  information  ; a view  of  the  signification  of  names 
which,  for  reasons  already  given,*  I can  not  admit,  and  which,  as  applied  to  the  class  of  names 
which  Socrates  belongs  to,  is  at  war  with  Mr.  Bain’s  own  definition  of  a Proper  Name  (i.,  148), 
“a  single  meaningless  mark  or  designation  appropriated  to  the  thing.”  Such  names,  Mr. 
Bain  proceeded  to  say,  do  not  necessarily  indicate  even  human  beings : much  less  then  does 
the  name  Socrates  include  the  meaning  of  wise  or  poor.  Otherwise  it  would  follow  that  if 
Socrates  had  grown  rich,  or  had  lost  his  mental  faculties  by  illness,  he  would  no  longer  have 
been  called  Socrates. 

The  second  part  of  Mr.  Bain’s  argument,  in  which  he  contends  that  even  when  the  premises 
convey  real  information,  the  conclusion  is  merely  the  premises  with  a part  left  out,  is  applica- 
ble, if  at  all,  as  much  to  universal  propositions  as  to  singular.  In  every  syllogism  the  con- 
clusion contains  less  than  is  asserted  in  the  two  premises  taken  together.  Suppose  the  syllo- 
gism to  be 

All  bees  are  intelligent, 

All  bees  are  insects,  therefore 
Some  insects  are  intelligent : 

one  might  use  the  same  liberty  taken  by  Mr.  Bajn,  of  joining  together  the  two  premises  as  if 
they  were  one — “All  bees  are  insects  and  intelligent” — and  might  say  that  in  omitting  the 
middle  term  bees  we  make  no  real  inference,  but  merely  reproduce  part  of  what  had  been  pre- 
viously said.  Mr.  Bain’s  is  really  an  objection  to  the  syllogism  itself,  or  at  all  events  to  the 
third  figure : it  has  no  special  applicability  to  singular  propositions. 

* Note  to  § 4 of  the  chapter  on  Definition,  supra , pp.  110,  111- 


RATIOCINATION,  OR  SYLLOGISM. 


129 


previously  admitted,  other  propositions  equally  or  less  general  are  inferred  ; 
may  be  exhibited  in  some  of  the  above  forms.  The  whole  of  Euclid,  for 
example,  might  be  thrown  without  difficulty  into  a series  of  syllogisms, 
regular  in  mood  and  figure. 

Though  a syllogism  framed  according  to  any  of  these  formulae  is  a valid 
argument,  all  correct  ratiocination  admits  of  being  stated  in  syllogisms  of 
the  first  figure  alone.  The  rules  for  throwing  an  argument  in  any  of  the 
other  figures  into  the  first  figure,  are  called  rules  for  the  reduction  of  syl- 
logisms. It  is  done  by  the  conversion  of  one  or  other,  or  both,  of  the  prem- 
ises. Thus  an  argument  in  the  first  mood  of  the  second  figure,  as — 

No  C is  B 
All  A is  B 
therefore 
No  A is  C, 

may  be  reduced  as  follows.  The  proposition,  No  C is  B,  being  a universal 
negative,  admits  of  simple  conversion,  and  may  be  changed  into  No  B is 
C,  which,  as  we  showed,  is  the  very  same  assertion  in  other  words — the 
same  fact  differently  expressed.  This  transformation  having  been  effected, 
the  argument  assumes  the  following  form : 

No  B is  C 
All  A is  B 
therefore 
No  A is  C, 

which  is  a good  syllogism  in  the  second  mood  of  the  first  figure.  Again, 
an  argument  in  the  first  mood  of  the  third  figure  must  resemble  the  fol- 
lowing : 

All  B is  C 
All  B is  A 
therefore 
Some  A is  C, 

where  the  minor  premise,  All  B is  A,  conformably  to  what  was  laid  down 
in  the  last  chapter  respecting  universal  affirmatives,  does  not  admit  of  sim- 
ple conversion,  but  may  be  converted  per  accidens,  thus,  Some  A is  B ; 
which,  though  it  does  not  express  the  whole  of  what  is  asserted  in  the 
proposition  All  B is  A,  expresses,  as  was  formerly  shown,  part  of  it,  and 
must  therefore  be  true  if  the  whole  is  true.  We  have,  then,  as  the  re- 
sult of  the  reduction,  the  following  syllogism  in  the  third  mood  of  the  first 
figure : 

All  B is  C 
Some  A is  B, 

from  which  it  obviously  follows,  that 

Some  A is  C. 

In  the  same  manner,  or  in  a manner  on  which  after  these  examples  it  is 
not  necessary  to  enlarge,  every  mood  of  the  second,  third,  and  fourth  fig- 
ures may  be  reduced  to  some  one  of  the  four  moods  of  the  first.  In  other 
words,  every  conclusion  which  can  be  proved  in  any  of  the  last  three  fig- 
ures, may  be  proved  in  the  first  figure  from  the  same  premises,  with  a 
slight  alteration  in  the  mere  manner  of  expressing  them.  Every  valid  ra- 
tiocination, therefore,  may  be  stated  in  the  first  figure,  that  is,  in  one  of  the 
following  forms : 


9 


130 


REASONING. 


B is  C 
is  B, 


is  B, 


No  B is  C 
All  A 
Some  A 

therefore 
No  A is 
Some  A is  not 

Or,  if  more  significant  symbols  are  preferred  : 

To  prove  an  affirmative,  the  argument  must  admit  of  being  stated  in  this 
form : 


Every 
All  A ) 
Some  A [ 
therefore 
All  A 


Some  A 


is  C. 


C. 


All  animals  are  mortal; 
All  men  ) 

Some  men  v are  animals; 
Socrates  ) 

therefore 


All  men  1 

Some  men  V are  mortal. 

Socrates  ) 


To  prove  a negative,  the  argument  must  be  capable  of  being  expressed 
in  this  form : 

No  one  who  is  capable  of  self-control  is  necessarily  vicious; 

All  negroes  ) 

Some  negroes  V are  capable  of  self-control; 

Mr.  A’s  negro  ) 

therefore 

No  negroes  are  1 

Some  negroes  are  not  v necessarily  vicious. 

Mr.  A’s  negro  is  not  ) 

Though  all  ratiocination  admits  of  being  thrown  into  one  or  the  other  of 
these  forms,  and  sometimes  gains  considerably  by  the  transformation,  both 
in  clearness  and  in  the  obviousness  of  its  consequence ; there  are,  no  doubt, 
cases  in  which  the  argument  falls  more  naturally  into  one  of  the  other  three 
figures,  and  in  which  its  conclusiveness  is  more  apparent  at  the  first  glance 
in  those  figures,  than  when  reduced  to  the  first.  Thus,  if  the  proposition 
were  that  pagans  may  be  virtuous,  and  the  evidence  to  prove  it  were  the 
example  of  Aristides ; a syllogism  in  the  third  figure, 

Aristides  was  virtuous, 

Aristides  was  a pagan, 
therefore 

Some  pagan  was  virtuous, 

would  be  a more  natural  mode  of  stating  the  argument,  and  would  carry 
conviction  more  instantly  home,  than  the  same  ratiocination  strained  into 
the  first  figure,  thus — 

Aristides  was  virtuous, 

Some  pagan  was  Aristides, 
therefore 

Some  pagan  was  virtuous. 

A German  philosopher,  Lambert,  whose  JVeues  Organon  (published  in 
the  year  1764)  contains  among  other  things  one  of  the  most  elaborate  and 
complete  expositions  which  had  ever  been  made  of  the  syllogistic  doctrine, 
has  expressly  examined  what  sort  of  arguments  fall  most  naturally  and  suit- 
ably into  each  of  the  four  figures;  and  his  investigation  is  characterized  by 


RATIOCINATION,  OR  SYLLOGISM. 


131 


great  ingenuity  and  clearness  of  thought.*  The  argument,  however,  is  one 
and  the  same, in  whichever  figure  it  is  expressed;  since, as  we  have  already 
seen,  the  premises  of  a syllogism  in  the  second,  third,  or  fourth  figure,  and 
those  of  the  syllogism  in  the  first  figure  to  whicli  it  may  be  reduced,  are 
the  same  premises  in  every  tiling  except  language,  or,  at  least,  as  much  of 
them  as  contributes  to  the  proof  of  the  conclusion  is  the  same.  We  are 
therefore  at  liberty,  in  conformity  with  the  general  opinion  of  logicians,  to 
consider  the  two  elementary  forms  of  the  first  figure  as  the  universal  types 
of  all  correct  ratiocination ; the  one,  when  the  conclusion  to  be  proved  is 
affirmative,  the  other,  when  it  is  negative ; even  though  certain  arguments 
may  have  a tendency  to  clothe  themselves  in  the  forms  of  the  second,  third, 
and  fourth  figures;  which,  however,  can  not  possibly  happen  with  the  only 
class  of  arguments  whicli  are  of  first-rate  scientific  importance,  those  in 
which  the  conclusion  is  a universal  affirmative,  such  conclusions  being  sus- 
ceptible of  proof  in  the  first  figure  alone.f 

* His  conclusions  are,  “The  first  figure  is  suited  to  the  discovery  or  proof  of  the  properties 
of  a thing  ; the  second  to  the  discovery  or  proof  of  the  distinctions  between  things  ; the  third 
to  the  discovery  or  proof  of  instances  and  exceptions;  the  fourth  to  the  discovery,  or  exclu- 
sion, of  the  different  species  of  a genus.”  The  reference  of  syllogisms  in  the  last  three  figures 
to  the  dictum  de  omni  et  nul/o  is,  in  Lambert’s  opinion,  strained  and  unnatural : to  each  of 
the  three  belongs,  according  to  him,  a separate  axiom,  co-ordinate  and  of  equal  authority  with 
that  dictum , and  to  which  he  gives  the  names  of  dictum  de  diverso  for  the  second  figure, 
dictum  de  exemplo  for  the  third,  and  dictum  de  reciproco  for  the  fourth.  See  part  i. , or  Dia- 
noiologie,  chap.  iv. , § 229  et  seqq.  Mr.  Bailey  ( Theory  of  Reasoning,  2d  ed.,  pp.  70-74) 
takes  a similar  view  of  the  subject. 

f Since  this  chapter  was  written,  two  treatises  have  appeared  (or  rather  a treatise  and  a 
fragment  of  a treatise),  which  aim  at  a further  improvement  in  the  theory  of  the  forms  of 
ratiocination:  Mr.  De  Morgan's  “Formal  Logic;  or,  the  Calculus  of  Inference,  Necessary 
and  Probable;”  and  the  “New  Analytic  of  Logical  Forms,”  attached  as  an  Appendix  to  Sir 
William  Hamilton’s  Discussions  on  Philosophy,  and  at  greater  length,  to  his  posthumous  Lec- 
tures on  Logic. 

In  Mr.  De  Morgan’s  volume — abounding,  in  its  more  popular  parts,  with  valuable  observa- 
tions felicitously  expressed — the  principal  feature  of  originality  is  an  attempt  to  bring  within 
strict  technical  rules  the  cases  in  which  a conclusion  can  be  drawn  from  premises  of  a form 
usually  classed  as  particular.  Mr.  De  Morgan  observes,  very  justly,  that  from  the  premises 
most  Bs  are  Cs,  most  Bs  are  As,  it  may  be  concluded  with  certainty  that  some  As  are  Cs, 
since  two  portions  of  the  class  B,  each  of  them  comprising  more  than  half,  must  necessarily 
in  part  consist  of  the  same  individuals.  Following  out  this  line  of  thought,  it  is  equally  evi- 
dent that  if  we  knew  exactly  what  proportion  the  “most”  in  each  of  the  premises  bear  to  the 
entire  class  B,  we  could  increase  in  a corresponding  degree  the  definiteness  of  the  conclusion. 
Thus  if  GO  per  cent,  of  B are  included  in  C,  and  70  per  cent,  in  A,  30  per  cent,  at  least  must 
be  common  to  both  ; in  other  words,  the  number  of  As  which  are  Cs,  and  of  Cs  which  are 
As,  must  be  at  least  equal  to  30  per  cent',  of  the  class  B.  Proceeding  on  this  conception  of 
“numerically  definite  propositions,”  and  extending  it  to  such  forms  as  these: — “45  Xs  (or 
more)  are  each  of  them  one  of  70  Ys,”  or  “45  Xs  (or  more)  are  no  one  of  them  to  be  found 
among  70  Ys,”and  examining  what  inferences  admit  of  being  drawn  from  the  various  com- 
binations which  may  be  made  of  premises  of  this  description,  Mr.  De  Morgan  establishes  uni- 
versal formulae  for  such  inferences ; creating  for  that  purpose  not  only  a new  technical  lan- 
guage, but  a formidable  array  of  symbols  analogous  to  those  of  algebra. 

Since  it  is  undeniable  that  inferences,  in  the  cases  examined  by  Mr.  De  Morgan,  can  legiti- 
mately be  drawn,  and  that  the  ordinary  theory  takes  no  account  of  them,  I will  not  say  that 
it  was  not  worth  while  to  show  in  detail  how  these  also  could  be  reduced  to  formula;  as  rigor- 
ous as  those  of  Aristotle.  What  Mr.  De  Morgan  has  done  was  worth  doing  once  (perhaps 
more  than  once,  as  a school  exercise) ; but  I question  if  its  results  are  worth  studying  and 
mastering  for  any  practical  purpose.  The  practical  use  of  technical  forms  of  reasoning  is  to 
bar  out  fallacies  : but  the  fallacies  which  require  to  be  guarded  against  in  ratiocination  properly 
so  called,  arise  from  the  incautious  use  of  the  common  forms  of  language ; and  the  logician 
must  track  the  fallacy  into  that  territory,  instead  of  waiting  for  it  on  a territory  of  his  own. 
While  he  remains  among  propositions  which  have  acquired  the  numerical  precision  of  the 
Calculus  of  Probabilities,  the  enemy  is  left  in  possession  of  the  only  ground  on  which  he  can 
be  formidable.  And  since  the  propositions  (short  of  universal)  on  which  a thinker  has  to  de- 


132 


REASONING. 


§ 2.  On  examining,  then,  these  two  general  formulae,  we  find  that  in 
both  of  them,  one  premise,  the  major,  is  a universal  proposition;  and  ac- 

pend,  either  for  purposes  of  speculation  or  of  practice,  do  not,  except  in  a few  peculiar  cases, 
admit  of  any  numerical  precision  ; common  reasoning  can  not  be  translated  into  Mr.  De 
Morgan's  forms,  which  therefore  can  not  serve  any  purpose  as  a test  of  it. 

Sir  William  Hamilton’s  theory  of  the  “ quantification  of  the  predicate  ” may  be  described  as 
follows : 

“Logically”  (I  quote  his  words)  “we  ought  to  take  into  account  the  quantity,  always  un- 
derstood in  thought,  but  usually,  for  manifest  reasons,  elided  in  its  expression,  not  only  of  the 
subject,  but  also  of  the  predicate  of  a judgment.”  All  A is  B,  is  equivalent  to  all  A is  some 
B.  No  A is  B,  to  No  A is  any  B.  Some  A is  B,  is  tantamount  to  some  A is  some  B. 
Some  A is  not  B,  to  Some  A is  not  any  B.  As  in  these  forms  of  assertion  the  predicate  is 
exactly  co-extensive  with  the  subject,  they  all  admit  of  simple  conversion ; and  by  this  we 
obtain  two  additional  forms — Some  B is  all  A,  and  No  B is  some  A.  We  may  also  make 
the  assertion  All  A 5s  all  B,  which  will  be  true  if  the  classes  A and  B are  exactly  co-extensive. 
The  last  three  forms,  though  conveying  real  assertions,  have  no  place  in  the  ordinary  classifi- 
cation of  Propositions.  All  propositions,  then,  being  supposed  to  be  translated  into  this  lan- 
guage, and  written  each  in  that  one  of  the  preceding  forms  which  answers  to  its  signification, 
there  emerges  a new  set  of  syllogistic  rules,  materially  different  from  the  common  ones.  A 
general  view  of  the  points  of  difference  may  be  given  in  the  words  of  Sir  W.  Hamilton  ( Dis- 
cussions, 2d  ed.,  p.  651)  : 

“The  revocation  of  the  two  terms  of  a Proposition  to  their  true  relation  ; a proposition  be- 
ing always  an  equation  of  its  subject  and  its  predicate. 

“The  consequent  reduction  of  the  Conversion  of  Propositions  from  three  species  to  one — 
that  of  Simple  Conversion. 

“ The  reduction  of  all  the  General  Laws  of  Categorical  Syllogisms  to  a single  Canon. 

“The  evolution  from  that  one  canon  of  all  the  Species  and  varieties  of  Syllogisms. 

“The  abrogation  of  all  the  Special  Laics  of  Syllogism. 

“A  demonstration  of  the  exclusive  possibility  of  Three  Syllogistic  Eigures ; and  (on  new 
grounds)  the  scientific  and  final  abolition  of  the  Fourth. 

“A  manifestation  that  Figure  is  an  unessential  variation  in  syllogistic  form;  and  the  con- 
sequent absurdity  of  Reducing  the  syllogisms  of  the  other  figures  to  the  first. 

“An  enouncement  of  one  Organic  Principle  for  each  Figure. 

“A  determination  of  the  true  number  of  the  Legitimate  Moods  ; with 

“Their  amplification  in  number  (thirty-six); 

“Their  numerical  equality  under  all  the  figures ; and 

“Their  relative  equivalence,  or  virtual  identity,  throughout  every  schematic  difference. 

“That,  in  the  second  and  third  figures,  the  extremes  holding  both  the  same  relation  to  the 
middle  term,  there  is  not,  as  in  the  first,  an  opposition  and  subordination  between  a term  ma- 
jor and  a term  minor,  mutually  containing  and  contained,  in  the  counter  wholes  of  Extension 
and  Comprehension. 

“Consequently,  in  the  second  and  third  figures,  there  is  no  determinate  major  and  minor 
premises,  and  there  are  two  indifferent  conclusions : whereas  in  the  first  the  premises  are  de- 
terminate, and  there  is  a single  proximate  conclusion.” 

This  doctrine,  like  that  of  Mr.  De  Morgan  previously  noticed,  is  a real  addition  to  the  syl- 
logistic theory  ; and  has  moreover  this  advantage  over  Mr.  De  Morgan’s  “numerically  definite 
Syllogism,”  that  the  forms  it  supplies  are  really  available  as  a test  of  the  correctness  of  ratioc- 
ination ; since  propositions  in  the  common  form  may  always  have  their  predicates  quantified, 
and  so  be  made  amenable  to  Sir  W.  Hamilton’s  rules.  Considered,  however,  as  a contribution 
to  the  Science  of  Logic,  that  is,  to  the  analysis  of  the  mental  processes  concerned  in  reasoning, 
the  new  doctrine  appears  to  me,  I confess,  not  merely  superfluous,  but  erroneous;  since  the 
form  in  which  it  clothes  propositions  does  not,  like  the  ordinary  form,  express  what  is  in  the 
mind  of  the  speaker  when  he  enunciates  the  proposition.  I can  not  think  Sir  William  Ham- 
ilton right  in  maintaining  that  the  quantity  of  the  predicate  is  “always  understood  in  thought.” 
It  is  implied,  but  is  not  present  to  the  mind  of  the  person  who  asserts  the  proposition.  The 
quantification  of  the  predicate,  instead  of  being  a means  of  bringing  out  more  clearly  the  mean- 
ing of  the  proposition,  actually  leads  the  mind  out  of  the  proposition,  into  another  order  of 
ideas.  For  when  we  say,  All  men  are  mortal,  we  simply  mean  to  affirm  the  attribute  mor- 
tality of  all  men ; without  thinking  at  all  of  the  class  mortal  in  the  concrete,  or  troubling  our- 
selves about  whether  it  contains  any  other  beings  or  not.  It  is  only  for  some  artificial  pur- 
pose that  we  ever  look  at  the  proposition  in  the  aspect  in  which  the  predicate  also  is  thought 
of  as  a class-name,  either  including  the  subject  only,  or  the  subject  and  something  more.  (See 
above,  p.  77,  78.) 

For  a fuller  discussion  of  this  subject,  see  the  twenty-second  chapter  of  a work  already  re- 
ferred to,  “An  Examination  of  Sir  William  Hamilton’s  Philosophy,” 


RATIOCINATION,  OR  SYLLOGISM. 


133 


cording  as  this  is  affirmative  or  negative,  the  conclusion  is  so  too.  All 
ratiocination,  therefore,  starts  from  a general  proposition,  principle,  or  as- 
sumption : a proposition  in  which  a predicate  is  affirmed  or  denied  of  an 
entire  class;  that  is,  in  which  some  attribute,  or  the  negation  of  some 
attribute,  is  asserted  of  an  indefinite  number  of  objects  distinguished 
by  a common  characteristic,  and  designated,  in  consequence,  by  a common 
name. 

The  other  premise  is  always  affirmative,  and  asserts  that  something  (which 
may  be  either  an  individual,  a class,  or  part  of  a class)  belongs  to,  or  is  in- 
cluded in,  the  class  respecting  which  something  was  affirmed  or  denied  in 
the  major  premise.  It  follows  that  the  attribute  affirmed  or  denied  of  the 
entire  class  may  (if  that  affirmation  or  denial  was  correct)  be  affirmed  or 
denied  of  the  object  or  objects  alleged  to  be  included  in  the  class:  and  this 
is  precisely  the  assertion  made  in  the  conclusion. 

Whether  or  not  the  foregoing  is  an  adequate  account  of  the  constituent 
parts  of  the  syllogism,  will  be  presently  considered ; but  as  far  as  it  goes  it 
is  a true  account.  It  has  accordingly  been  generalized,  and  erected  into  a 
logical  maxim,  on  which  all  ratiocination  is  said  to  be  founded,  insomuch 
that  to  reason,  and  to  apply  the  maxim,  are  supposed  to  be  one  and  the 
same  thing.  The  maxim  is,  That  whatever  can  be  affirmed  (or  denied)  of 
a class,  may  be  affirmed  (or  denied)  of  every  thing  included  in  the  class. 
This  axiom,  supposed  to  be  the  basis  of  the  syllogistic  theory,  is  termed  by 
logicians  the  dictum  de  omni  et  nullo. 

This  maxim,  however,  when  considered  as  a principle  of  reasoning,  ap- 
pears suited  to  a system  of  metaphysics  once  indeed  generally  received,  but 
which, for  the  last  two  centuries  has  been  considered  as  finally  abandoned, 
though  there  have  not  been  wanting  in  our  own  day  attempts  at  its  revival. 
So  long  as  what  are  termed  Universals  were  regarded  as  a peculiar  kind  of 
substances,  having  an  objective  existence  distinct  from  the  individual  ob 
jects  classed  under  them,  the  dictum  de  omni  conveyed  an  important  mean- 
ing; because  it  expressed  the  intercommunity  of  nature,  which  it  was  nec- 
essary on  that  theory  that  we  should  suppose  to  exist  between  those  gen- 
eral substances  and  the  particular  substances  which  were  subordinated  to 
them.  That  every  thing  predicable  of  the  universal  was  predicable  of  the 
various  individuals  contained  under  it,  was  then  no  identical  proposition, 
but  a statement  of  what  was  conceived  as  a fundamental  law  of  the  uni- 
verse. The  assertion  that  the  entire  nature  and  properties  of  the  substan- 
tia secunda  formed  part  of  the  nature  and  properties  of  each  of  the  indi- 
vidual substances  called  by  the  same  name ; that  the  properties  of  Man,  for 
example,  were  properties  of  all  men ; was  a proposition  of  real  significance 
when  man  did  not  mean  all  men,  but  something  inherent  in  men,  and  vast- 
ly superior  to  them  in  dignity.  Now,  however,  when  it  is  known  that  a 
class,  a universal,  a genus  or  species,  is  not  an  entity  per  se,  but  neither 
more  nor  less  than  the  individual  substances  themselves  which  are  placed 
in  the  class,  and  that  there  is  nothing  real  in  the  matter  except  those  objects, 
a common  name  given  to  them,  and  common  attributes  indicated  by  the 
name;  what,  I should  be  glad  to  know,  do  we  learn  by  being  told,  that 
whatever  can  be  affirmed  of  a class,  may  be  affirmed  of  every  object  con- 
tained in  the  class?  The  class  is  nothing  but  the  objects  contained  in  it: 
and  the  dictum  de  omni  merely  amounts  to  the  identical  proposition,  that 
whatever  is  true  of  certain  objects,  is  true  of  each  of  those  objects.  If  all 
ratiocination  were  no  more  than  the  application  of  this  maxim  to  particular 
cases,  the  syllogism  would  indeed  be,  what  it  has  so  often  been  declared  to 


134 


REASONING. 


be,  solemn  trifling.  The  dictum  de  omni  is  on  a par  with  another  truth, 
which  in  its  time  was  also  reckoned  of  great  importance,  “Whatever  is, 
is.”  To  give  any  real  meaning  to  the  dictum  de  omni,  we  must  consider 
it  not  as  an  axiom,  but  as  a definition ; we  must  look  upon  it  as  intended 
to  explain,  in'a  circuitous  and  paraphrastic  manner,  the  meaning  of  the 
word  class. 

An  error  which  seemed  finally  refuted  and  dislodged  from  thought,  often 
needs  only  put  on  a new  suit  of  phrases,  to  be  welcomed  back  to  its  old 
quarters,  and  allowed  to  repose  unquestioned  for  another  cycle  of  ages. 
Modern  philosophers  have  not  been  sparing  in  their  contempt  for  the  scho- 
lastic dogma  that  genera  and  species  are  a peculiar  kind  of  substances,  which 
general  substances  being  the  only  permanent  things,  while  the  individual 
substances  comprehended  under  them  are  in  a perpetual  flux,  knowledge, 
which  necessarily  imports  stability,  can  only  have  relation  to  those  general 
substances  or  universals,  and  not  to  the  facts  or  particulars  included  un- 
der them.  Yet,  though  nominally  rejected,  this  very  doctrine,  whether  dis- 
guised under  the  Abstract  Ideas  of  Locke  (whose  speculations,  however,  it 
has  less  vitiated  than  those  of  perhaps  any  other  writer  who  has  been  in- 
fected with  it),  under  the  ultra-nominalism  of  Hobbes  and  Condillac,  or  the 
ontology  of  the  later  German  schools,  has  never  ceased  to  poison  philosophy. 
Once  accustomed  to  consider  scientific  investigation  as  essentially  consist- 
ing in  the  study  of  universals,  men  did  not  drop  this  habit  of  thought  when 
they  ceased  to  regard  universals  as  possessing  an  independent  existence : 
and  even  those  who  went  the  length  of  considering  them  as  mere  names, 
could  not  free  themselves  from  the  notion  that  the  investigation  of  truth 
consisted  entirely  or  partly  in  some  kind  of  conjuration  or  juggle  with  those 
names.  When  a philosopher  adopted  fully  the  Nominalist  view  of  the 
signification  of  general  language,  retaining  along  with  it  the  dictum  de 
omni  as  the  foundation  of  all  reasoning,  two  such  premises  fairly  put  to- 
gether were  likely,  if  he  was  a consistent  thinker,  to  land  him  in  rather 
startling  conclusions.  Accordingly  it  has  been  seriously  held,  by  writers 
of  deserved  celebrity,  that  the  process  of  arriving  at  new  truths  by  reason- 
ing consists  in  the  mere  substitution  of  one  set  of  arbitrary  signs  for  an- 
other ; a doctrine  which  they  suppose  to  derive  irresistible  confirmation 
from  the  example  of  algebra.  If  there  were  any  process  in  sorcery  or 
necromancy  more  preternatural  than  this,  I should  be  much  surprised. 
The  culminating  point  of  this  philosophy  is  the  noted  aphorism  of  Condil- 
lac, that  a science  is  nothing,  or  scarcely  any  thing,  but  une  langue  bien 
faite  • in  other  words,  that  the  one  sufficient  rule  for  discovering  the  nature 
and  properties  of  objects  is  to  name  them  properly:  as  if  the  reverse  were 
not  the  truth,  that  it  is  impossible  to  name  them  properly  except  in  propor- 
tion as  we  are  already  acquainted  with  their  nature  and  properties.  Can 
it  be  necessary  to  say,  that  none,  not  even  the  most  trivial  knowledge  with 
respect  to  Things,  ever  was  or  could  be  originally  got  at  by  any  conceivable 
manipulation  of  mere  names,  as  such  ; and  that  what  can  be  learned  from 
names,  is  only  what  somebody  who  used  the  names  knew  before?  Philo- 
sophical analysis  confirms  the  indication  of  common  sense,  that  the  func- 
tion of  names  is  but  that  of  enabling  us  to  remember  and  to  communicate 
our  thoughts.  That  they  also  strengthen,  even  to  an  incalculable  extent, 
the  power  of  thought  itself,  is  most  true : but  they  do  this  by  no  intrinsic 
and  peculiar  virtue;  they  do  it  by  the  power  inherent  in  an  artificial  mem- 
ory, an  instrument  of  which  few  have  adequately  considered  the  immense 
potency.  As  an  artificial  memory,  language  truly  is,  what  it  has  so  often 


RATIOCINATION,  OR  SYLLOGISM. 


135 


been  called,  an  instrument  of  thought ; but  it  is  one  thing  to  be  the  instru- 
ment, and  another  to  be  the  exclusive  subject  upon  which  the  instrument 
is  exercised.  We  think,  indeed,  to  a considerable  extent,  by  means  of 
names,  but  what  we  think  of,  are  the  things  called  by  those  names;  and 
there  can  not  be  a greater  error  than  to  imagine  that  thought  can  be  car- 
ried on  with  nothing  in  our  mind  but  names,  or  that  we  can  make  the 
names  think  for  us. 

§ 3.  Those  who  considered  the  dictum  de  omni  as  the  foundation  of  the 
syllogism,  looked  upon  arguments  in  a manner  corresponding  to  the  erro- 
neous view  which  Hobbes  took  of  propositions.  Because  there  are  some 
propositions  which  are  merely  verbal,  Hobbes,  in  order  apparently  that  his 
definition  might  be  rigorously  universal,  defined  a proposition  as  if  no 
propositions  declared  any  thing  except  the  meaning  of  words.  If  Hobbes 
was  right;  if  no  further  account  than  this  could  be  given  of  the  import  of 
propositions ; no  theory  could  be  given  but  the  commonly  received  one, 
of  the  combination  of  propositions  in  a syllogism.  If  the  minor  premise 
asserted  nothing  more  than  that  something  belongs  to  a class,  and  if  the 
major  premise  asserted  nothing  of  that  class  except  that  it  is  included  in 
another  class,  the  conclusion  would  only  be  that  what  was  included  in  the 
lower  class  is  included  in  the  higher,  and  the  result,  therefore,  nothing  ex- 
cept that  the  classification  is  consistent  with  itself.  But  we  have  seen  that 
it  is  no  sufficient  account  of  the  meaning  of  a proposition,  to  say  that  it 
refers  something  to,  or  excludes  something  from,  a class.  Every  proposi- 
tion which  conveys  real  information  asserts  a matter  of  fact,  dependent  on 
the  laws  of  nature,  and  not  on  classification.  It  asserts  that  a given  object 
does  or  does  not  possess  a given  attribute;  or  it  asserts  that  two  attri- 
butes, or  sets  of  attributes,  do  or  do  not  (constantly  or  occasionally)  co-ex- 
ist. Since  such  is  the  purport  of  all  propositions  which  convey  any  real 
knowledge,  and  since  ratiocination  is  a mode  of  acquiring  real  knowledge, 
any  theory  of  ratiocination  which  does  not  recognize  this  import  of  propo- 
sitions, can  not,  we  may  be  sure,  be  the  true  one. 

Applying  this  view  of  propositions  to  the  two  premises  of  a syllogism, 
wre  obtain  the  following  results.  The  major  premise,  which,  as  already 
remarked,  is  always  universal,  asserts,  that  all  things  which  have  a certain 
attribute  (or  attributes)  have  or  have  not  along  with  it,  a certain  other  at- 
tribute (or  attributes).  The  minor  premise  asserts  that  the  thing  or  set 
of  things  which  are  the  subject  of  that  premise,  have  the  first-mentioned 
attribute;  and  the  conclusion  is,  that  they  have  (or  that  they  have  not),  the 
second.  Thus  in  our  former  example, 

All  men  are  mortal, 

Socrates  is  a man, 
therefore 

Socrates  is  mortal, 

the  subject  and  predicate  of  the  major  premise  are  connotative  terms,  de- 
noting objects  and  connoting  attributes.  The  assertion  in  the  major  prem- 
ise is,  that  along  with  one  of  the  two  sets  of  attributes,  we  always  find 
the  other:  that  the  attributes  connoted  by  “man”  never  exist  unless  con- 
joined with  the  attribute  called  mortality.  The  assertion  in  the  minor  prem- 
ise is  that  the  individual  named  Socrates  possesses  the  former  attributes; 
and  it  is  concluded  that  he  possesses  also  the  attribute  mortality.  Or,  if 
both  the  premises  are  general  propositions,  as 


136 


REASONING. 


All  men  are  mortal, 

All  kings  are  men, 
therefore 

All  kings  are  mortal, 

the  minor  premise  asserts  that  the  attributes  denoted  by  kingship  only 
exist  in  conjunction  Avith  those  signified  by  the  word  man.  The  major 
asserts  as  before,  that  the  last-mentioned  attributes  are  never  found  without 
the  attribute  of  mortality.  The  conclusion  is,  that  wherever  the  attributes 
of  kingship  are  found,  that  of  mortality  is  found  also. 

If  the  major  premise  were  negative,  as,  No  men  are  omnipotent,  it  would 
assert,  not  that  the  attributes  connoted  by  “ man”  never  exist  without,  but 
that  they  never  exist  with,  those  connoted  by  “omnipotent:”  from  which, 
together  with  the  minor  premise,  it  is  concluded,  that  the  same  incompati- 
bility exists  between  the  attribute  omnipotence  and  those  constituting  a 
king.  In  a similar  manner  we  might  analyze  any  other  example  of  the 
syllogism. 

If  we  generalize  this  process,  and  look  out  for  the  principle  or  law  in- 
volved in  every  such  inference,  and  presupposed  in  every  syllogism,  the 
propositions  of  which  are  any  thing  more  than  merely  verbal;  we  find,  not 
the  unmeaning  dictum  de  omni  et  nullo,  but  a fundamental  principle,  or 
rather  two  principles,  strikingly  resembling  the  axioms  of  mathematics. 
The  first,  which  is  the  principle  of  affirmative  syllogisms,  is,  that  things 
which  co-exist  with  the  same  thing,  co-exist  with  one  another:  or  (still  more 
precisely)  a thing  which  co-exists  with  another  thing,  which  other  co-exists 
with  a third  thing,  also  co-exists  with  that  third  thing.  The  second  is  the 
principle  of  negative  syllogisms,  and  is  to  this  effect:  that  a thing  which 
co-exists  with  another  thing,  with  which  other  a third  thing  does  not  co-ex- 
ist,  is  not  co-existent  with  that  third  thing.  These  axioms  manifestly  relate 
to  facts,  and  not  to  conventions ; and  one  or  other  of  them  is  the  ground  of 
the  legitimacy  of  every  argument  in  which  facts  and  not  conventions  are 
the  matter  treated  of.* 

* Mr.  Herbert  Spencer  (Princij)les  of  Psychology,  pp.  125-7),  though  his  theory  of  the  syl- 
logism coincides  with  all  that  is  essential  of  mine,  thinks  it  a logical  fallacy  to  present  the  two 
axioms  in  the  text,  as  the  regulating  principles  of  syllogism.  He  charges  me  with  falling 
into  the  error  pointed  out  by  Archbishop  Whately  and  myself,  of  confounding  exact  likeness 
with  literal  identity ; and  maintains,  that  we  ought  not  to  say  that  Socrates  possesses  the 
same  attributes  which  are  connoted  by  the  word  Man,  but  only  that  he  possesses  attributes 
exactly  like  them  : according  to  which  phraseology,  Socrates,  and  the  attribute  mortality, 
are  not  two  things  co-existing  with  the  same  thing,  as  the  axiom  asserts,  but  two  things  co- 
existing with  two  different  things. 

The  question  between  Mr.  Spencer  and  me  is  merely  one  of  language  ; for  neither  of  us  (if 
I understand  Mr.  Spencer’s  opinions  rightly)  believes  an  attribute  to  be  a real  thing,  possessed 
of  objective  existence ; we  believe  it  to  be  a particular  mode  of  naming  our  sensations,  or  our 
expectations  of  sensation,  when  looked  at  in  their  relation  to  an  external  object  which  excites 
them.  The  question  raised  by  Mr.  Spencer  does  not,  therefore,  concern  the  properties  of  any 
really  existing  thing,  but  the  comparative  appropriateness,  for  philosophical  purposes,  of  two 
different  modes  of  using  a name.  Considered  in  this  point  of  view,  the  phraseology  1 have 
employed,  which  is  that  commonly  used  by  philosophers,  seems  to  me  to  be  the  best.  Mr. 
Spencer  is  of  opinion  that  because  Socrates  and  Alcibiades  are  not  the  same  man,  the  attri- 
bute which  constitutes  them  men  should  not  be  called  the  same  attribute ; that  because  the 
humanity  of  one  man  and  that  of  another  express  themselves  to  our  senses  not  by  the  same 
individual  sensations  but  by  sensations  exactly  alike,  humanity  ought  to  be  regarded  as  a dif- 
ferent attribute  in  every  different  man.  But  on  this  showing,  the  humanity  even  of  any  one 
man  should  be  considered  as  different  attributes  now  and  half  an  hour  hence ; for  the  sensa- 
tions by  which  it  will  then  manifest  itself  to  my  organs  will  not  be  a continuation  of  my  pres- 
ent sensations,  but  a repetition  of  them ; fresh  sensations,  not  identical  with,  but  only  exactly 


RATIOCINATION,  OR  SYLLOGISM. 


137 


§ 4.  It  remains  to  translate  this  exposition  of  the  syllogism  from  the 
one  into  the  other  of  the  two  languages  in  which  we  formerly  remarked* 
that  all  propositions,  and  of  course  therefore  all  combinations  of  proposi- 
tions, might  be  expressed.  TVe  observed  that  a proposition  might  be  con-, 
sidered  in  two  different  lights;  as  a portion  of  our  knowledge  of  nature, 
or  as  a memorandum  for  our  guidance.  Under  the  former,  or  speculative 
aspect,  an  affirmative  general  proposition  is  an  assertion  of  a speculative 
truth,  viz., that  whatever  has  a certain  attribute  has  a certain  other  attribute. 
Under  the  other  aspect,  it  is  to  be  regarded  not  as  a part  of  our  knowledge, 
but  as  an  aid  for  our  practical  exigencies,  by  enabling  us,  when  we  see  or 
learn  that  an  object  possesses  one  of  the  two  attributes,  to  infer  that  it  pos- 
sesses the  other;  thus  employing  the  first  attribute  as  a mark  or  evidence 
of  the  second.  Thus  regarded,  every  syllogism  comes  within  the  following 
general  formula : 

Attribute  A is  a mark  of  attribute  B, 

The  given  object  has  the  mark  A, 
therefore 

The  given  object  has  the  attribute  B. 

Referred  to  this  type,  the  arguments  which  we  have  lately  cited  as 
specimens  of  the  syllogism,  will  express  themselves  in  the  following 
manner : 

The  attributes  of  man  are  a mark  of  the  attribute  mortality, 

Socrates  has  the  attributes  of  man, 
therefore 

Socrates  has  the  attribute  mortality. 

like  the  present.  If  every  general  conception,  instead  of  being  “the  One  in  the  Many,”  were 
considered  to  be  as  many  different  conceptions  as  there  are  things  to  which  it  is  applicable, 
there  would  be  no  such  thing  as  general  language.  A name  would  have  no  general  meaning 
if  man  connoted  one  thing  when  predicated  of  John,  and  another,  though  closely  resembling, 
thing  when  predicated  of  William.  Accordingly  a recent  pamphlet  asserts  the  impossibility 
of  general  knowledge  on  this  precise  ground. 

The  meaning  of  any  general  name  is  some  outward  or  inward  phenomenon,  consisting,  in 
the  last  resort,  of  feelings ; and  these  feelings,  if  their  continuity  is  for  an  instant  broken,  are 
no  longer  the  same  feelings,  in  the  sense  of  individual  identity.  What,  then,  is  the  common 
something  which  gives  a meaning  to  the  general  name  ? Mr.  Spencer  can  only  say,  it  is  the 
similarity  of  the  feelings  ; and  I rejoin,  the  attribute  is  precisely  that  similarity.  The  names 
of  attributes  are  in  their  ultimate  analysis  names  for  the  resemblances  of  our  sensations  (or 
other  feelings).  Every  general  name,  whether  abstract  or  concrete,  denotes  or  connotes  one 
or  more  of  those  resemblances.  It  will  not,  probably,  be  denied,  that  if  a hundred  sensations 
are  undistinguishably  alike,  their  resemblance  ought  to  he  spoken  of  as  one  resemblance,  and 
not  a hundred  resemblances  which  merely  resemble  one  another.  The  things  compared  are 
many,  hut  the  something  common  to  all  of  them  must  be  conceived  as  one,  just  as  the  name 
is  conceived  as  one,  though  corresponding  to  numerically  different  sensations  of  sound  each 
time  it  is  pronounced.  The  general  term  man  does  not  connote  the  sensations  derived  once 
from  one  man,  which,  once  gone,  can  no  more  occur  again  than  the  same  flash  of  light- 
ning. It  connotes  the  general  type  of  the  sensations  derived  always  from  all  men,  and  the 
power  (always  thought  of  as  one)  of  producing  sensations  of  that  type.  And  the  axiom 
might  be  thus  worded : Two  types  of  sensation  each  of  which  co-exists  with  a third  type, 
co-exist  with  another ; or  Two  powers  each  of  which  co-exists  with  a third  power  co-exist 
with  one  another. 

Mr.  Spencer  has  misunderstood  me  in  another  particular.  He  supposes  that  the  co-exist- 
ence spoken  of  in  the  axiom,  of  two  things  with  the  same  third  thing,  means  simultaneousness 
in  time.  The  co-existence  meant  is  that  of  being  jointly  attributes  of  the  same  subject.  The 
attribute  of  being  born  without  teeth,  and  the  attribute  of  having  thirty-two  teeth  in  mature 
age,  are  in  this  sense  co-existent,  both  being  attributes  of  man,  though  ex  vi  termini  never  of 
the  same  man  at  the  same  time. 

* Supra,  p.  93. 


138 


REASONING. 


And  again, 

Tiie  attributes  of  man  are  a mark  of  the  attribute  mortality, 

The  attributes  of  a king  are  a mark  of  the  attributes  of  man, 
therefore 

The  attributes  of  a king  are  a mark  of  the  attribute  mortality. 

And,  lastly, 

The  attributes  of  man  are  a mark  of  the  absence  of  the  attribute 
omnipotence, 

The  attributes  of  a king  are  a mark  of  the  attributes  of  man, 
therefore 

The  attributes  of  a king  are  a mark  of  the  absence  of  the  attribute 
signified  by  the  word  omnipotent 
(or,  are  evidence  of  the  absence  of  that  attribute). 

To  correspond  with  this  alteration  in  the  form  of  the  syllogisms,  the  ax- 
ioms on  which  the  syllogistic  process  is  founded  must  undergo  a corre- 
sponding transformation.  In  this  altered  phraseology,  both  those  axioms 
may  be  brought  under  one  general  expression ; namely,  that  whatever  has 
any  mark,  has  that  which  it  is  a mark  of.  Or,  when  the  minor  premise  as 
well  as  the  major  is  universal,  we  may  state  it  thus:  Whatever  is  a mark 
of  any  mark,  is  a mark  of  that  which  this  last  is  a mark  of.  To  trace  the 
identity  of  these  axioms  with  those  previously  laid  down,  may  be  left  to  the 
intelligent  reader.  We  shall  find,  as  we  proceed,  the  great  convenience  of 
the  phraseology  into  which  we  have  last  thrown  them,  and  which  is  better 
adapted  than  any  I am  acquainted  with,  to  express  with  precision  and  force 
what  is  aimed  at,  and  actually  accomplished,  in  every  case  of  the  ascertain- 
ment of  a truth  by  ratiocination.* 

* Professor  Bain  (Logic,  i.,  157)  considers  the  axiom  (or  rather  axioms)  here  proposed  as 
a substitute  for  the  dictum  de  omni,  to  possess  certain  advantages,  but  to  be  “unworkable  as 
a basis  of  the  syllogism.  The  fatal  defect  consists  in  this,  that  it  is  ill-adapted  to  bring  out 
the  difference  between  total  and  partial  coincidence  of  terms,  the  observation  of  which  is  the 
essential  precaution  in  syllogizing  correctly.  If  all  the  terms  were  co-extensive,  the  axiom 
would  flow  on  admirably ; A carries  B,  all  B and  none  but  B ; B carries  C in  the  same  man- 
ner ; at  once  A carries  C,  without  limitation  or  reserve.  But  in  point  of  fact,  we  know  that 
while  A carries  B,  other  things  carry  B also;  whence  a process  of  limitation  is  required,  in 
transferring  A to  C through  B.  A (in  common  with  other  things)  carries  B ; B (in  common 
with  other  things)  carries  C ; whence  A (in  common  with  other  things)  carries  C.  The  ax- 
iom provides  no  means  of  making  this  limitation ; if  we  were  to  follow  A literally,  we  should 
be  led  to  suppose  A and  C co-extensive : for  such  is  the  only  obvious  meaning  of  ‘ the  attri- 
bute A coincides  with  the  attribute  C.’” 

It  is  certainly  possible  that  a careless  learner  here  and  there  may  suppose  that  if  A carries 
B,  it  follows  that  B carries  A.  But  if  any  one  is  so  incautious  as  to  commit  this  mistake,  the 
very  earliest  lesson  in  the  logic  of  inference,  the  Conversion  of  propositions,  will  correct  it. 
The  first  of  the  two  forms  in  which  I have  stated  the  axiom,  is  in  some  degree  open  to  Mr. 
Bain’s  criticism : when  B is  said  to  co-exist  with  A (it  must  be  by  a lapsus  calami  that  Mr. 
Bain  uses  the  word  coincide),  it  is  possible,  in  the  absence  of  warning,  to  suppose  the  meaning 
to  be  that  the  two  things  are  only  found  together.  But  this  misinterpretation  is  excluded  by 
the  other,  or  practical,  form  of  the  maxim  ; Nota  notce  est  nota  rei  ipsius.  No  one  would  be 
in  any  danger  of  inferring  that  because  a is  a mark  of  b,  b can  never  exist  without  a ; that 
because  being  in  a confirmed  consumption  is  a mark  of  being  about  to  die,  no  one  dies  who  is 
not  in  a consumption;  that  because  being  coal  is  a mark  of  having  come  out  of  the  earth, 
nothing  can  come  out  of  the  earth  except  coal.  Ordinary  knowledge  of  English  seems  a 
sufficient  protection  against  these  mistakes,  since  in  speaking  of  a mark  of  any  thing  we  are 
never  understood  as  implying  reciprocity. 

A more  fundamental  objection  is  stated  by  Mr.  Bain  in  a subsequent  passage  (p.  158). 
“The  axiom  does  not  accommodate  itself  to  the  type  of  Deductive  Reasoning  as  contrasted 
with  Induction — the  application  of  a general  principle  to  a special  case.  Any  thing  that  fails 
to  make  prominent  this  circumstance  is  not  adapted  as  a foundation  for  the  syllogism.”  But 


FUNCTIONS  AND  VALUE  OF  THE  SYLLOGISM. 


139 


CHAPTER  III. 

OP  THE  P TJNCTIONS  AND  LOGICAL  VALUE  OP  THE  SYLLOGISM. 

§ 1.  We  have  shown  what  is  the  real  nature  of  the  truths  with  which 
the  Syllogism  is  conversant,  in  contradistinction  to  the  more  superficial 
manner  in  which  their  import  is  conceived  in  the  common  theory ; and 
what  are  the  fundamental  axioms  on  which  its  probative  force  or  conclu- 
siveness depends.  We  have  now  to  inquire,  whether  the  syllogistic  proc- 
ess, that  of  reasoning  from  generals  to  particulars,  is,  or  is  not,  a process 
of  inference  ; a progress  from  the  known  to  the  unknown  : a means  of  com- 
ing to  a knowledge  of  something  which  we  did  not  know  before. 

Logicians  have  been  remarkably  unanimous  in  their  mode  of  answering 
this  question.  It  is  universally  allowed  that  a syllogism  is  vicious  if  there 
be  any  thing  more  in  the  conclusion  than  was  assumed  in  the  premises. 
But  this  is,  in  fact,  to  say,  that  nothing  ever  was,  or  can  be,  proved  by  syl- 
logism, which  was  not  known,  or  assumed  to  be  known,  before.  Is  ratioci- 
nation, then,  not  a process  of  inference?  And  is  the  syllogism,  to  which 
the  word  reasoning  has  so  often  been  represented  to  be  exclusively  appro- 
priate, not  really  entitled  to  be  called  reasoning  at  all?  This  seems  an  in- 
evitable consequence  of  the  doctrine,  admitted  by  all  writers  on  the  sub- 
ject, that  a syllogism  can  prove  no  more  than  is  involved  in  the  premises. 
Yet  the  acknowledgment  so  explicitly  made,  has  not  prevented  one  set  of 
writers  from  continuing  to  represent  the  syllogism  as  the  correct  analysis 
of  what  the  mind  actually  performs  in  discovering  and  proving  the  larger 
half  of  the  truths,  whether  of  science  or  of  daily  life,  which  we  believe; 
while  those  who  have  avoided  this  inconsistency,  and  followed  out  the  gen- 
eral theorem  respecting  the  logical  value  of  the  syllogism  to  its  legitimate 
corollary,  have  been  led  to  impute  uselessness  and  frivolity  to  the  syllogis- 
tic theory  itself,  on  the  ground  of  the  petitio  principii  which  they  allege 
to  be  inherent  in  every  syllogism.  As  I believe  both  these  opinions  to  be 
fundamentally  erroneous,  I must  request  the  attention  of  the  reader  to  cer- 
tain considerations,  without  which  any  just  appreciation  of  the  true  char- 
acter of  the  syllogism,  and  the  functions  it  performs  in  philosophy,  appears 
to  me  impossible;  but  which  seem  to  have  been  either  overlooked,  or  in- 
sufficiently adverted  to,  both  by  the  defenders  of  the  syllogistic  theory  and 
by  its  assailants. 

§ 2.  It  must  be  granted  that  in  every  syllogism,  considered  as  an 

though  it  may  be  proper  to  limit  the  term  Deduction  to  the  application  of  a general  principle 
to  a special  case,  it  has  never  been  held  that  Ratiocination  or  Syllogism  is  subject  to  the  same 
limitation ; and  the  adoption  of  it  would  exclude  a great  amount  of  valid  and  conclusive  syl- 
logistic reasoning.  Moreover,  if  the  dictum  de  omni  makes  prominent  the  fact  of  the  applica- 
tion of  a general  principle  to  a particular  case,  the  axiom  I propose  makes  prominent  the 
condition  which  alone  makes  that  application  a real  inference. 

I conclude,  therefore,  that  both  forms  have  their  value,  and  their  place  in  Logic.  The 
dictum  de  omni  should  be  retained  as  the  fundamental  axiom  of  the  logic  of  mere  consistency, 
often  called  Formal  Logic;  nor  have  I ever  quarreled  with  the  use  of  it  in  that  character, 
nor  proposed  to  banish  it  from  treatises  on  Formal  Logic.  But  the  other  is  the  proper  axiom 
for  the  logic  of  the  pursuit  of  truth  by  way  of  Deduction  ; and  the  recognition  of  it  can  alone 
show  how  it  is  possible  that  deductive  reasoning  can  be  a road  to  truth. 


140 


REASONING. 


argument  to  prove  the  conclusion,  there  is  a petitio  principii.  When 
we  say, 

All  men  are  mortal, 

Socrates  is  a man, 
therefore 

Socrates  is  mortal ; 

it  is  unanswerably  urged  by  the  adversaries  of  the  syllogistic  theory,  that 
the  proposition,  Socrates  is  mortal,  is  presupposed  in  the  more  general  as- 
sumption, All  men  are  mortal:  that  we  can  not  be  assured  of  the  mortali- 
ty of  all  men,  unless  we  are  already  certain  of  the  mortality  of  every  indi- 
vidual man:  that  if  it  be  still  doubtful  whether  Socrates,  or  any  other  in- 
dividual we  choose  to  name,  be  mortal  or  not,  the  same  degree  of  uncer- 
tainty must  hang  over  the  assertion,  All  men  are  mortal:  that  the  general 
principle,  instead  of  being  given  as  evidence  of  the  particular  case,  can  not 
itself  be  taken  for  true  without  exception,  until  every  shadow  of  doubt 
which  could  affect  any  case  comprised  with  it,  is  dispelled  by  evidence 
aliundb  / and  then  what  remains  for  the  syllogism  to  prove?  That,  in 
short,  no  reasoning  from  generals  to  particulars  can,  as  such,  prove  any 
thing:  since  from  a general  principle  we  can  not  infer  any  particulars, but 
those  which  the  principle  itself  assumes  as  known. 

This  doctrine  appears  to  me  irrefragable;  and  if  logicians,  though  una- 
ble to  dispute  it,  have  usually  exhibited  a strong  disposition  to  explain  it 
away,  this  was  not  because  they  could  discover  any  flaw  in  the  argument 
itself,  but  because  the  contrary  opinion  seemed  to  rest  on  arguments  equal- 
ly indisputable.  In  the  syllogism  last  referred  to,  for  example,  or  in  any  of 
those  which  we  previously  constructed,  is  it  not  evident  that  the  conclu- 
sion may,  to  the  person  to  whom  the  syllogism  is  presented,  be  actually 
and  bona  fide,  a new  truth?  Is  it  not  matter  of  daily  experience  that 
truths  previously  unthought  of,  facts  which  have  not  been,  and  can  not  be, 
directly  observed,  are  arrived  at  by  way  of  general  reasoning?  We  be- 
lieve that  the  Duke  of  Wellington  is  mortal.  We  do  not  know  this  by  di- 
rect observation,  so  long  as  he  is  not  yet  dead.  If  we  'were  asked  how, 
this  being  the  case,  we  know  the  duke  to  be  mortal,  we  should  probably 
answer,  Because  all  men  are  so.  Here,  therefore,  we  arrive  at  the  knowl- 
edge of  a truth  not  (as  yet)  susceptible  of  observation,  by  a reasoning 
which  admits  of  being  exhibited  in  the  following  syllogism: 

All  men  are  mortal, 

The  Duke  of  Wellington  is  a man, 
therefore 

The  Duke  of  Wellington  is  mortal. 

And  since  a large  portion  of  our  knowledge  is  thus  acquired,  logicians 
have  persisted  in  representing  the  syllogism  as  a process  of  inference  or 
proof;  though  none  of  them  has  cleared  up  the  difficulty  which  arises  from 
the  inconsistency  between  that  assertion,  and  the  principle,  that  if  there  be 
any  thing  in  the  conclusion  which  was  not  already  asserted  in  the  premi- 
ses, the  argument  is  vicious.  For  it  is  impossible  to  attach  any  serious 
scientific  value  to  such  a mere  salvo,  as  the  distinction  drawn  between  be- 
ing involved  by  implication  in  the  premises,  and  being  directly  asserted  in 
them.  When  Archbishop  Whately  says*  that  the  object  of  reasoning  is 
“ merely  to  expand  and  unfold  the  assertions  wrapped  up,  as  it  were,  and 


Logic , p.  239  (9th  ed.). 


FUNCTIONS  AND  VALUE  OF  THE  SYLLOGISM. 


141 


implied  in  those  with  which  we  set  out,  and  to  bring  a person  to  perceive 
and  acknowledge  the  full  force  of  that  which  he  has  admitted,”  he  does 
not,  I think,  meet  the  real  difficulty  requiring  to  be  explained,  namely,  how 
it  happens  that  a science,  like  geometry,  can  be  all  “ wrapped  up  ” in  a 
few  definitions  and  axioms.  Nor  does  this  defense  of  the  syllogism  differ 
much  from  what  its  assailants  urge  against  it  as  an  accusation,  when  they 
charge  it  with  being  of  no  use  except  to  those  who  seek  to  press  the  con- 
sequences of  an  admission  into  which  a person  has  been  entrapped  without 
having  considered  and  understood  its  full  force.  When  you  admitted  the 
major  premise, you  asserted  the  conclusion;  but,  says  Archbishop  Whate- 
ly,  you  asserted  it  by  implication  merely:  this,  however,  can  here  only 
mean  that  you  asserted  it  unconsciously ; that  you  did  not  know  you  were 
asserting  it ; but,  if  so,  the  difficulty  revives  in  this  shape — Ought  you  not 
to  have  known?  Were  you  warranted  in  asserting  the  general  proposi- 
tion without  having  satisfied  yourself  of  the  truth  of  every  thing  which  it 
fairly  includes?  And  if  not,  is  not  the  syllogistic  art prima  facie  what  its 
assailants  affirm  it  to  be,  a contrivance  for  catching  you  in  a trap,  and  hold- 
ing you  fast  in  it  ?* 

§ 3.  From  this  difficulty  there  appears  to  be  but  one  issue.  The  propo- 
sition that  the  Duke  of  Wellington  is  mortal,  is  evidently  an  inference;  it 
is  got  at  as  a conclusion  from  something  else;  but  do  we,  in  reality,  con- 
clude it  from  the  proposition,  All  men  are  mortal?  I answer, no. 

The  error  committed  is,  I conceive,  that  of  overlooking  the  distinction  be- 
tween two  parts  of  the  process  of  philosophizing,  the  inferring  part,  and  the 
registering  part;  and  ascribing  to  the  latter  the  functions  of  the  former. 
The  mistake  is  that  of  referring  a person  to  his  own  notes  for  the  origin  of 
his  knowledge.  If  a person  is  asked  a question,  and  is  at  the  moment  una- 
ble to  answer  it,  he  may  refresh  his  memory  by  turning  to  a memorandum 
which  he  carries  about  with  him.  But  if  he  were  asked,  how  the  fact  came 
to  his  knowledge,  he  would  scarcely  answer,  because  it  was  set  down  in  his 
note-book : unless  the  book  was  written,  like  the  Koran,  with  a quill  from 
the  wing  of  the  angel  Gabriel. 

Assuming  that  the  proposition,  The  Duke  of  Wellington  is  mortal,  is 
immediately  an  inference  from  the  proposition,  All  men  are  mortal;  whence 
do  we  derive  our  knowledge  of  that  general  truth?  Of  course  from  ob- 
servation. Now,  all  which  man  can  observe  are  individual  cases.  From 
these  all  general  truths  must  be  drawn,  and  into  these  they  may  be  again 
resolved  ; for  a general  truth  is  but  an  aggregate  of  particular  truths ; a 
comprehensive  expression,  by  which  an  indefinite  number  of  individual 
facts  are  affirmed  or  denied  at  once.  But  a general  proposition  is  not 
merely  a compendious  form  for  recording  and  preserving  in  the  memory  a 
number  of  particular  facts,  all  of  which  have  been  observed.  Generaliza- 

* It  is  hardly  necessary  to  say,  that  I am  not  contending  for  any  such  absurdity  as  that  we 
actually  “ought  to  have  known”  and  considered  the  case  of  every  individual  man,  past,  pres- 
ent, and  future,  before  affirming  that  all  men  are  mortal : although  this  interpretation  has  been, 
strangely  enough,  put  upon  the  preceding  observations.  There  is  no  difference  between  me 
and  Archbishop  Whatelv,  or  any  other  defender  of  the  syllogism,  on  the  practical  part  of  the 
matter;  I am  only  pointing  out  an  inconsistency  in  the  logical  theory  of  it,  as  conceived  by 
almost  all  writers.  I do  not  say  that  a person  who  affirmed,  before  the  Duke  of  Wellington 
was  born,  that  all  men  are  mortal,  knew  that  the  Duke  of  Wellington  was  mortal ; but  I do 
say  that  he  asserted  it ; and  I ask  for  an  explanation  of  the  apparent  logical  fallacy,  of  ad- 
ducing in  proof  of  the  Duke  of  Wellington’s  mortality,  a general  statement  which  presupposes 
it.  Finding  no  sufficient  resolution  of  this  difficulty  in  any  of  the  writers  on  Logic,  I have 
attempted  to  supply  one. 


142 


REASONING. 


tion  is  not  a process  of  mere  naming,  it  is  also  a process  of  inference. 
From  instances  which  we  have  observed,  we  feel  warranted  in  concluding, 
that  what  we  found  true  in  those  instances,  holds  in  all  similar  ones,  past, 
present,  and  future,  however  numerous  the)'  may  be.  We  then,  by  that 
valuable  contrivance  of  language  which  enables  us  to  speak  of  many  as  if 
they  were  one,  record  all  that  we  have  observed,  together  with  all  that  we 
infer  from  our  observations,  in  one  concise  expression ; and  have  thus  only 
one  proposition,  instead  of  an  endless  number,  to  remember  or  to  commu- 
nicate. The  results  of  many  observations  and  inferences,  and  instructions 
for  making  innumerable  inferences  in  unforeseen  cases,  are  compressed 
into  one  short  sentence. 

When,  therefore,  we  conclude  from  the  death  of  John  and  Thomas,  and 
every  other  person  we  ever  heard  of  in  whose  case  the  experiment  had 
been  fairly  tried,  that  the  Duke  of  Wellington  is  mortal  like  the  rest;  we 
may,  indeed,  pass  through  the  generalization,  All  men  are  mortal,  as  an  in- 
termediate stage;  but  it  is  not  in  the  latter  half  of  the  process,  the  de- 
scent from  all  men  to  the  Duke  of  Wellington,  that  the  inference  resides. 
The  inference  is  finished  when  we  have  asserted  that  all  men  are  mortal. 
What  remains  to  be  performed  afterward  is  merely  deciphering  our  own 
notes. 

Archbishop  Whately  has  contended  that  syllogizing,  or  reasoning  from 
generals  to  particulars,  is  not,  agreeably  to  the  vulgar  idea,  a peculiar  mode 
of  reasoning,  but  the  philosophical  analysis  of  the  mode  in  which  all  men 
reason,  and  must  do  so  if  they  reason  at  all.  With  the  deference  due  to  so 
high  an  authority,  I can  not  help  thinking  that  the  vulgar  notion  is,  in  this 
case,  the  more  correct.  If,  from  our  experience  of  John,  Thomas,  etc.,  who 
once  were  living,  but  are  now  dead,  we  are  entitled  to  conclude  that  all  hu- 
man beings  are  mortal,  we  might  surely  without  any  logical  inconsequence 
have  concluded  at  once  from  those  instances,  that  the  Duke  of  Wellington 
is  mortal.  The  mortality  of  John,  Thomas,  and  others  is,  after  all,  the 
whole  evidence  we  have  for  the  mortality  of  the  Duke  of  Wellington.  Not 
one  iota  is  added  to  the  proof  by  interpolating  a general  proposition. 
Since  the  individual  cases  are  all  the  evidence  we  can  possess,  evidence 
which  no  logical  form  into  which  we  choose  to  throw  it  can  make  greater 
than  it  is ; and  since  that  evidence  is  either  sufficient  in  itself,  or,  if  insuf- 
ficient for  the  one  purpose,  can  not  be  sufficient  for  the  other;  I am  una- 
ble to  see  why  we  should  be  forbidden  to  take  the  shortest  cut  from  these 
sufficient  premises  to  the  conclusion,  and  constrained  to  travel  the  “high 
priori  road,”  by  the  arbitrary  fiat  of  logicians.  I can  not  perceive  why  it 
should  bo  impossible  to  journey  from  one  place  to  another  unless  we 
“march  up  a hill,  and  then  march  down  again.”  It  may  be  the  safest 
road,  and  there  may  be  a resting-place  at  the  top  of  the  hill,  affording  a 
commanding  view  of  the  surrounding  country;  but  for  the  mere  purpose 
of  arriving  at  our  journey’s  end,  our  taking  that  road  is  perfectly  optional ; 
it  is  a question  of  time,  trouble,  and  danger. 

Not  only  may  we  reason  from  particulars  to  particulars  without  passing 
through  generals,  but  we  perpetually  do  so  reason.  All  our  earliest  infer- 
ences are  of  this  nature.  From  the  first  dawn  of  intelligence  we  draw  in- 
ferences, but  years  elapse  before  Ave  learn  the  use  of  general  language. 
The  child,  who,  having  burned  his  fingers,  avoids  to  thrust  them  again  into 
the  fire,  has  reasoned  or  inferred,  though  he  has  never  thought  of  the  gen- 
eral maxim,  Fire  burns.  He  knows  from  memory  that  he  has  been  burn- 
ed, and  on  this  evidence  believes,  when  he  sees  a candle,  that  if  he  puts  his 


FUNCTIONS  AND  VALUE  OF  THE  SYLLOGISM. 


143 


linger  into  the  flame  of  it,  he  will  be  burned  again.  He  believes  this  in  ev- 
ery case  which  happens  to  arise ; but  without  looking,  in  each  instance,  be- 
yond the  present  case.  He  is  not  generalizing;  he  is  inferring  a partic- 
ular from  particulars.  In  the  same  way,  also,  brutes  reason.  There  is 
no  ground  for  attributing  to  any  of  the  lower  animals  the  use  of  signs,  of 
such  a nature  as  to  render  general  propositions  possible.  But  those  ani- 
mals profit  by  experience,  and  avoid  what  they  have  found  to  cause  them 
pain,  in  the  same  manner,  though  not  always  with  the  same  skill,  as  a 
human  creature.  Not  only  the  burned  child,  but  the  burned  dog,  dreads 
the  fire. 

I believe  that,  in  point  of  fact,  when  drawing  inferences  from  our  per- 
sonal experience,  and  not  from  maxims  handed  down  to  us  by  books  or 
tradition,  we  much  oftener  conclude  from  particulars  to  particulars  directly, 
than  through  the  intermediate  agency  of  any  general  proposition.  We  are 
constantly  reasoning  from  ourselves  to  other  people,  or  from  one  person  to 
another,  without  giving  ourselves  the  trouble  to  erect  our  observations  into 
general  maxims  of  human  or  external  nature.  When  we  conclude  that  some 
person  will,  on  some  given  occasion,  feel  or  act  so  and  so,  we  sometimes 
judge  from  an  enlarged  consideration  of  the  manner  in  which  human  beings 
in  general,  or  persons  of  some  particular  character,  are  accustomed  to  feel 
and  act ; but  much  oftener  from  merely  recollecting  the  feelings  and  con- 
duct of  the  same  person  in  some  previous  instance,  or  from  considering 
how  we  should  feel  or  act  ourselves.  It  is  not  only  the  village  matron, 
who,  when  called  to  a consultation  upon  the  case  of  a neighbor’s  child,  pro- 
nounces on  the  evil  and  its  remedy  simply  on  the  recollection  and  authority 
of  what  she  accounts  the  similar  case  of  her  Lucy.  We  all,  where  we  have 
no  definite  maxims  to  steer  by,  guide  ourselves  in  the  same  way:  and  if  we 
have  an  extensive  experience,  and  retain  its  impressions  strongly,  we  may 
acquire  in  this  manner  a very  considerable  power  of  accurate  judgment, 
which  we  may  be  utterly  incapable  of  justifying  or  of  communicating  to 
others.  Among  the  higher  order  of  practical  intellects  there  have  been 
many  of  whom  it  was  remarked  how  admirably  they  suited  their  means  to 
their  ends,  without  being  able  to  give  any  sufficient  reasons  for  what  they 
did;  and  applied,  or  seemed  to  apply,  recondite  principles  which  they  were 
wholly  unable  to  state.  This  is  a natural  consequence  of  having  a mind 
stored  with  appropriate  particulars,  and' having  been  long  accustomed  to 
reason  at  once  from  these  to  fresh  particulars,  without  practicing  the  habit 
of  stating  to  one’s  self  or  to  others  the  corresponding  general  propositions. 
An  old  warrior,  on  a rapid  glance  at  the  outlines  of  the  ground,  is  able  at 
once  to  give  the  necessary  orders  for  a skillful  arrangement  of  his  troops ; 
though  if  he  has  received  little  theoretical  instruction,  and  has  seldom  been 
called  upon  to  answer  to  other  people  for  his  conduct,  he  may  never  have 
had  in  his  mind  a single  general  theorem  respecting  the  relation  between 
ground  and  array.  But  his  experience  of  encampments,  in  circumstances 
more  or  less  similar,  has  left  a number  of  vivid,  unexpressed,  ungeneralized 
analogies  in  his  mind,  the  most  appropriate  of  which,  instantly  suggesting 
itself,  determines  him  to  a judicious  arrangement. 

The  skill  of  an  uneducated  person  in  the  use  of  weapons,  or  of  tools,  is 
of  a precisely  similar  nature.  The  savage  who  executes  unerringly  the  ex- 
act throw  which  brings  down  his  game,  or  his  enemy,  in  the  manner  most 
suited  to  his  purpose,  under  the  operation  of  all  the  conditions  necessarily 
involved,  the  weight  and  form  of  the  weapon,  the  direction  and  distance  of 
the  object,  the  action  of  the  wind,  etc.,  owes  this  power  to  a long  series  of 


14-4 


REASONING. 


previous  experiments,  tlie  results  of  which  lie  certainly  never  framed  into 
any  verbal  theorems  or  rules.  The  same  thing  may  generally  be  said  of 
any  other  extraordinary  manual  dexterity.  Not  long  ago  a Scotch  manu- 
facturer procured  from  England,  at  a high  rate  of  wages,  a working  dyer, 
famous  for  producing  very  fine  colors,  with  the  view  of  teaching  to  his 
other  workmen  the  same  skill.  The  workman  came;  but  his  mode  of  pro- 
portioning the  ingredients,  in  which  lay  the  secret  of  the  effects  he  pro- 
duced, was  by  taking  them  up  in  handfuls,  while  the  common  method  was 
to  weigh  them.  The  manufacturer  sought  to  make  him  turn  his  handling 
system  into  an  equivalent  weighing  system,  that  the  general  principle  of 
his  peculiar  mode  of  proceeding  might  be  ascertained.  This,  however,  the 
man  found  himself  quite  unable  to  do,  and  therefore  could  impart  his  skill 
to  nobody.  He  had,  from  the  individual  cases  of  his  own  experience,  es- 
tablished a connection  in  his  mind  between  fine  effects  of  color,  and  tactual 
perceptions  in  handling  his  dyeing  materials ; and  from  these  perceptions 
lie  could,  in  any  particular  case,  infer  the  means  to  be  employed,  and  the 
effects  which  would  be  produced,  but  could  not  put  others  in  possession  of 
the  grounds  on  which  he  proceeded,  from  having  never  generalized  them 
in  his  own  mind,  or  expressed  them  in  language. 

Almost  every  one  knows  Lord  Mansfield’s  advice  to  a man  of  practical 
good  sense,  who,  being  appointed  governor  of  a colony,  had  to  preside  in 
its  courts  of  justice,  without  previous  judicial  practice  or  legal  education. 
The  advice  was  to  give  his  decision  boldly,  for  it  would  probably  be  right ; 
but  never  to  venture  on  assigning  reasons,  for  they  would  almost  infallibly 
be  wrong.  In  cases  like  this,  which  are  of  no  uncommon  occurrence,  it 
would  be  absurd  to  suppose  that  the  bad  reason  was  the  source  of  the 
good  decision.  Lord  Mansfield  knew  that  if  any  reason  were  assigned  it 
would  be  necessarily  an  afterthought,  the  judge  being  in  fact  guided  by 
impressions  from  past  experience,  without  the  circuitous  process  of  fram- 
ing general  principles  from  them,  and  that  if  he  attempted  to  frame  any 
such  he  would  assuredly  fail.  Lord  Mansfield,  however,  would  not  have 
doubted  that  a man  of  equal  experience  who  had  also  a mind  stored  with 
general  propositions  derived  by  legitimate  induction  from  that  experience, 
would  have  been  greatly  preferable  as  a judge,  to  one,  however  sagacious, 
who  could  not  be  trusted  with  the  explanation  and  justification  of  his  own 
judgments.  The  cases  of  men  of  talent  performing  wonderful  things  they 
know  not  how,  are  examples  of  the  rudest  and  most  spontaneous  form  of 
the  operations  of  superior  minds.  It  is  a defect  in  them,  and  often  a 
source  of  errors,  not  to  have  generalized  as  they  went  on  ; but  general- 
ization, though  a help,  the  most  important  indeed  of  all  helps,  is  not  an 
essential. 

Even  the  scientifically  instructed,  who  possess,  in  the  form  of  general 
propositions,  a systematic  record  of  the  results  of  the  experience  of  man- 
kind, need  not  always  revert  to  those  general  propositions  in  order  to  ap- 
ply that  experience  to  a new  case.  It  is  justly  remarked  by  Dugald  Stew- 
art, that  though  the  reasonings  in  mathematics  depend  entirely  on  the 
axioms,  it  is  by  no  means  necessary  to  our  seeing  the  conclusiveness  of 
the  proof,  that  the  axioms  should  be  expressly  adverted  to.  When  it  is 
inferred  that  AB  is  equal  to  CD  because  each  of  them  is  equal  to  EF,  the 
most  uncultivated  understanding,  as  soon  as  the  propositions  were  under- 
stood, would  assent  to  the  inference,  without  having  ever  heard  of  the  gen- 
eral truth  that  “ things  which  are  equal  to  the  same  thing  are  equal  to  one 
another.”  This  remark  of  Stewart,  consistently  followed  out,  goes  to  the 


FUNCTIONS  AND  VALUE  OF  THE  SYLLOGISM. 


145 


root,  as  I conceive,  of  the  philosophy  of  ratiocination ; and  it  is  to  be  re- 
gretted that  he  himself  stopped  short  at  a much  more  limited  application 
of  it.  He  saw  that  the  general  propositions  on  which  a reasoning  is  said 
to  depend,  may,  in  certain  cases,  be  altogether  omitted,  without  impairing 
its  probative  force.  But  he  imagined  this  to  be  a peculiarity  belonging 
to  axioms ; and  argued  from  it,  that  axioms  are  not  the  foundations  or  first 
principles  of  geometry,  from  which  all  the  other  truths  of  the  science  are 
synthetically  deduced  (as  the  laws  of  motion  and  of  the  composition  of 
forces  in  dynamics,  the  equal  mobility  of  fluids  in  hydrostatics,  the  laws  of 
reflection  and  refraction  in  optics,  are  the  first  principles  of  those  sciences) ; 
but  are  merely  necessary  assumptions,  self-evident  indeed,  and  the  denial 
of  which  would  annihilate  all  demonstration,  but  from  which,  as  premises, 
nothing  can  be  demonstrated.  In  the  present,  as  in  many  other  instances, 
this  thoughtful  and  elegapt  writer  has  perceived  an  important  truth,  but 
only  by  halves.  Finding,  in  the  case  of  geometrical  axioms,  that  general 
names  have  not  any  talismanic  virtue  for  conjuring  new  truths  out  of  the 
well  where  they  lie  hid,  and  not  seeing  that  this  is  equally  true  in  even- 
other  case  of  generalization,  he  contended  that  axioms  are  in  their  nature 
barren  of  consequences,  and  that  the  really  fruitful  truths,  the  real  first 
principles  of  geometry,  are  the  definitions;  that  the  definition,  for  exam- 
ple, of  the  circle  is  to  the  properties  of  the  circle,  what  the  laws  of  equi- 
librium and  of  the  pressure  of  the  atmosphere  are  to  the  rise  of  the  mer- 
cury in  the  Torricellian  tube.  Yet  all  that  he  had  asserted  respecting  the 
function  to  which  the  axioms  are  confined  in  the  demonstrations  of  geome- 
try, holds  equally  true  of  the  definitions.  Every  demonstration  in  Euclid 
might  be  crrried  on  without  them.  This  is  apparent  from  the  ordinary 
process  of  proving  a proposition  of  geometry  by  means  of  a diagram. 
What  assumption,  in  fact,  do  we  set  out  from,  to  demonstrate  by  a dia- 
gram any  of  the  properties  of  the  circle?  Not  that  in  all  circles  the  radii 
are  equal,  but  only  that  they  are  so  in  the  circle  ABC.  As  our  warrant 
for  assuming  this,  we  appeal,  it  is  true,  to  the  definition  of  a circle  in  gen- 
eral ; but  it  is  only  necessary  that  the  assumption  be  granted  in  the  case  of 
the  particular  circle  supposed.  From  this,  which  is  not  a general  but  a sin- 
gular proposition,  combined  with  other  propositions  of  a similar  kind,  some 
of  which  when  generalized  are  called  definitions,  and  other  axioms,  we 
prove  that  a certain  conclusion  is  true,  not  of  all  circles,  but  of  the  partic- 
ular circle  ABC  ; or  at  least  would  be  so,  if  the  facts  precisely  accorded 
with  our  assumptions.  The  enunciation,  as  it  is  called,  that  is,  the  gener- 
al theorem  which  stands  at  the  head  of  the  demonstration,  is  not  the  propo- 
sition actually  demonstrated.  One  instance  only  is  demonstrated : but  the 
process  by  which  this  is  done,  is  a process  which,  when  we  consider  its 
nature,  we  perceive  might  be  exactly  copied  in  an  indefinite  number  of  oth- 
er instances  ; in  every  instance  which  conforms  to  certain  conditions.  The 
contrivance  of  general  language  furnishing  us  with  terms  which  connote 
these  conditions,  we  are  able  to  assert  this  indefinite  multitude  of  truths 
in  a single  expression,  and  this  expression  is  the  general  theorem.  By 
dropping  the  use  of  diagrams,  and  substituting,  in  the  demonstrations, 
general  phrases  for  the  letters  of  the  alphapet,  we  might  prove  the  general 
theorem  directly,  that  is,  we  might  demonstrate  all  the  cases  at  once  ; and 
to  do  this  we  must,  of  course,  employ  as  our  premises,  the  axioms  and 
definitions  in  their  general  form.  But  this  only  means,  that  if  we  can 
prove  an  individual  conclusion  by  assuming  an  individual  fact,  then  in 
whatever  case  we  are  warranted  in  making  an  exactly  similar  assumption, 

10 


146 


REASONING. 


we  may  draw  an  exactly  similar  conclusion.  The  definition  is  a sort  of 
notice  to  ourselves  and  others,  what  assumptions  we  think  ourselves  en- 
titled to  make.  And  so  in  all  cases,  the  general  propositions,  whether 
called  definitions,  axioms,  or  laws  of  nature,  which  we  lay  down  at  the 
beginning  of  our  reasonings,  are  merely  abridged  statements,  in  a kind  of 
short-hand,  of  the  particular  facts,  which,  as  occasion  arises,  we  either 
think  we  may  proceed  on  as  proved,  or  intend  to  assume.  In  any  one 
demonstration  it  is  enough  if  we  assume  for  a particular  case  suitably  se- 
lected, what  by  the  statement  of  the  definition  or  principle  we  announce 
that  we  intend  to  assume  in  all  cases  which  may  arise.  The  definition  of 
the  circle,  therefore,  is  to  one  of  Euclid’s  demonstrations,  exactly  what,  ac- 
cording to  Stewart,  the  axioms  are  ; that  is,  the  demonstration  does  not 
depend  on  it,  but  yet  if  we  deny  it  the  demonstration  fails.  The  proof 
does  not  rest  on  the  general  assumption,  but  on  a similar  assumption  con- 
fined to  the  particular  case:  that  case,  however,  being  chosen  as  a speci- 
men or  paradigm  of  the  whole  class  of  cases  included  in  the  theorem,  there 
can  be  no  ground  for  making  the  assumption  in  that  case  which  does  not 
exist  in  every  other;  and  to  deny  the  assumption  as  a general  truth,  is  to 
deny  the  right  of  making  it  in  the  particular  instance. 

There  are,  undoubtedly,  the  most  ample  reasons  for  stating  both  the 
principles  and  the  theorems  in  their  general  form,  and  these  will  be  ex- 
plained presently,  so  far  as  explanation  is  requisite.  But,  that  unpracticed 
learners,  even  in  making  use  of  one  theorem  to  demonstrate  another,  rea- 
son rather  from  particular  to  particular  than  from  the  general  proposition, 
is  manifest  from  the  difficulty  they  find  in  applying  a theorem  to  a case  in 
which  the  configuration  of  the  diagram  is  extremely  unlike  that  of  the  dia- 
gram by  which  the  original  theorem  was  demonstrated.  A difficulty 
which,  except  in  cases  of  unusual  mental  power,  long  practice  can  alone  re- 
move, and  removes  chiefly  by  rendering  us  familiar  with  all  the  configura- 
tions consistent  with  the  general  conditions  of  the  theorem. 

§ 4.  From  the  considerations  now  adduced,  the  following  conclusions 
seem  to  be  established.  All  inference  is  from  particulars  to  particulars : 
General  propositions  are  merely  registers  of  such  inferences  already  made, 
and  short  formulae  for  making  more:  The  major  premise  of  a syllogism, 
consequently,  is  a formula  of  this  description : and  the  conclusion  is  not  an 
inference  drawn  from  the  formula,  but  an  inference  drawn  according  to 
the  formula : the  real  logical  antecedent,  or  premise,  being  the  particular 
facts  from  which  the  general  proposition  was  collected  by  induction. 
Those  facts,  and  the  individual  instances  which  supplied  them,  may  have 
been  forgotten : but  a record  remains,  not  indeed  descriptive  of  the  facts 
themselves,  but  showing  how  those  cases  may  be  distinguished,  respecting 
which,  the  facts,  when  known,  were  considered  to  warrant  a given  infer- 
ence. According  to  the  indications  of  this  record  we  draw  our  conclusion  : 
which  is,  to  all  intents  and  purposes,  a conclusion  from  the  forgotten  facts. 
For  this  it  is  essential  that  we  should  read  the  record  correctly:  and  the 
rules  of  the  syllogism  are  a set  of  precautions  to  insure  our  doing  so. 

This  view  of  the  functions  of  the  syllogism  is  confirmed  by  the  consid- 
eration of  precisely  those  cases  which  might  be  expected  to  be  least  favor- 
able to  it,  namely,  those  in  which  ratiocination  is  independent  of  any  pre- 
vious induction.  We  have  already  observed  that  the  syllogism,  in  the  or- 
dinary course  of  our  reasoning,  is  only  the  latter  half  of  the  process  of 
traveling  from  premises  to  a conclusion.  There  are,  however,  some  pecul- 


FUNCTIONS  AND  VALUE  OF  THE  SYLLOGISM. 


147 


iar  cases  in  which  it  is  the  whole  process.  Particulars  alone  are  capable 
of  being  subjected  to  observation;  and  all  knowledge  which  is  derived 
from  observation,  begins,  therefore,  of  necessity,  in  particulars;  but  our 
knowledge  may,  in  cases  of  certain  descriptions,  be  conceived  as  coming  to 
us  from  other  sources  than  observation.  It  may  present  itself  as  coming 
from  testimony,  which,  on  the  occasion  and  for  the  purpose  in  hand,  is  ac- 
cepted as  of  an  authoritative  character : and  the  information  thus  commu- 
nicated, may  be  conceived  to  comprise  not  only  particular  facts  but  general 
propositions,  as  when  a scientific  doctrine  is  accepted  without  examination 
on  the  authority  of  writers,  or  a theological  doctrine  on  that  of  Scripture. 
Or  the  generalization  may  not  be,  in  the  ordinary  sense,  an  assertion  at  all, 
but  a command;  a law,  not  in  the  philosophical,  but  in  the  moral  and  po- 
litical sense  of  the  term : an  expression  of  the  desire  of  a superior,  that  we, 
or  any  number  of  other  persons,  shall  conform  our  conduct  to  certain  gen- 
eral instructions.  So  far  as  this  asserts  a fact,  namely,  a volition  of  the 
legislator,  that  fact  is  an  individual  fact,  and  the  proposition,  therefore,  is 
not  a general  proposition.  But  the  description  therein  contained  of  the 
conduct  which  it  is  the  will  of  the  legislator  that  his  subjects  should  ob- 
serve, is  general.  The  proposition  asserts,  not  that  all  men  are  any  thing, 
but  that  all  men  shall  do  something. 

In  both  these  cases  the  generalities  are  the  original  data,  and  the  partic- 
ulars are  elicited  from  them  by  a process  which  correctly  resolves  itself 
into  a series  of  syllogisms.  The  real  nature,  however,  of  the  supposed  de- 
ductive process,  is  evident  enough.  The  only  point  to  be  determined  is, 
whether  the  authority  which  declared  the  general  proposition,  intended  to 
include  this  case  in  it ; and  whether  the  legislator  intended  his  command 
to  apply  to  the  present  case  among  others,  or  not.  This  is  ascertained  by 
examining  whether  the  case  possesses  the  marks  by  which,  as  those  author- 
ities have  signified,  the  cases  which  they  meant  to  certify  or  to  influence 
may  be  known.  The  object  of  the  inquiry  is 'to  make  out  the  witness’s  or 
the  legislator’s  intention,  through  the  indication  given  by  their  words. 
This  is  a question,  as  the  Germans  express  it,  of  hermeneutics.  The  opera- 
tion is  not  a process  of  inference,  but  a process  of  interpretation. 

In  this  last  phrase  we  have  obtained  an  expression  which  appears  to  me 
to  characterize,  more  aptly  than  any  other,  the  functions  of  the  syllogism 
in  all  cases.  When  the  premises  are  given  by  authority,  the  function  of 
Reasoning  is  to  ascertain  the  testimony  of  a witness,  or  the  will  of  a 
legislator,  by  interpreting  the  signs  in  which  the  one  has  intimated  his  as- 
sertion and  the  other  his  command.  In  like  manner,  when  the  premises 
are  derived  from  observation,  the  function  of  Reasoning  is  to  ascertain 
what  we  (or  our  predecessors)  formerly  thought  might  be  inferred  from 
the  observed  facts,  and  to  do  this  by  interpreting  a memorandum  of  ours, 
or  of  theirs.  The  memorandum  reminds  us,  that  from  evidence,  more  or 
less  carefully  weighed,  it  formerly  appeared  that  a certain  attribute  might 
be  inferred  wherever  we  perceive  a certain  mark.  The  proposition,  All 
men  are  mortal  (for  instance)  shows  that  we  have  had  experience  from 
which  we  thought  it  followed  that  the  attributes  connoted  by  the  term  man, 
are  a mark  of  mortality.  But  when  we  conclude  that  the  Duke  of  Wel- 
lington is  mortal,  we  do  not  infer  this  from  the  memorandum,  but  from 
the  former  experience.  All  that  we  infer  from  the  memorandum  is  our 
own  previous  belief,  (or  that  of  those  who  transmitted  to  us  the  proposi- 
tion), concerning  the  inferences  which  that  former  experience  would  war- 
rant. 


14S 


REASONING. 


This  view  of  the  nature  of  the  syllogism  renders  consistent  and  intel- 
ligible what  otherwise  remains  obscure  and  confused  in  the  theory  of 
Archbishop  AYhately  and  other  enlightened  defenders  of  the  syllogistic 
doctrine,  respecting  the  limits  to  which  its  functions  are  confined.  They 
affirm  in  as  explicit  terms  as  can  be  used,  that  the  sole  office  of  general 
reasoning  is  to  prevent  inconsistency  in  our  opinions;  to  prevent  us  from 
assenting  to  any  thing,  the  truth  of  which  would  contradict  something  to 
which  we  had  previously  on  good  grounds  given  our  assent.  And  they 
tell  us,  that  the  sole  ground  which  a syllogism  affords  for  assenting  to  the 
conclusion,  is  that  the  supposition  of  its  being  false,  combined  with  the 
supposition  that  the  premises  are  true,  would  lead  to  a contradiction  in 
terms.  Now  this  would  be  but  a lame  account  of  the  real  grounds  which 
we  have  for  believing  the  facts  which  we  learn  from  reasoning,  in  contra- 
distinction to  observation.  The  true  reason  why  we  believe  that  the  Duke 
of  AVellington  will  die,  is  that  his  fathers,  and  our  fathers,  and  all  other 
persons  who  were  contemporary  with  them,  have  died.  Those  facts  are  the 
real  premises  of  the  reasoning.  But  we  are  not  led  to  infer  the  conclusion 
from  those  premises,  by  the  necessity  of  avoiding  any  verbal  inconsistency. 
There  is  no  contradiction  in  supposing  that  all  those  persons  have  died, 
and  that  the  Duke  of  Wellington  may,  notwithstanding,  live  forever.  But 
there  would  be  a contradiction  if  we  first,  on  the  ground  of  those  same 
premises,  made  a general  assertion  including  and  covering  the  case  of  the 
Duke  of  Wellington,  and  then  refused  to  stand  to  it  in  the  individual  case. 
There  is  an  inconsistency  to  be  avoided  between  the  memorandum  we 
make  of  the  inferences  which  may  be  justly  drawn  in  future  cases,  and 
the  inferences  we  actually  draw  in  those  cases  when  they  arise.  With 
this  view  we  interpret  our  own  formula,  precisely  as  a judge  interprets  a 
law:  in  order  that  we  may  avoid  drawing  any  inferences  not  conformable 
to  our  former  intention,  as  a judge  avoids  giving  any  decision  not  conform- 
able to  the  legislator’s  intention.  The  rules  for  this  interpretation  are  the 
rules  of  the  syllogism:  and  its  sole  purpose  is  to  maintain  consistency  be- 
tween the  conclusions  we  draw  in  every  particular  case,  and  the  previous 
general  directions  for  drawing  them;  whether  those  general  directions 
were  framed  by  ourselves  as  the  result  of  induction,  or  were  received 
by  us  from  an  authority  competent  to  give  them. 

§ 5.  In  the  above  observations  it  has,  I think,  been  shown,  that,  though 
there  is  always  a process  of  reasoning  or  inference  where  a syllogism  is 
used,  the  syllogism  is  not  a correct  analysis  of  that  process  of  reasoning  or 
inference;  which  is,  on  the  contrary  (when  not  a mere  inference  from  tes- 
timony), an  inference  from  particulars  to  particulars;  authorized  by  a pre- 
vious inference  from  particulars  to  generals,  and  substantially  the  same  with 
it;  of  the  nature,  therefore,  of  Induction.  But  while  these  conclusions  ap- 
pear to  me  undeniable,  I must  yet  enter  a protest,  as  strong  as  that  of  Arch- 
bishop Whately  himself,  against  the  doctrine  that  the  syllogistic  art  is  use- 
less for  the  purposes  of  reasoning.  The  reasoning  lies  in  the  act  of  gener- 
alization, not  in  interpreting  the  record  of  that  act;  but  the  syllogistic  form 
is  an  indispensable  collateral  security  for  the  correctness  of  the  generaliza- 
tion itself. 

It  has  already  been  seen,  that  if  we  have  a collection  of  particulars  suffi- 
cient for  grounding  an  induction,  we  need  not  frame  a general  proposition ; 
we  may  reason  at  once  from  those  particulars  to  other  particulars.  But  it 
is  to  be  remarked  withal,  that  whenever,  from  a set  of  particular  cases,  we 
can  legitimately  draw  any  inference,  we  may  legitimately  make  our  infer- 


FUNCTIONS  AND  VALUE  OE  THE  SYLLOGISM. 


149 


ence  a general  one.  If,  from  observation  and  experiment,  we  can  conclude 
to  one  new  case,  so  may  we  to  an  indefinite  number.  If  that  which  has 
held  true  in  our  past  experience  will  therefore  hold  in  time  to  come,  it  will 
hold  not  merely  in  some  individual  case,  but  in  all  cases  of  some  given 
description.  Every  induction,  therefore,  which  suffices  to  prove  one  fact, 
proves  an  indefinite  multitude  of  facts:  the  experience  which  justifies  a sin- 
gle prediction  must  be  such  as  will  suffice  to  bear  out  a general  theorem. 
This  theorem  it  is  extremely  important  to  ascertain  and  declare,  in  its 
broadest  form  of  generality ; and  thus  to  place  before  our  minds,  in  its  full 
extent,  the  whole  of  what  our  evidence  must  prove  if  it  proves  any  thing. 

This  throwing  of  the  whole  body  of  possible  inferences  from  a given  set 
of  particulars,  into  one  general  expression,  operates  as  a security  for  their 
being  just  inferences,  in  more  ways  than  one.  First,  the  general  principle 
presents  a larger  object  to  the  imagination  than  any  of  the  singular  prop- 
ositions which  it  contains.  A process  of  thought  which  leads  to  a com- 
prehensive generality,  is  felt  as  of  greater  importance  than  one  which  ter- 
minates in  an  insulated  fact;  and  the  mind  is,  even  unconsciously,  led  to 
bestow  greater  attention  upon  the  process,  and  to  weigh  more  caVefully 
the  sufficiency  of  the  experience  appealed  to,  for  supporting  the  inference 
grounded  upon  it.  There  is  another,  and  a more  important,  advantage. 
In  reasoning  from  a course  of  individual  observations  to  some  new  and  un- 
observed case,  which  we  are  but  imperfectly  acquainted  with  (or  we  should 
not  be  inquiring  into  it),  and  in  which,  since  we  are  inquiring  into  it,  we 
probably  feel  a peculiar  interest ; there  is  very  little  to  prevent  us  from 
giving  way  to  negligence,  or  to  any  bias  which  may  affect  our  wishes  or 
our  imagination,  and,  under  that  influence,  accepting  insufficient  evidence 
as  sufficient.  But  if,  instead  of  concluding  straight  to  the  particular  case, 
we  place  before  ourselves  an  entire  class  of  facts — the  whole  contents  of  a 
general  proposition,  every  tittle  of  which  is  legitimately  inferable  from  our 
premises,  if  that  one  particular  conclusion  is  so ; there  is  then  a considera- 
ble likelihood  that  if  the  premises  are  insufficient,  and  the  general  inference 
therefore,  groundless,  it  will  comprise  within  it  some  fact  or  facts  the  re- 
verse of  which  we  already  know  to  be  true;  and  we  shall  thus  discover 
the  error  in  our  generalization  by  a reductio  ad  impossibile. 

Thus  if,  during  the  reign  of  Marcus  Aurelius,  a subject  of  the  Roman 
empire,  under  the  bias  naturally  given  to  the  imagination  and  expectations 
by  the  lives  and  characters  of  the  Antonines,  had  been  disposed  to  expect 
that  Commodus  would  be  a just  ruler;  supposing  him  to  stop  there,  he 
might  only  have  been  undeceived  by  sad  experience.  But  if  he  reflected 
that  this  expectation  could  not  be  justifiable  unless  from  the  same  evidence 
he  was  warranted  in  concluding  some  general  proposition,  as,  for  instance, 
that  all  Roman  emperors  are  just  rulers;  he  would  immediately  have 
thought  of  Hero,  Domitian,  and  other  instances,  which,  showing  the  falsity 
of  the  general  conclusion,  and  therefore  the  insufficiency  of  the  premises, 
would  have  warned  him  that  those  premises  could  not  prove  in  the  instance 
of  Commodus,  what  they  were  inadequate  to  prove  in  any  collection  of 
cases  in  which  his  was  included. 

The  advantage,  in  judging  whether  any  controverted  inference  is  legiti- 
mate, of  referring  to  a parallel  case,  is  universally  acknowledged.  But  by 
ascending  to  the  general  proposition,  we  bring  under  our  view  not  one  par- 
allel case  only,  but  all  possible  parallel  cases  at  once;  all  cases  to  which  the 
same  set  of  evidentiary  considerations  are  applicable. 

When,  therefore,  we  argue  from  a number  of  known  cases  to  another  case 


150 


REASONING. 


supposed  to  be  analogous,  it  is  always  possible,  and  generally  advantageous, 
to  divert  our  argument  into  the  circuitous  channel  of  an  induction  from 
those  known  cases  to  a general  proposition,  and  a subsequent  application 
of  that  general  proposition  to  the  unknown  case.  This  second  part  of  the 
operation,  which,  as  before  observed,  is  essentially  a process  of  interpreta- 
tion, will  be  resolvable  into  a syllogism  or  a series  of  syllogisms,  the  majors 
of  which  will  be  general  propositions  embracing  whole  classes  of  cases  ; 
every  one  of  which  propositions  must  be  true  in  all  its  extent,  if  the  argu- 
ment is  maintainable.  If,  therefore,  any  fact  fairly  coming  within  the 
range  of  one  of  these  general  propositions,  and  consequently  asserted  by  it, 
is  known  or  suspected  to  be  other  than  the  proposition  asserts  it  to  be,  this 
mode  of  stating  the  argument  causes  us  to  know  or  to  suspect  that  the 
original  observations,  which  are  the  real  grounds  of  our  conclusion,  are  not 
sufficient  to  support  it.  And  in  proportion  to  the  greater  chance  of  our 
detecting  the  inconclusiveness  of  our  evidence,  will  be  the  increased  reli- 
ance we  are  entitled  to  place  in  it  if  no  such  evidence  of  defect  shall  appear. 

The  value,  therefore,  of  the  syllogistic  form,  and  of  the  rules  for  using  it 
correctly,  does  not  consist  in  their  being  the  form  and  the  rules  according 
to  which  our  reasonings  are  necessarily,  or  even  usually,  made ; but  in  their 
furnishing  us  with  a mode  in  which  those  reasonings  may  always  be  repre- 
sented, and  which  is  admirably  calculated,  if  they  are  inconclusive,  to  bring 
their  inconclusiveness  to  light.  An  induction  from  particulars  to  generals, 
followed  by  a syllogistic  process  from  those  generals  to  other  particulars,  is 
a form  in  which  we  may  always  state  our  reasonings  if  we  please.  It  is 
not  a form  in  which  we  must  reason,  but  it  is  a form  in  which  we  may  rea- 
son, and  into  which  it  is  indispensable  to  throw  our  reasoning,  when  there 
is  any  doubt  of  its  validity : though  when  the  case  is  familiar  and  little 
complicated,  and  there  is  no  suspicion  of  error,  we  may,  and  do,  reason  at 
once  from  the  known  particular  cases  to  unknown  ones.* 

These  are  the  uses  of  syllogism,  as  a mode  of  verifying  any  given  argu- 
ment. Its  ulterior  uses,  as  respects  the  general  course  of  our  intellectual 
operations,  hardly  require  illustration,  being  in  fact  the  acknowledged  uses 
of  general  language.  They  amount  substantially  to  this,  that  the  induc- 
tions may  be  made  once  for  all : a single  careful  interrogation  of  experi- 
ence may  suffice,  and  the  result  may  be  registered  in  the  form  of  a general 
proposition,  which  is  committed  to  memory  or  to  writing,  and  from  which 
afterward  we  have  only  to  syllogize.  The  particulars  of  our  experiments 
may  then  be  dismissed  from  the  memory,  in  which  it  would  be  impossible 
to  retain  so  great  a multitude  of  details  ; while  the  knowledge  which  those 
details  afforded  for  future  use,  and  which  would  otherwise  be  lost  as  soon 
as  the  observations  were  forgotten,  or  as  their  record  became  too  bulky  for 
reference,  is  retained  in  a commodious  and  immediately  available  shape  by 
means  of  general  language. 

Against  this  advantage  is  to  be  set  the  countervailing  inconvenience,  that 
inferences  originally  made  on  insufficient  evidence  become  consecrated,  and, 
as  it  were,  hardened  into  general  maxims;  and  the  mind  cleaves  to  them 

* The  language  of  ratiocination  would,  I think,  be  brought  into  closer  agreement  with  the 
real  nature  of  the  process,  if  the  general  propositions  employed  in  reasoning,  instead  of  being 
in  the  form  All  men  are  mortal,  or  Every  man  is  mortal,  were  expressed  in  the  form  Any 
man  is  mortal.  This  mode  of  expression,  exhibiting  as  the  type  of  all  reasoning  from  expe- 
rience “The  men  A,  B,  C,  etc.,  are  so  and  so,  therefore  any  man  is  so  and  so,”  would  much 
better  manifest  the  true  idea — that  inductive  reasoning  is  always,  at  bottom,  inference  from 
particulars  to  particulars,  and  that  the  whole  function  of  general  propositions  in  reasoning,  is 
to  vouch  for  the  legitimacy  of  such  inferences. 


FUNCTIONS  AND  VALUE  OF  THE  SYLLOGISM. 


151 


from  habit,  after  it  has  outgrown  any  liability  to  be  misled  by  similar  falla- 
cious appearances  if  they  were  now  for  the  first  time  presented  ; but  hav- 
ing forgotten  the  particulars,  it  does  not  think  of  revising  its  own  former 
decision.  An  inevitable  drawback,  which,  however  considerable  in  itself, 
forms  evidently  but  a small  set-off  against  the  immense  benefits  of  general 
language. 

The  use  of  the  syllogism  is  in  truth  no  other  than  the  use  of  general 
propositions  in  reasoning.  We  can  reason  without  them;  in  simple  and 
obvious  cases  we  habitually  do  so;  minds  of  great  sagacity  can  do  it  in 
cases  not  simple  and  obvious,  provided  their  experience  supplies  them  with 
instances  essentially  similar  to  every  combination  of  circumstances  likely 
to  arise.  But  other  minds,  and  the  same  minds  where  they  have  not  the 
same  pre-eminent  advantages  of  personal  experience,  are  quite  helpless 
without  the  aid  of  general  propositions,  wherever  the  case  presents  the 
smallest  complication ; and  if  we  made  no  general  propositions,  few  per- 
sons would  get  much  beyond  those  simple  inferences  which  are  drawn  by 
the  more  intelligent  of  the  brutes.  Though  not  necessary  to  reasoning, 
general  propositions  are  necessary  to  any  considerable  progress  in  reason- 
ing. It  is,  therefore,  natural  and  indispensable  to  separate  the  process  of 
investigation  into  two  parts ; and  obtain  general  formulae  for  determining 
what  inferences  may  be  drawn,  before  the  occasion  arises  for  drawing  the 
inferences.  The  work  of  drawing  them  is  then  that  of  applying  the  for- 
mulae ; and  the  rules  of  syllogism  are  a system  of  securities  for  the  correct- 
ness of  the  application. 

§ 6.  To  complete  the  series  of  considerations  connected  with  tlA  philo- 
sophical character  of  the  syllogism,  it  is  requisite  to  consider,  since  "die  syl- 
logism is  not  the  universal  type  of  the  reasoning  process,  what  is  the  real 
type.  This  resolves  itself  into  the  question,  what  is  the  nature  of  the  mi- 
nor premise,  and  in  what  manner  it  contributes  to  establish  the  conclusion  : 
for  as  to  the  major,  we  now  fully  understand,  that  the  place  which  it  nom- 
inally occupies  in  our  reasonings,  properly  belongs  to  the  individual  facts 
or  observations  of  which  it  expresses  the  general  result;  the  major  itself 
being  no  real  part  of  the  argument,  but  an  intermediate  halting-place  for 
the  mind,  interposed  by  an  artifice  of  language  between  the  real  premises 
and  the  conclusion,  by  way  of  a security,  which  it  is  in  a most  material  de- 
gree, for  the  correctness  of  the  process.  The  minor,  however,  being  an  in- 
disjjensable  part  of  the  syllogistic  expression  of  an  argument,  without 
doubt  either  is,  or  corresponds  to,  an  equally  indispensable  part  of  the  ar- 
gument itself,  and  we  have  only  to  inquire  what  part. 

It  is  perhaps  worth  wdiile  to  notice  here  a speculation  of  a philosopher 
to  whom  mental  science  is  much  indebted,  but  who,  though  a very  pene- 
trating, was  a very  hasty  thinker,  and  whose  want  of  due  circumspection 
rendered  him  fully  as  remarkable  for  what  he  did  not  see,  as  for  what  he 
saw.  I allude  to  Dr.  Thomas  Brown,  whose  theory  of  ratiocination  is  pe- 
culiar. He  saw  the  petitio  principii  which  is  inherent  in  every  syllogism, 
if  we  consider  the  major  to  be  itself  the  evidence  by  which  the  conclusion 
is  proved,  instead  of  being,  what  in  fact  it  is,  an  assertion  of  the  existence 
of  evidence  sufficient  to  prove  any  conclusion  of  a given  description.  See- 
ing this,  Dr.  Brown  not  only  failed  to  see  the  immense  advantage,  in  point 
of  security  for  correctness,  which  is  gained  by  interposing  this  step  be- 
tween the  real  evidence  and  the  conclusion ; but  he  thought  it  incumbent 
on  him  to  strike  out  the  major  altogether  from  the  reasoning  process,  with- 


REASONING. 


152 

out  substituting  any  thing  else,  and  maintained  that  our  reasonings  consist 
only  of  the  minor  premise  and  the  conclusion,  Socrates  is  a man,  therefore 
Socrates  is  mortal : thus  actually  suppressing,  as  an  unnecessary  step  in 
the  argument,  the  appeal  to  former  experience.  The  absurdity  of  this  was 
disguised  from  him  by  the  opinion  he  adopted,  that  reasoning  is  merely  an- 
alyzing our  own  general  notions,  or  abstract  ideas ; and  that  the  proposi- 
tion, Socrates  is  mortal,  is  evolved  from  the  proposition,  Socrates  is  a man, 
simply  by  recognizing  the  notion  of  mortality  as  already  contained  in  the 
notion  we  form  of  a man. 

After  the  explanations  so  fully  entered  into  on  the  subject  of  proposi- 
tions, much  further  discussion  can  not  be  necessary  to  make  the  radical 
error  of  this  view  of  ratiocination  apparent.  If  the  word  man  connoted 
mortality;  if  the  meaning  of  “mortal”  were  involved  in  the  meaning  of 
“ man we  might,  undoubtedly,  evolve  the  conclusion  from  the  minor 
alone,  because  the  minor  would  have  already  asserted  it.  But  if,  as  is  in 
fact  the  case,  the  word  man  does  not  connote  mortality,  how  does  it  appear 
that  in  the  mind  of  every  person  who  admits  Socrates  to  be  a man,  the 
idea  of  man  must  include  the  idea  of  mortality?  Dr.  Brown  could  not 
help  seeing  this  difficulty,  and  in  order  to  avoid  it,  was  led,  contrary  to  his 
intention,  to  re-establish,  under  another  name,  that  step  in  the  argument 
which  corresponds  to  the  major,  by  affirming  the  necessity  of  previously 
■perceiving  the  relation  between  the  idea  of  man  and  the  idea  of  mortal.  If 
the  reasoner  has  not  previously  perceived  this  relation,  he  will  not,  says  Dr. 
Brown,  infer  because  Socrates  is  a man,  that  Socrates  is  mortal.  But  even 
this  admission,  though  amounting  to  a surrender  of  the  doctrine  that  an 
argument  consists  of  the  minor  and  the  conclusion  alone,  will  not  save  the 
remainder  of  Dr.  Brown’s  theory.  The  failure  of  assent  to  the  argument 
does  not  take  place  merely  because  the  reasoner,  for  want  of  due  analysis, 
does  not  perceive  that  his  idea  of  man  includes  the  idea  of  mortality;  it 
takes  place,  much  more  commonly,  because  in  his  mind  that  relation  be- 
tween the  two  ideas  has  never  existed.  And  in  truth  it  never  does  exist, 
except  as  the  result  of  experience.  Consenting,  for  the  sake  of  the  argu- 
ment, to  discuss  the  question  on  a supposition  of  which  we  have  recog- 
nized the  radical  incorrectness,  namely,  that  the  meaning  of  a proposition 
relates  to  the  ideas  of  the  things  spoken  of,  and  not  to  the  things  them- 
selves ; I must  yet  observe,  that  the  idea  of  man,  as  a universal  idea,  the 
common  property  of  all  rational  creatures,  can  not  involve  any  thing  but 
what  is  strictly  implied  in  the  name.  If  any  one  includes  in  his  own  pri- 
vate idea  of  man,  as  no  doubt  is  always  the  case,  some  other  attributes,  such 
for  instance  as  mortality,  lie  does  so  only  as  the  consequence  of  experience, 
after  having  satisfied  himself  that  all  men  possess  that  attribute:  so  that 
whatever  the  idea  contains,  in  any  person’s  mind,  beyond  what  is  included 
in  the  conventional  signification  of  the  word,  has  been  added  to  it  as  the 
result  of  assent  to.  a proposition;  while  Dr.  Brown’s  theory  requires  us  to 
suppose,  on  the  contrary,  that  assent  to  the  proposition  is  produced  by 
evolving,  through  an  analytic  process,  this  very  element  out  of  the  idea. 
This  theory,  therefore,  may  he  considered  as  sufficiently  refuted;  and  the 
minor  premise  must  be  regarded  as  totally  insufficient  to  prove  the  conclu- 
sion, except  with  the  assistance  of  the  major,  or  of  that  which  the  major 
represents,  namely,  the  various  singular  propositions  expressive  of  the  se- 
ries of  observations,  of  which  the  generalization  called  the  major  premise  is 
the  result. 

In  the  argument,  then,  which  proves  that  Socrates  is  mortal,  one  indis- 


FUNCTIONS  AND  VALUE  OF  THE  SYLLOGISM. 


153 


pensable  part  of  the  premises  will  be  as  follows:  “My  father,  and  my  fa- 
ther’s father,  A,  B,  C,  and  an  indefinite  number  of  other  persons,  were  mor- 
tal;” which  is  only  an  expression  in  different  words  of  the  observed  fact 
that  they  have  died.  This  is  the  major  premise  divested  of  the  petitio 
principii,  and  cut  down  to  as  much  as  is  really  known  by  direct  evidence. 

In  order  to  connect  this  proposition  with  the  conclusion  Socrates  is  mor- 
tal, the  additional  link  necessary  is  such  a proposition  as  the  following: 

Socrates  resembles  my  father,  and  my  father’s  father,  and  the  other  indi- 
viduals specified.”  This  proposition  we  assert  when  we  say  that  Socrates 
is  a man.  By  saying  so  we  likewise  assert  in  what  respect  he  resembles 
them,  namely,  in  the  attributes  connoted  by  the  word  man.  And  we  con- 
clude that  he  further  resembles  them  in  the  attribute  mortality. 

§ 7.  We  have  thus  obtained  what  we  were  seeking,  a universal  type  of 
the  reasoning  process.  We  find  it  resolvable  in  all  cases  into  the  follow- 
ing elements : Certain  individuals  have  a given  attribute ; an  individual  or 
individuals  resemble  the  former  in  certain  other  attributes ; therefore  they 
resemble  them  also  in  the  given  attribute.  This  type  of  ratiocination  does 
not  claim,  like  the  syllogism,  to  be  conclusive  from  the  mere  form  of  the 
expression ; nor  can  it  possibly  be  so.  That  one  proposition  does  or  does 
not  assert  the  very  fact  which  was  already  asserted  in  another,  may  appear 
from  the  form  of  the  expression,  that  is,  from  a comparison  of  the  lan- 
guage; but  when  the  two  propositions  assert  facts  which  are  bona  fide 
different,  whether  the  one  fact  proves  the  other  or  not  can  never  appear 
from  the  language,  but  must  depend  on  other  considerations.  Whether, 
from  the  attributes  in  which  Socrates  resembles  those  men  who  have  here- 
tofore died,  it  is  allowable  to  infer  that  he  resembles  them  also  in  being 
mortal,  is  a question  of  Induction ; and  is  to  be  decided  by  the  principles 
or  canons  which  we  shall  hereafter  recognize  as  tests  of  the  correct  per- 
formance of  that  great  mental  operation. 

Meanwhile,  however,  it  is  certain,  as  before  remarked,  that  if  this  infer- 
ence can  be  drawn  as  to  Socrates,  it  can  be  drawn  as  to  all  others  who  re- 
semble the  observed  individuals  in  the  same  attributes  in  which  he  resem- 
bles them ; that  is  (to  express  the  thing  concisely)  of  all  mankind.  If, 
therefore,  the  argument  be  admissible  in  the  case  of  Socrates,  we  are  at  lib- 
erty, once  for  all,  to  treat  the  possession  of  the  attributes  of  man  as  a mark, 
or  satisfactory  evidence,  of  the  attribute  of  mortality.  This  we  do  by  lay- 
ing down  the  universal  proposition,  All  men  are  mortal,  and  interpreting 
this,  as  occasion  arises,  in  its  application  to  Socrates  and  others.  By  this 
means  we  establish  a very  convenient  division  of  the  entire  logical  opera- 
tion into  two  steps ; first,  that  of  ascertaining  what  attributes  are  marks 
of  mortality ; and,  secondly,  whether  any  given  individuals  possess  those 
marks.  And  it  will  generally  be  advisable,  in  our  speculations  on  the  rea- 
soning process,  to  consider  this  double  operation  as  in  fact  taking  jfiace, 
and  all  reasoning  as  carried  on  in  the  form  into  which  it  must  necessarily 
be  thrown  to  enable  us  to  apply  to  it  any  test  of  its  correct  performance. 

Although,  therefore,  all  processes  of  thought  in  which  the  ultimate  prem- 
ises are  particulars,  whether  we  conclude  from  particulars  to  a general  for- 
mula, or  from  particulars  to  other  particulars  according  to  that  formula,  are 
equally  Induction ; we  shall  yet,  conformably  to  usage,  consider  the  name 
Induction  as  more  peculiarly  belonging  to  the  process  of  establishing  the 
general  proposition,  and  the  remaining  operation,  which  is  substantially 
that  of  interpreting  the  general  proposition,  we  shall  call  by  its  usual  name, 


154 


REASONING. 


Deduction.  And  \vc  shall  consider  every  process  by  which  any  thing  is 
inferred  respecting  an  unobserved  case,  as  consisting  of  an  Induction  fol- 
lowed by  a Deduction  ; because,  although  the  process  needs  not  necessarily 
be  carried  on  in  this  form,  it  is  always  susceptible  of  the  form,  and  must 
be  thrown  into  it  when  assurance  of  scientific  accuracy  is  needed  and  de- 
sired. 

§ 8.  The  theory  of  the  syllogism  laid  down  in  the  preceding  pages,  has 
obtained,  among  other  important  adhesions,  three  of  peculiar  value:  those 
of  Sir  John  Herschel,*  Dr.  Whewell,f  and  Mr.  Bailey  Sir  John  Herschel 
considering  the  doctrine,  though  not  strictly  “ a discovery,”  having  been 
anticipated  by  Berkeley, § to  be  “ one  of  the  greatest  steps  which  have  yet 
been  made  in  the  philosophy  of  Logic.”  “When  we  consider”  (to  quote 
the  further  words  of  the  same  authority)  “ the  inveteracy  of  the  habits  and 
prejudices  which  it  has  cast  to  the  winds,”  there  is  no  cause  for  misgiving 
in  the  fact  that  other  thinkers,  no  less  entitled  to  consideration,  have  formed 
a very  different  estimate  of  it.  Their  principal  objection  can  not  be  bet- 
ter or  more  succinctly  stated  than  by  borrowing  a sentence  from  Archbish- 
op Whately.||  “In  every  case  where  an  inference  is  drawn  from  Induc- 
tion (unless  that  name  is  to  be  given  to  a mere  random  guess  without  any 
grounds  at  all)  we  must  form  a judgment  that  the  instance  or  instances  ad- 
duced are  sufficient  to  authorize  the  conclusion  ; that  it  is  allowable  to  take 
these  instances  as  a sample  warranting  an  inference  respecting  the  whole 
class;”  and  the  expression  of  this  judgment  in  words  (it  has  been  said  by 
several  of  my  critics)  is  the  major  premise. 

I quite  admit  that  the  major  is  an  affirmation  of  the  sufficiency  of  the 
evidence  on  which  the  conclusion  rests.  That  it  is  so,  is  the  very  essence 
of  my  own  theory.  And  whoever  admits  that  the  major  premise  is  only 
this,  adopts  the  theory  in  its  essentials. 

But  I can  not  concede  that  this  recognition  of  the  sufficiency  of  the  evi- 
dence-— that  is,  of  the  correctness  of  the  induction — is  a part  of  the  induc- 
tion itself;  unless  we  ought  to  say  that  it  is  a part  of  every  thing  we  do, 
to  satisfy  ourselves  that  it  has  been  done  rightly.  We  conclude  from 
known  instances  to  unknown  by  the  impulse  of  the  generalizing  propensi- 
ty; and  (until  after  a considerable  amount  of  practice  and  mental  disci- 
pline) the  question  of  the  sufficiency  of  the  evidence  is  only  raised  by  a re- 
trospective act,  turning  back  upon  our  own  footsteps,  and  examining  wheth- 
er we  were  warranted  in  doing  what  we  have  provisionally  done.  To 
speak  of  this  reflex  operation  as  part  of  the  original  one,  requiring  to  be 
expressed  in  words  in  order  that  the  verbal  formula  may  correctly  repre- 
sent the  psychological  process,  appears  to  me  false  psychology.^  We  re- 
view our  syllogistic  as  well  as  our  inductive  processes,  and  recognize  that 

* Review  of  Quetelet  on  Probabilities,  Essays,  p.  367. 

f Philosophy  of'  Discovery,  p.  289. 

t Theory  of  Reasoning,  chap,  iv.,  to  which  I may  refer  for  an  able  statement  and  enforce- 
ment of  the  grounds  of  the  doctrine. 

§ On  a recent  careful  repernsal  of  Berkeley’s  whole  works,  I have  been  unable  to  find  this 
doctrine  in  them.  Sir  John  Herschel  probably  meant  that  it  is  implied  in  Berkeley’s  argu- 
ment against  abstract  ideas.  But  I can  not  find  that  Berkeley  saw  the  implication,  or  had 
ever  asked  himself  what  bearing  his  argument  had  on  the  theory  of  the  syllogism.  Still  less 
can  I admit  that  the  doctrine  is  (as  has  been  affirmed  by  one  of  my  ablest  and  most  candid 
critics)  “ among  the  standing  marks  of  what  is  called  the  empirical  philosophy.” 

||  Logic , book  iv.,  chap,  i.,  sect.  1. 

See  the  important  chapter  on  Belief,  in  Professor  Bain’s  great  treatise,  The  Ernotions  and 
the  Will,  pp.  581-4. 


FUNCTIONS  AND  VALUE  OE  THE  SYLLOGISM. 


155 


they  have  been  correctly  performed;  but  logicians  do  not  add  a third 
premise  to  the  syllogism,  to  express  this  act  of  recognition.  A careful 
copyist  verifies  his  transcript  by  collating  it  with  the  original ; and  if  no 
error  appears,  he  recognizes  that  the  transcript  has  been  correctly  made. 
But  we  do  not  call  the  examination  of  the  copy  a part  of  the  act  of  copying. 

The  conclusion  in  an  induction  is  inferred  from  the  evidence  itself,  and 
not  from  a recognition  of  the  sufficiency  of  the  evidence ; as  I infer  that 
my  friend  is  walking  toward  me  because  I see  him,  and  not  because  I rec- 
ognize that  my  eyes  are  open,  and  that  eyesight  is  a means  of  knowledge. 
In  all  operations  which  require  care,  it  is  good  to  assure  ourselves  that 
the  process  has  been  performed  accurately;  but  the  testing  of  the  proc- 
ess is  not  the  process  itself ; and,  besides,  may  have  been  omitted  alto- 
gether, and  yet  the  process  be  correct.  It  is  precisely  because  that  opera- 
tion is  omitted  in  ordinary  unscientific  reasoning,  that  there  is  any  thing 
gained  in  certainty  by  throwing  reasoning  into  the  syllogistic  form.  To 
make  sure,  as  far  as  possible,  that  it  shall  not  be  omitted,  we  make  the  test- 
ing operation  a part  of  the  reasoning  process  itself.  We  insist  that  the 
inference  from  particulars  to  particulars  shall  pass  through  a general  propo- 
sition. But  this  is  a security  for  good  reasoning,  not  a condition  of  all  rea- 
soning; and  in  some  cases  not  even  a security.  Our  most  familiar  infer- 
ences are  all  made  before  we  learn  the  use  of  general  propositions ; and  a 
person  of  untutored  sagacity  will  skillfully  apply  his  acquired  experience 
to  adjacent  cases,  though  he  would  bungle  grievously  in  fixing  the  limits 
of  the  appropriate  general  theorem.  But  though  he  may  conclude  rightly, 
he  never,  properly  speaking,  knows  whether  he  has  done  so  or  not;  he  has 
not  tested  his  reasoning.  Now,  this  is  precisely  what  forms  of  reasoning 
do  for  us.  We  do  not  need  them  to  enable  us  to  reason,  but  to  enable  us 
to  know  whether  we  reason  correctly. 

In  still  further  answer  to  the  objection,  it  may  be  added  that — even  when 
the  test  has  been  applied,  and  the  sufficiency  of  the  evidence  recognized — 
if  it  is  sufficient  to  support  the  general  proposition,  it  is  sufficient  also  to 
support  an  inference  from  particulars  to  particulars  without  passing 
through  the  general  proposition.  The  inquirer  who  has  logically  satisfied 
himself  that  the  conditions  of  legitimate  induction  were  realized  in  the 
cases  A,  B,  C,  would  be  as  much  justified  in  concluding  directly  to  the 
Duke  of  Wellington  as  in  concluding  to  all  men.  The  general  conclusion 
is  never  legitimate,  unless  the  particular  one  would  be  so  too ; and  in  no 
sense,  intelligible  to  me,  can  the  particular  conclusion  be  said  to  be  drawn 
from  the  general  one.  Whenever  there  is  ground  for  drawing  any  conclu- 
sion at  all  from  particular  instances,  there  is  ground  for  a general  conclu- 
sion; but  that  this  general  conclusion  should  be  actually  drawn,  however 
useful,  can  not  be  an  indispensable  condition  of  the  validity  of  the  inference 
in  the  particular  case.  A man  gives  away  sixpence  by  the  same  power  by 
which  he  disposes  of  his  whole  fortune ; but  it  is  not  necessary  to  the  le- 
gality of  the  smaller  act,  that  he  should  make  a formal  assertion  of  his  right 
to  the  greater  one. 

Some  additional  remarks,  in  reply  to  minor  objections,  are  appended.* 

* A writer  in  the  “British  Quarterly  Review”  (August,  1846),  in  a review  of  this  treatise, 
endeavors  to  show  that  there  is  no  petitio  principii  in  the  syllogism,  by  denying  that  the 
proposition,  All  men  are  mortal,  asserts  or  assumes  that  Socrates  is  mortal.  In  support  of 
this  denial,  he  argues  that  we  may,  and  in  fact  do,  admit  the  general  proposition  that  all  men 
are  mortal,  without  having  particularly  examined  the  case  of  Socrates,  and  even  without 
knowing  whether  the  individual  so  named  is  a man  or  something  else.  But  this  of  course 


156 


REASONING. 


§ 0.  The  preceding  considerations  enable  ns  to  understand  the  true  na- 
ture of  what  is  termed,  by  recent  writers,  Formal  Logic,  and  the  relation 

was  never  denied.  That  we  can  and  do  draw  conclusions  concerning  cases  specifically  un- 
known to  us,  is  the  datum  from  which  all  who  discuss  this  subject  must  set  out.  The  ques- 
tion is,  in  what  terms  the  evidence,  or  ground,  on  which  we  draw  these  conclusions,  may  best 
he  designated — whether  it  is  most  correct  to  say,  that  the  unknown  case  is  proved  by  known 
cases,  or  that  it  is  proved  by  a general  proposition  including  both  sets  of  cases,  the  unknown 
and  the  known?  I contend  for  the  former  mode  of  expression.  I hold  it  an  abuse  of  lan- 
guage to  say,  that  the  proof  that  Socrates  is  mortal,  is  that  all  men  are  mortal.  Turn  it  in 
what  way  we  will,  this  seems  to  me  to  be  asserting  that  a thing  is  the  proof  of  itself.  Who- 
ever pronounces  the  words,  All  men  are  mortal,  has  afiirmed  that  Socrates  is  mortal,  though 
he  may  never  have  heard  of  Socrates ; for  since  Socrates,  whether  known  to  be  so  or  not, 
really  is  a man,  he  is  included  in  the  words,  All  men,  and  in  every  assertion  of  which  they 
are  the  subject.  If  the  reviewer  does  not  see  that  there  is  a difficulty  here,  I can  only  advise 
him  to  reconsider  the  subject  until  he  does : after  which  he  will  be  a better  judge  of  the  suc- 
cess or  failure  of  an  attempt  to  remove  the  difficulty.  That  he  had  reflected  very  little  on  the 
point  when  he  wrote  his  remarks,  is  shown  by  his  oversight  respecting  the  dictum  de  omni  et 
radio.  He  acknowledges  that  this  maxim  as  commonly  expressed — “Whatever  is  true  of  a 
class,  is  true  of  every  tiling  included  in  the  class,”  is  a mere  identical  proposition,  since  the 
class  is  nothing  but  the  things  included  in  it.  But  he  thinks  this  defect  would  be  cured  by 
wording  the  maxim  thus  — “Whatever  is  true  of  a class,  is  true  of  every  thing  which  can  be 
shown  to  be  a member  of  the  class:”  as  if  a thing  could  “be  shown”  to  be  a member  of  the 
class  without  being  one.  If  a class  means  the  sum  of  all  the  things  included  in  the  class,  the 
things  which  can  “be  shown”  to  be  included  in  it  are  part  of  the  sum,  and  the  dictum  is  as 
much  an  identical  proposition  with  respect  to  them  as  to  the  rest.  One  tvould  almost  imagine 
that,  in  the  reviewer’s  opinion,  things  are  not  members  of  a class  until  they  are  called  up  pub- 
licly to  take  their  place  in  it — that  so  long,  in  fact,  as  Socrates  is  not  known  to  be  a man,  he 
is  not  a man,  and  any  assertion  which  can  be  made  concerning  men  does  not  at  all  regard 
him,  nor  is  affected  as  to  its  truth  or  falsity  by  any  thing  in  which  he  is  concerned. 

The  difference  between  the  reviewer’s  theory  and  mine  may  be  thus  stated.  Both  admit 
that  when  we  say.  All  men  are  mortal,  we  make  an  assertion  reaching  beyond  the  sphere  of 
our  knowledge  of  individual  cases;  and  that  when  a new  individual,  Socrates,  is  brought  with- 
in the  field  of  our  knowledge  by  means  of  the  minor  premise,  we  learn  that  we  have  already 
made  an  assertion  respecting  Socrates  without  knowing  it : our  own  general  formula  being,  to 
that  extent,  for  the  first  time  interpreted  to  us.  But  according  to  the  reviewer’s  theory,  the 
smaller  assertion  is  proved  by  the  larger : while  I contend,  that  both  assertions  are  proved  to- 
gether, by  the  same  evidence,  namely,  the  grounds  of  experience  on  which  the  general  asser- 
tion was  made,  and  by  which  it  must  be  justified. 

The  reviewer  says,  that  if  the  major  premise  included  the  conclusion,  “we  should  be  able 
to  affirm  the  conclusion  without  the  intervention  of  the  minor  premise;  but  every  one  sees 
that  that  is  impossible.”  A similar  argument  is  urged  by  Mr.  De  Morgan  ( Formal  Logic,  p. 
259):  “The  whole  objection  tacitly  assumes  the  superfluity  of  the  minor;  that  is,  tacitly  as- 
sumes we  know  Socrates*  to  be  a man  as  soon  as  we  know  him  to  be  Socrates.”  The  objec- 
tion would  be  well  grounded  if  the  assertion  that  the  major  premise  includes  the  conclusion, 
meant  that  it  individually  specifies  all  it  includes.  As,  however,  the  only  indication  it  gives  is 
a description  by  marks,  we  have  still  to  compare  any  new  individual  with  the  marks ; and  to 
show  that  this  comparison  has  been  made,  is  the  office  of  the  minor.  But  since,  by  supposi- 
tion, the  new  individual  has  the  marks,  whether  we  have  ascertained  him  to  have  them  or 
not ; if  we  have  affirmed  the  major  premise,  we  have  asserted  him  to  be  mortal.  Now  my 
position  is  that  this  assertion  can  not  be  a necessary  part  of  the  argument.  It  can  not  be  a 
necessary  condition  of  reasoning  that  we  should  begin  by  making  an  assertion,  which  is  after- 
ward to  be  employed  in  proving  a part  of  itself.  I can  conceive  only  one  way  out  of  this  dif- 
ficulty, viz.,  that  what  really  forms  the  proof  is  the  other  part  of  the  assertion  ; the  portion  of 
it,  the  truth  of  which  has  been  ascertained  previously : and  that  the  unproved  part  is  bound 
up  in  one  formula  with  the  proved  part  in  mere  anticipation,  and  as  a memorandum  of  the 
nature  of  the  conclusions  which  we  are  prepared  to  prove. 

With  respect  to  the  minor  premise  in  its  formal  shape,  the  minor  as  it  stands  in  the  syllo- 
gism, predicating  of  Socrates  a definite  class  name,  I readily  admit  that,  it  is  no  more  a neces- 
sary part  of  reasoning  than  the  major.  When  there  is  a major,  doing  its  work  by  means  of  a 
class  name,  minors  are  needed  to  interpret  it:  hut  reasoning  can  be  carried  on  without  either 
the  one  or  the  other.  They  are  not  the  conditions  of  reasoning,  but  a precaution  against  er- 
roneous reasoning.  The  only  minor  premise  necessary  to  reasoning  in  the  example  under 


* Mr.  De  Morgan  says  “Plato,”  but  to  prevent  confusion  I have  kept  to  my  own  exemplum. 


FUNCTIONS  AND  VALUE  OF  THE  SYLLOGISM. 


157 


between  it  and  Logic  in  the  widest  sense.  Logic,  as  I conceive  it,  is  the 
entire  theory  of  the  ascertainment  of  reasoned  or  inferred  truth.  Formal 
Logic,  therefore,  which  Sir  William  Hamilton  from  his  own  point  of  view, 
and  Archbishop  Whately  from  his,  have  represented  as  the  whole  of  Logic 
properly  so  called,  is  really  a very  subordinate  part  of  it,  not  being  direct- 
ly concerned  with  the  process  of  Reasoning  or  Inference  in  the  sense  in 
which  that  process  is  a part  of  the  Investigation  of  Truth.  What,  then, 
is  Formal  Logic  ? The  name  seems  to  be  properly  applied  to  all  that  por- 
tion of  doctrine  which  relates  to  the  equivalence  of  different  modes  of  ex- 
pression; the  rules  for  determining  when  assertions  in  a given  form  imply 
or  suppose  the  truth  or  falsity  of  other  assertions.  This  includes  the  theo- 
ry of  the  Import  of  Propositions,  and  of  their  Conversion,  AEquipollence, 
and  Opposition ; of  those  falsely  called  Inductions  (to  be  hereafter  spoken 
of)*,  in  which  the  apparent  generalization  is  a mere  abridged  statement  of 
cases  known  individually;  and  finally,  of  the  syllogism:  while  the  theory  of 
Naming,  and  of  (what  is  inseparably  connected  with  it)  Definition,  though 
belonging  still  more  to  the  other  and  larger  kind  of  logic  than  to  this,  is  a 
necessary  preliminary  to  this.  The  end  aimed  at  by  Formal  Logic,  and 
attained  by  the  observance  of  its  precepts,  is  not  truth,  but  consistency. 
It  has  been  seen  that  this  is  the  only  direct  purpose  of  the  rules  of  the 
syllogism;  the  intention  and  effect  of  which  is  simply  to  keep  our  infer- 
ences or  conclusions  in  complete  consistency  with  our  general  formulae  or 
directions  for  drawing  them.  The  Logic  of  Consistency  is  a necessary 
auxiliary  to  the  logic  of  truth,  not  only  because  what  is  inconsistent  with 
itself  or  with  other  truths  can  not  be  true,  but  also  because  truth  can  only 
be  successfully  pursued  by  drawing  inferences  from  experience,  which,  if 
warrantable  at  all,  admit  of  being  generalized,  and,  to  test  their  warrant- 
ableness, require  to  be  exhibited  in  a generalized  form ; after  which  the 
correctness  of  their  application  to  particular  cases  is  a question  which  spe- 
cially concerns  the  Logic  of  Consistency.  This  Logic,  not  requiring  any 
preliminary  knowledge  of  the  processes  or  conclusions  of  the  various  sci- 
ences, may  be  studied  with  benefit  in  a much  earlier  stage  of  education 
than  the  Logic  of  Truth : and  the  practice  which  has  empirically  obtained 
of  teaching  it  apart,  through  elementary  treatises  which  do  not  attempt  to 
include  any  thing  else,  though  the  reasons  assigned  for  the  practice  are  in 
general  very  far  from  philosophical,  admits  of  philosophical  justification. 

consideration,  is,  Socrates  is  like  A,  B,  C,  and  the  other  individuals  who  are  known  to  have 
died.  And  this  is  the  only  universal  type  of  that  step  in  the  reasoning  process  which  is  rep- 
resented by  the  minor.  Experience,  however,  of  the  uncertainty  of  this  loose  mode  of  infer- 
ence, teaches  the  expediency  of  determining  beforehand  what  kind  of  likeness  to  the  cases  ob- 
served, is  necessary  to  bring  an  unobserved  case  within  the  same  predicate ; and  the  answer 
to  this  question  is  the  major.  The  minor  then  identifies  the  precise  kind  of  likeness  possessed 
by  Socrates,  as  being  the  kind  required  by  the  formula.  Thus  the  syllogistic  major  and  the 
syllogistic  minor  start  into  existence  together,  and  are  called  forth  by  the  same  exigency. 
When  we  conclude  from  personal  experience  without  referring  to  any  record — to  any  general 
theorems,  either  written,  or  traditional,  or  mentally  registered  by  ourselves  as  conclusions  of 
our  own  drawing — we  do  not  use,  in  our  thoughts,  either  a major  or  a minor,  such  as  the  syl- 
logism puts  into  words.  When,  however,  we  revise  this  rough  inference  from  particulars  to 
particulars,  and  substitute  a careful  one,  the  revision  consists  in  selecting  two  syllogistic  prem- 
ises. But  this  neither  alters  nor  adds  to  the  evidence  we  had  before ; it  only  puts  us  in  a 
better  position  for  judging  whether  our  inference  from  particulars  to  particulars  is  well 
grounded. 

* Infra,  book  iii.,  chap.  ii. 


15S 


REASONING. 


CHAPTER  IV. 

OP  TRAINS  OP  REASONING,  AND  DEDUCTIVE  SCIENCES. 

§ 1.  In  our  analysis  of  the  syllogism,  it  appeared  that  the  minor  premise 
always  affirms  a resemblance  between  a new  case  and  some  cases  previous- 
ly known  ; while  the  major  premise  asserts  something  which,  having  been 
found  true  of  those  known  cases,  we  consider  ourselves  warranted  in  hold- 
ing true  of  any  other  case  resembling  the  former  in  certain  given  particu- 
lars. 

If  all  ratiocinations  resembled,  as  to  the  minor  premise,  the  examples 
which  were  exclusively  employed  in  the  preceding  chapter;  if  the  resem- 
blance, which  that  premise  asserts,  were  obvious  to  the  senses,  as  in  the 
proposition  “ Socrates  is  a man,”  or  were  at  once  ascertainable  by  direct 
observation  ; there  would  be  no  necessity  for  trains  of  reasoning,  and  De- 
ductive or  Ratiocinative  Sciences  would  not  exist.  Trains  of  reasoning 
exist  only  for  the  sake  of  extending  an  induction  founded,  as  all  inductions 
must  be,  on  observed  cases,  to  other  cases  in  which  we  not  only  can  not  di- 
rectly observe  the  fact  which  is  to  be  proved,  but  can  not  directly  observe 
even  the  mark  which  is  to  prove  it. 

§ 2.  Suppose  the  syllogism  to  be,  All  cows  ruminate,  the  animal  which 
is  before  me  is  a cow,  therefore  it  ruminates.  The  minor,  if  true  at  all,  is 
obviously  so : the  only  premise  the  establishment  of  which  requires  any 
anterior  process  of  inquiry,  is  the  major;  and  provided  the  induction  of 
which  that  premise  is  the  expression  was  correctly  performed,  the  conclu- 
sion respecting  the  animal  now  present  will  be  instantly  drawn ; because, 
as  soon  as  she  is  compared  with  the  formula,  she  will  be  identified  as  being 
included  in  it.  But  suppose  the  syllogism  to  be  the  following:  All  arsenic 
is  poisonous,  the  substance  which  is  before  me  is  arsenic,  therefore  it  is  poi- 
sonous. The  truth  of  the  minor  may  not  here  be  obvious  at  first  sight; 
it  may  not  be  intuitively  evident,  but  may  itself  be  known  only  by  infer- 
ence. It  may  be  the  conclusion  of  another  argument,  which,  thrown  into 
the  syllogistic  form,  would  stand  thus:  Whatever  when  lighted  produces 
a dark  spot  on  a piece  of  white  porcelain  held  in  the  flame,  which  spot  is 
soluble  in  hypochloride  of  calcium, is  arsenic;  the  substance  before  me  con- 
forms to  this  condition ; therefore  it  is  arsenic.  To  establish,  therefore, 
the  ultimate  conclusion,  The  substance  before  me  is  poisonous,  requires  a 
process,  which,  in  order  to  be  syllogistically  expressed,  stands  in  need  of 
two  syllogisms ; and  we  have  a Train  of  Reasoning. 

When,  however,  we  thus  add  syllogism  to  syllogism,  we  are  really  add- 
ing induction  to  induction.  Two  separate  inductions  must  have  taken 
place  to  render  this  chain  of  inference  possible;  inductions  founded,  prob- 
ably, on  different  sets  of  individual  instances,  but  which  converge  in  their 
results,  so  that  the  instance  which  is  the  subject  of  inquiry  comes  within 
the  range  of  them  both.  The  record  of  these  inductions  is  contained  in 
the  majors  of  the  two  syllogisms.  First,  we,  or  others  for  us,  have  exam- 
ined various  objects  which  yielded  under  the  given  circumstances  a dark 


TEAINS  OF  REASONING. 


159 


spot  with  the  given  property,  and  found  that  they  possessed  the  properties 
connoted  by  the  word  arsenic;  they  were  metallic,  volatile,  their  vapor  had 
a smell  of  garlic,  and  so  forth.  Next,  we,  or  others  for  us,  have  examined 
various  specimens  which  possessed  this  metallic  and  volatile  character, 
whose  vapor  had  this  smell,  etc.,  and  have  invariably  found  that  they  were 
poisonous.  The  first  observation  we  judge  that  we  may  extend  to  all  sub- 
stances whatever  which  yield  that  particular  kind  of  dark  spot;  the  second, 
to  all  metallic  and  volatile  substances  resembling  those  we  examined;  and 
consequently,  not  to  those  only  which  are  seen  to  be  such,  but  to  those 
which  are  concluded  to  be  such  by  the  prior  induction.  The  substance 
before  us  is  only  seen  to  come  within  one  of  these  inductions;  but  by 
means  of  this  one,  it  is  brought  within  the  other.  We  are  still,  as  before, 
concluding  from  particulars  to  particulars ; but  we  are  now  concluding 
from  particulars  observed,  to  other  particulars  which  are  not,  as  in  the 
simple  case,  seen  to  resemble  them  in  material  points,  but  inferred  to  d 
so,  because  resembling  them  in  something  else,  which  we  have  been  led  b; 
quite  a different  set  of  instances  to  consider  as  a mark  of  the  former  re 
semblance. 

This  first  example  of  a train  of  reasoning  is  still  extremely  simple,  tin 
series  consisting  of  only  two  syllogisms.  The  following  is  somewhat  more 
complicated:  No  government,  which  earnestly  seeks  the  good  of  its  sub- 
jects, is  likely  to  be  overthrown  ; some  particular  government  earnestly  seeks 
the  good  of  its  subjects,  therefore  it  is  not  likely  to  be  overthrown.  The  ma- 
jor premise  in  this  argument  we  shall  suppose  not  to  be  derived  from  con- 
siderations a priori,  but  to  be  a generalization  from  history,  which,  wheth- 
er correct  or  erroneous,  must  have  been  founded  on  observation  of  govern- 
ments concerning  whose  desire  of  the  good  of  their  subjects  there  was  no 
doubt.  It  has  been  found,  or  thought  to  be  found,  that  these  were  not 
easily  overthrown,  and  it  has  been  deemed  that  those  instances  warranted 
an  extension  of  the  same  predicate  to  any  and  every  government  which 
resembles  them  in  the  attribute  of  desiring  earnestly  the  good  of  its  sub- 
jects. But  does  the  government  in  question  thus  resemble  them?  This 
may  be  debated  pro  and  con  by  many  arguments,  and  must,  in  any  case,  be 
proved  by  another  induction ; for  we  can  not  directly  observe  the  senti- 
ments and  desii’es  of  the  persons  who  carry  on  the  government.  To  prove 
the  minor,  therefore,  we  require  an  argument  in  this  form : Every  govern- 
ment which  acts  in  a certain  manner, desires  the  good  of  its  subjects;  the 
supposed  government  acts  in  that  particular  manner,  therefore  it  desires 
the  good  of  its  subjects.  But  is  it  true  that  the  government  acts  in  the 
manner  supposed  ? This  minor  also  may  require  proof ; still  another  in- 
duction, as  thus : What  is  asserted  by  intelligent  and  disinterested  witness- 
es, may  be  believed  to  be  true ; that  the  government  acts  in  this  manner, 
is  asserted  by  such  witnesses,  therefore  it  may  be  believed  to  be  true.  The 
argument  hence  consists  of  three  steps.  Having  the  evidence  of  our  senses 
that  the  case  of  the  government  under  consideration  resembles  a number 
of  former  cases, in  the  circumstance  of  having  something  asserted  respect- 
ing it  by  intelligent  and  disinterested  witnesses,  we  infer,  first,  that,  as  in 
those  former  instances,  so  in  this  instance,  the  assertion  is  true.  Secondly, 
what  was  asserted  of  the  government  being  that  it  acts  in  a particular 
manner,  and  other  governments  or  persons  having  been  observed  to  act 
in  the  same  manner,  the  government  in  question  is  brought  into  known  re- 
semblance with  those  other  governments  or  persons ; and  since  they  were 
known  to  desire  the  good  of  the  people,  it  is  thereupon,  by  a second  indue- 


160 


REASONING. 


tion,  inferred  that  the  particular  government  spoken  of,  desires  the  good  of 
the  people.  This  brings  that  government  into  known  resemblance  with  the 
other  governments  which  were  thought  likely  to  escape  revolution,  and 
thence,  by  a third  induction,  it  is  concluded  that  this  particular  govern- 
ment is  also  likely  to  escape.  This  is  still  reasoning  from  particulars  to 
particulars,  but  we  now  reason  to  the  new  instance  from  three  distinct  sets 
of  former  instances:  to  one  only  of  those  sets  of  instances  do  we  directly 
perceive  the  new  one  to  be  similar;  but  from  that  similarity  we  induc- 
tively infer  that  it  has  the  attribute  by  which  it  is  assimilated  to  the  next 
set,  and  brought  within  the  corresponding  induction  ; after  which  by  a 
repetition  of  the  same  operation  we  infer  it  to  be  similar  to  the  third  set, 
and  hence  a third  induction  conducts  us  to  the  ultimate  conclusion. 

§ 3.  Notwithstanding  the  superior  complication  of  these  examples,  com- 
pared with  those  by  which  in  the  preceding  chapter  we  illustrated  the 
general  theory  of  reasoning,  every  doctrine  which  we  then  laid  down  holds 
equally  true  in  these  more  intricate  cases.  The  successive  general  proposi- 
tions are  not  steps  in  the  reasoning,  are  not  intermediate  links  in  the  chain 
of  inference,  between  the  particulars  observed  and  those  to  which  we  ap- 
ply the  observation.  If  we  had  sufficiently  capacious  memories,  and  a suf- 
ficient power  of  maintaining  order  among  a huge  mass  of  details,  the  rea- 
soning could  go  on  without  any  general  propositions ; they  are  mere  for- 
mulae for  inferring  particulars  from  particulars.  The  principle  of  gener- 
al reasoning  is  (as  before  explained),  that  if,  from  observation  of  certain 
known  particulars,  what  was  seen  to  be  true  of  them  can  be  inferred  to  be 
true  of  any  others,  it  may  be  inferred  of  all  others  which  are  of  a certain 
description.  And  in  order  that  we  may  never  fail  to  draw  this  conclusion 
in  a new  case  when  it  can  be  drawn  correctly,  and  may  avoid  drawing  it 
when  it  can  not,  we  determine  once  for  all  what  are  the  distinguishing  marks 
by  which  such  cases  may  be  recognized.  The  subsequent  process  is  mere- 
ly that  of  identifying  an  object,  and  ascertaining  it  to  have  those  marks; 
whether  we  identify  it  by  the  very  marks  themselves,  or  by  others  which 
we  have  ascertained  (through  another  and  a similar  process)  to  be  marks 
of  those  marks.  The  real  inference  is  always  from  particulars  to  particu- 
lars, from  the  observed  instances  to  an  unobserved  one:  but  in  drawing 
this  inference,  we  conform  to  a formula  which  we  have  adopted  for  our 
guidance  in  such  operations,  and  which  is  a record  of  the  criteria  by  which 
we  thought  we  had  ascertained  that  we  might  distinguish  when  the  infer- 
ence could,  and  when  it  could  not,  be  drawn.  The  real  premises  are  the  in- 
dividual observations,  even  though  they  may  have  been  forgotten,  or,  being 
the  observations  of  others  and  not  of  ourselves,  may,  to  us,  never  have  been 
known:  but  we  have  before  us  proof  that  we  or  others  once  thought  them 
sufficient  for  an  induction,  and  we  have  marks  to  show  whether  any  new 
case  is  one  of  those  to  which,  if  then  known,  the  induction  would  have  been 
deemed  to  extend.  These  marks  we  either  recognize  at  once,  or  by  the 
aid  of  other  marks,  which  by  another  previous  induction  we  collected  to  be 
marks  of  the  first.  Even  these  marks  of  marks  may  only  be  recognized 
through  a third  set  of  marks;  and  we  may  have  a train  of  reasoning,  of 
any  length,  to  bring  a new  case  within  the  scope  of  an  induction  ground- 
ed on  particulars  its  similarity  to  which  is  only  ascertained  in  this  indirect 
manner. 

Thus,  in  the  preceding  example,  the  ultimate  inductive  inference  was, 
that  a certain  government  was  not  likely  to  be  overthrown ; this  inference 


TRAINS  OF  REASONING. 


161 


was  drawn  according  to  a formula  in  which  desire  of  the  public  good  was 
set  down  as  a mark  of  not  being  likely  to  be  overthrown ; a mark  of  this 
mark  was,  acting  in  a particular  manuer;  and  a mark  of  acting  in  that 
manner  was,  being  asserted  to  do  so  by  intelligent  and  disinterested  wit- 
nesses : this  mark,  the  government  under  discussion  was  recognized  by  the 
senses  as  possessing.  Hence  that  government  fell  within  the  last  induc- 
tion, and  by  it  was  brought  within  all  the  others.  The  perceived  resem- 
blance of  the  case  to  one  set  of  observed  particular  cases,  brought  it  into 
known  resemblance  with  another  set,  and  that  with  a third. 

In  the  more  complex  branches  of  knowledge,  the  deductions  seldom  con- 
sist, as  in  the  examples  hitherto  exhibited,  of  a single  chain,  a a mark  of  b, 
b of  c,  c of  cl,  therefore  a a mark  of  d.  They  consist  (to  carry  on  the  same 
metaphor)  of  several  chains  united  at  the  extremity,  as  thus : a a mark  of 
d,  b of  e,  c of  /,  cl  ef  of  n,  therefore  a b c a mark  of  n.  Suppose,  for  exam- 
ple, the  following  combination  of  circumstances:  1st,  rays  of  light  impin- 
ging on  a reflecting  surface;  2d,  that  surface  parabolic;  3d,  those  rays 
parallel  to  each  other  and  to  the  axis  of  the  surface.  It  is  to  be  proved 
that  the  concourse  of  these  three  circumstances  is  a mark  that  the  reflected 
rays  will  pass  through  the  focus  of  the  parabolic  surface.  How,  each  of 
the  three  circumstances  is  singly  a mark  of  something  material  to  the  case. 
Rays  of  light  impinging  on  a reflecting  surface  are  a mark  that  those  rays 
will  be  reflected  at  an  angle  equal  to  the  angle  of  incidence.  The  parabol- 
ic form  of  the  surface,  is  a mark  that,  from  any  point  of  it,  a line  drawn  to 
the  focus  and  a line  parallel  to  the  axis  will,  make  equal  angles  with  the 
surface.  And  finally,  the  parallelism  of  the  rays  to  the  axis  is  a mark  that 
their  angle  of  incidence  coincides  with  one  of  these  equal  angles.  The 
three  marks  taken  together  are  therefore  a mark  of  all  these  three  things 
united.  But  the  three  united  are  evidently  a mark  that  the- angle  of  re- 
flection must  coincide  with  the  other  of  the  two  equal  angles,  that  formed 
by  a line  drawn  to  the  focus ; and  this  again,  by  the  fundamental  axiom 
concerning  straight  lines,  is  a mark  that  the  reflected  rays  pass  through 
the  focus.  Most  chains  of  physical  deduction  are  of  this  more  complicated 
type ; and  even  in  mathematics  such  are  abundant,  as  in  all  propositions 
where  the  hyjjothesis  includes  numerous  conditions:  “If  a circle  be  taken, 
and  if  within  that  circle  a point  be  taken,  not  the  centre,  and  if  straight 
lines  be  drawn  from  that  point  to  the  circumference,  then,”  etc. 

§ 4.  The  considerations  now  stated  remove  a serious  difficulty  from  the 
view  we  have  taken  of  reasoning;  which  view  might  otherwise  have 
seemed  not  easily  reconcilable  with  the  fact  that  there  are  Deductive  or 
Ratiocinative  Sciences.  It  might  seem  to  follow,  if  all  reasoning  be  induc- 
tion, that  the  difficulties  of  philosophical  investigation  must  lie  in  the  in- 
ductions exclusively,  and  that  when  these  were  easy,  and  susceptible  of  no 
doubt  or  hesitation,  there  could  be  no  science,  or,  at  least,  no  difficulties  in 
science.  The  existence,  for  example,  of  an  extensive  Science  of  Mathemat- 
ics, requiring  the  highest  scientific  genius  in  those  who  contributed  to  its 
creation,  and  calling  for  a most  continued  and  vigorous  exertion  of  intel- 
lect in  order  to  appropriate  it  when  created,  may  seem  hard  to  be  accounted 
for  on  the  foregoing  theory.  But  the  considerations  more  recently  adduced 
remove  the  mystery,  by  showing,  that  even  when  the  inductions  themselves 
are  obvious,  there  may  be  much  difficulty  in  finding  whether  the  particular 
case  which  is  the  subject  of  inquiry  comes  within  them ; and  ample  room 
for  scientific  ingenuity  in  so  combining  various  inductions,  as,  by  means  of 

11 


162 


' REASONING. 


one  within  which  the  case  evidently  falls,  to  bring  it  within  others  in  which 
it  can  not  be  directly  seen  to  be  included. 

When  the  more  obvious  of  the  inductions  which  can  be  made  in  any 
science  from  direct  observations,  have  been  made,  and  general  formulas 
have  been  framed,  determining  the  limits  within  which  these  inductions 
are  applicable ; as  often  as  a new  case  can  be  at  once  seen  to  come  within 
one  of  the  formulas,  the  induction  is  applied  to  the  new  case,  and  the  busi- 
ness is  ended.  But  new  cases  are  continually  arising,  which  do  not  obvi- 
ously come  within  any  formula  whereby  the  question  we  want  solved  in 
respect  of  them  could  be  answered.  Let  us  take  an  instance  from  geome- 
try : and  as  it  is  taken  only  for  illustration,  let  the  reader  concede  to  us 
for  the  present,  what  we  shall  endeavor  to  prove  in  the  next  chapter,  that 
the  first  principles  of  geometry  are  results  of  induction.  Our  example 
shall  be  the  fifth  proposition  of  the  first  book  of  Euclid.  The  inquiry  is, 
Are  the  angles  at  the  base  of  an  isosceles  triangle  equal  or  unequal?  The 
first  thing  to  be  considered  is,  what  inductions  we  have,  from  which  we  can 
infer  equality  or  inequality.  For  inferring  equality  we  have  the  following 
formulm:  Things  which  being  applied  to  each  other  coincide,  are  equals. 
Things  which  are  equal  to  the  same  thing  are  equals.  A whole  and  the 
sunt  of  its  parts  are  equals.  The  sums  of  equal  things  are  equals.  The 
differences  of  equal  things  are  equals.  There  are  no  other  original  formu- 
lae to  prove  equality.  For  inferring  inequality  we  have  the  following:  A 
whole  and  its  parts  are  unequals.  The  sums  of  equal  things  and  unequal 
things  are  unequals.  The  differences  of  equal  things  and  unequal  things 
are  unequals.  In  all,  eight  formulae.  The  angles  at  the  base  of  an  isos- 
celes triangle  do  not  obviously  come  within  any  of  these.  The  formulae 
specify  certain  marks  of  equality  and  of  inequality,  but  the  angles  can  not 
be  perceived  intuitively  to  have  any  of  those  marks.  On  examination  it 
appears  that  they  have  ; and  we  ultimately  succeed  in  bringing  them  within 
the  formula, “The  differences  of  equal  things  are  equal.”  Whence  comes 
the  difficulty  of  recognizing  these  angles  as  the  differences  of  equal  things? 
Because  each  of  them  is  the  difference  not  of  one  pair  only,  but  of  innu- 
merable pairs  of  angles ; and  out  of  these  we  had  to  imagine  and  select  two, 
which  could  either  be  intuitively  perceived  to  be  equals,  or  possessed  some 
of  the  marks  of  equality  set  down  in  the  various  formulae.  By  an  exercise 
of  ingenuity,  which,  on  the  part  of  the  first  inve.ntor,  deserves  to  be  re- 
garded as  considerable,  two  pairs  of  angles  were  hit  upon,  which  united 
these  requisites.  First,  it  could  be  perceived  intuitively  that  their  differ- 
ences were  the  angles  at  the  base ; and,  secondly,  they  possessed  one  of  the 
marks  of  equality,  namely,  coincidence  when  applied  to  one  another.  This 

coincidence,  however,  was  not  perceived  intui- 
tively, but  inferred,  in  conformity  to  another 
formula. 

For  greater  clearness,  I subjoin  an  analysis 
of  the  demonstration.  Euclid,  it  will  be  re- 
membered, demonstrates  his  fifth  proposition 
by  means  of  the  fourth.  This  it  is  not  allow- 
able for  us  to  do,  because  we  are  undertaking 
to  trace  deductive  truths  not  to  prior  deduc- 
tions, but  to  their  original  inductive  founda- 
tion. We  must,  therefore,  use  the  premises  of 
the  fourth  proposition  instead  of  its  conclusion,  and  prove  the  fifth  directly 
from  first  principles.  To  do  so  requires  six  formulas.  (We  must  begin,  as 


TRAINS  OF  REASONING. 


163 


in  Euclid,  by  prolonging  the  equal  sides  AB,  AC,  to  equal  distances,  and 
joining  the  extremities  BE,  DC.) 

First  Formula. — The  sums  of  equals  are  equal. 

AD  and  AE  are  sums  of  equals  by  the  supposition.  Having  that  mark 
of  equality,  they  are  concluded  by  this  formula  to  be  equal. 

Second  Formula. — Equal  straight  lines  or  angles , being  applied  to  one 

another , coincide. 

AC,  AB,  are  within  this  formula  by  supposition ; AD,  AE,  have  been 
brought  within  it  by  the  preceding  step.  The  angle  at  A considered  as  an 
angle  of  the  triangle  ABE,  and  the  same. angle  considered  as  an  angle  of 
the  triangle  ACD,  are  of  course  within  the  formula.  All  these  pairs,  there- 
fore, possess  the  property  which,  according  to  the  second  formula,  is  a 
mark  that  when  applied  to  one  another  they  will  coincide.  Conceive 
them,  then,  applied  to  one  another,  by  turning  over  the  triangle  ABE,  and 
laying  it  on  the  triangle  ACD  in  such  a manner  that  AB  of  the  one  shall 
lie  upon  AC  of  the  other.  Then,  by  the  equality  of  the  angles,  AE  will  lie 
on  AD.  But  AB  and  AC,  AE  and  AD  are  equals ; therefore  they  will  co- 
incide altogether,  and  of  course  at  their  extremities,  D,  E,  and  B,  C. 

Third  Formula. — Straight  lines,  having  their  extremities  coincident, 

coincide. 

BE  and  CD  have  been  brought  within  this  formula  by  the  preceding  in- 
duction ; they  will,  therefore,  coincide. 

Fourth  Formula. — Angles,  having  their  sides  coincident,  coincide. 

The  third  induction  having  shown  that  BE  and  CD  coincide,  and  the 
second  that  AB,  AC,  coincide,  the  angles  ABE  and  ACD  are  thereby 
brought  within  the  fourth  formula,  and  accordingly  coincide. 

Fifth  Formula. — Things  which  coincide  are  equal. 

The  angles  ABE  and  ACD  are  brought  within  this  formula  by  the  in- 
duction immediately  preceding.  This  train  of  reasoning  being  also  appli- 
cable, mutatis  mutandis,  to  the  angles  EBC,  DCB,  these  also  are  brought 
within  the  fifth  formula.  And,  finally, 

Sixth  Formula. — The  differences  of  equals  are  equal. 

The  angle  ABC  being  the  difference  of  ABE,  CBE,  and  the  angle  ACB 
being  the  difference  of  ACD,  DCB ; which  have  been  proved  to  be  equals ; 
ABC  and  ACB  are  brought  within  the  last  formula  by  the  whole  of  the 
previous  process. 

The  difficulty  here  encountered  is  chiefly  that  of  figuring  to  ourselves 
the  two  angles  at  the  base  of  the  triangle  AJ3C  as  remainders  made  by  cut- 
ting one  pair  of  angles  out  of  another,  while  each  pair  shall  be  correspond- 
ing angles  of  triangles  which  have  two  sides  and  the  intervening  angle 

O G O O O 

equal.  It  is  by  this  happy  contrivance  that  so  many  different  inductions 
are  brought  to  bear  upon  the  same  particular  case.  And  this  not  being 
at  all  an  obvious  thought,  it  may  be  seen  from  an  example  so  near  the 
threshold  of  mathematics,  how  much  scope  there  may  well  be  for  scientific 
dexterity  in  the  higher  branches  of  that  and  other  sciences,  in  order  so  to 
combine  a few  simple  inductions,  as  to  bring  within  each  of  them  innumer- 
able cases  which  are  not  obviously  included  in  it ; and  how  long,  and  nu- 


1G4 


REASONING. 


merous,  and  complicated  may  be  the  processes  necessary  for  bringing  the 
inductions  together,  even  when  each  induction  may  itself  be  very  easy  and 
simple.  All  the  inductions  involved  in  all  geometry  are  comprised  in  those 
simple  ones,  the  formulae  of  which  are  the  Axioms,  and  a few  of  the  so-call- 
ed Definitions.  The  remainder  of  the  science  is  made  up  of  the  processes 
employed  for  bringing  unforeseen  cases  within  these  inductions;  or  (in  syl- 
logistic language)  for  proving  the  minors  necessary  to  complete  the  'syllo- 
gisms; the  majors  being  the  definitions  and  axioms.  In  those  definitions 
and  axioms  are  laid  down  the  whole  of  the  marks,  by  an  artful  combina- 
tion of  which  it  has  been  found  possible  to  discover  and  prove  all  that  is 
proved  in  geometry.  The  marks  being  so  few,  and  the  inductions  which 
furnish  them  being  so  obvious  and  familiar ; the  connecting  of  several  of 
them  together,  which  constitutes  Deductions,  or  Trains  of  Reasoning, 
forms  the  whole  difficulty  of  the  science,  and,  with  a trilling  exception,  its 
whole  bulk ; and  hence  Geometry  is  a Deductive  Science. 

§ 5.  It  will  be  seen  hereafter*  that  there  are  weighty  scientific  reasons 
for  giving  to  every  science  as  much  of  the  character  of  a Deductive  Sci- 
ence as  possible;  for  endeavoring  to  construct  the  science  from  the  fewest 
and  the  simplest  possible  inductions,  and  to  make  these,  by  any  combina- 
nations  however  complicated,  suffice  for  proving  even  such  truths,  relating 
to  complex  cases,  as  could  be  proved,  if  we  chose,  by  inductions  from  spe- 
cific experience.  Every  branch  of  natural  philosophy  was  originally  exper- 
imental ; each  generalization  rested  on  a special  induction,  and  was  derived 
from  its  own  distinct  set  of  observations  and  experiments.  From  being 
sciences  of  pure  experiment,  as  the  phrase  is,  or,  to  speak  more  correctly, 
sciences  in  which  the  reasonings  mostly  consist  of  no  more  than  one  step, 
and  are  expressed  by  single  syllogisms,  all  these  sciences  have  become  to 
some  extent,  and  some  of  them  in  nearly  the  whole  of  their  extent,  sciences 
of  pure  reasoning;  whereby  multitudes  of  truths,  already  known  by  induc- 
tion from  as  many  different  sets  of  experiments,  have  come  to  be  exhibited 
as  deductions  or  corollaries  from  inductive  propositions  of  a simpler  and 
more  universal  character.  Thus  mechanics,  hydrostatics,  optics,  acoustics, 
thermology,  have  successively  been  rendered  mathematical ; and  astronomy 
was  brought  by  Newton  within  the  laws  of  general  mechanics.  Why  it  is 
that  the  substitution  of  this  circuitous  mode  of  proceeding  for  a process 
apparently  much  easier  and  more  natural,  is  held,  and  justly,  to  be  the 
greatest  triumph  of  the  investigation  of  nature,  we  are  not,  in  this  stage 
of  our  inquiry,  prepared  to  examine.  But  it  is  necessary  to  remark,  that 
although,  by  this  progressive  transformation,  all  sciences  tend  to  become 
more  and  more  Deductive,  they  are  not,  therefore,  the  less  Inductive ; every 
step  in  the  Deduction  is  still  an  Induction.  The  opposition  is  not  between 
the  terms  Deductive  and  Inductive,  but  between  Deductive  and  Experi- 
mental. A science  is  experimental,  in  proportion  as  every  new  case,  which 
presents  any  peculiar  features,  stands  in  need  of  a new  set  of  observations 
and  experiments — a fresh  induction.  It  is  deductive,  in  proportion  as  it 
can  draw  conclusions,  respecting  cases  of  a new  kind,  by  processes  which 
bring  those  cases  under  old  inductions;  by  ascertaining  that  cases  which 
can  not  be  observed  to  have  the  requisite  marks,  have,  however,  marks  of 
those  marks. 

We  can  now,  therefore,  perceive  what  is  the  generic  distinction  between 


Infra,  book  iii. , ch.  iv.,  § 3,  and  elsewhere. 


TRAINS  OF  REASONING. 


165 


sciences  which  can  be  made  Deductive,  and  those  which  must  as  yet  re- 
main Experimental.  The  difference  consists  in  our  having  been  able,  or 
not  yet  able,  to  discover  marks  of  marks.  If  by  our  various  inductions  we 
have  been  able  to  proceed  no  further  than  to  such  propositions  as  these,  a 
a mark  of  b,  or  a and  b marks  of  one  another,  e a mark  of  d,  or  c and  d 
marks  of  one  another,  without  any  thing  to  connect  a or  b with  c or  d;  we 
have  a science  of  detached  and  mutually  independent  generalizations,  such 
as  these,  that  acids  redden  vegetable  blues,  and  that  alkalies  color  them 
green ; from  neither  of  which  propositions  could  we,  directly  or  indirectly, 
infer  the  other : and  a science,  so  far  as  it  is  composed  of  such  proposi- 
tions, is  purely  experimental.  Chemistry,  in  the  present  state  of  our 
knowledge,  has  not  yet  thrown  off  this  character.  There  are  other  sci- 
ences, however,  of  which  the  propositions  are  of  this  kind : a a mark  of  b, 
b a mark  of  c,  c of  d,  d of  e,  etc.  In  these  sciences  we  can  mount  the  lad- 
der from  a to  e by  a process  of  ratiocination ; we  can  conclude  that  a is  a 
mark  of  e,  and  that  every  object  which  has  the  mark  a has  the  property  e, 
although,  perhaps,  we  never  were  able  to  observe  a and  e together,  and  al- 
though even  d,  our  only  direct  mark  of  e,  may  not  be  perceptible  in  those 
objects,  but  only  inferable.  Or,  varying  the  first  metaphor,  we  may  be 
said  to  get  from  a to  e underground : the  marks  b,  c,  d,  which  indicate  the 
route,  must  all  be  possessed  somewhere  by  the  objects  concerning  which 
we  are  inquiring ; but  they  are  below  the  surface : a is  the  only  mark  that 
is  visible,  and  by  it  we  are  able  to  trace  in  succession  all  the  rest. 

§ 6.  We  can  now  understand  how  an  experimental  may  transform  itself 
into  a deductive  science  by  the  mere  progress  of  experiment.  In  an  experi- 
mental science,  the  inductions,  as  we  have  said,  lie  detached,  as,  a a mark  of 
b,c  a mark  of  d , e a mark  of  f,  and  so  on  : now,  a new  set  of  instances,  and' 
a consequent  new  induction,  may  at  any  time  bridge  over  the  interval  be- 
tween two  of  these  unconnected  arches ; b,  for  example,  may  be  ascertained 
to  be  a mark  of  c,  which  enables  us  thenceforth  to  prove  deductively  that 
a is  a mark  of  c.  Or,  as  sometimes  happens,  some  comprehensive  induc- 
tion may  raise  an  arch  high  in  the  air,  which  'bridges  over  hosts  of  them 
at  once;  b,  d,f,  and  all  the  rest,  turning  out  to  be  marks  of  some  one  thing, 
or  of  things  between  which  a connection  has  already  been  traced.  As 
when  Newton  discovered  that  the  motions,  whether  regular  or  apparently 
anomalous,  of  all  the  bodies  of  the  solar  system  (each  of  which  motions 
had  been  inferred  by  a separate  logical  operation,  from  separate  marks), 
were  all  marks  of  moving  round  a common  centre,  with  a centripetal  force 
varying  directly  as  the  mass,  and  inversely  as  the  square  of  the  distance 
from  that  centi-e.  This  is  the  greatest  example  which  has  yet  occurred  of 
the  transformation,  at  one  stroke,  of  a scieuce  which  was  still  to  a great  de- 
gree merely  experimental,  into  a deductive  science. 

Transformations  of  the  same  nature,  but  on  a smaller  scale,  continually 
take  place  in  the  less  advanced  branches  of  physical  knowledge,  without 
enabling  them  to  throw  off  the  character  of  experimental  sciences.  Thus 
with  regard  to  the  two  unconnected  propositions  before  cited,  namely, 
Acids  redden  vegetable  blues,  Alkalies  make  them  green  ; it  is  remarked  by 
Liebig,  that  all  blue  coloring  matters  which  are  reddened  by  acids  (as  well 
as,  reciprocally,  all  red  coloring  matters  which  are  rendered  blue  by  alka- 
lies) contain  nitrogen : and  it  is  quite  possible  that  this  circumstance  may 
one  day  furnish  a bond  of  connection  between  the  two  propositions  in 
question,  by  showing  that  the  antagonistic  action  of  acids  and  alkalies  in 


166 


REASONING. 


producing  or  destroying  the  color  blue,  is  the  result  of  some  one,  more- 
general,  law.  Although  this  connecting  of  detached  generalizations  is  so 
much  gain,  it  tends  but  little  to  give  a deductive  character  to  any  science 
as  a whole ; because  the  new  courses  of  observation  and  experiment,  which 
thus  enable  us  to  connect  together  a few  general  truths,  usually  make 
known  to  us  a still  greater  number  of  unconnected  new  ones.  Hence 
chemistry,  though  similar  extensions  and  simplifications  of  its  generaliza- 
tions are  continually  taking  place,  is  still  in  the  main  an  experimental  sci- 
ence ; and  is  likely  so  to  continue  unless  some  comprehensive  induction 
should  be  hereafter  arrived  at,  which,  like  Newton’s,  shall  connect  a vast 
number  of  the  smaller  known  inductions  together,  and  change  the  whole 
method  of  the  science  at  once.  Chemistry  has  already  one  great  generali- 
zation, which,  though  relating  to  one  of  the  subordinate  aspects  of  chemical 
phenomena,  possesses  within  its  limited  sphere  this  comprehensive  charac- 
ter ; the  principle  of  Dalton,  called  the  atomic  theory,  or  the  doctrine  of 
chemical  equivalents : which  by  enabling  us  to  a certain  extent  to  foresee 
the  proportions  in  which  two  substances  will  combine,  before  the  experi- 
ment has  been  tried,  constitutes  undoubtedly  a source  of  new  chemical 
truths  obtainable  by  deduction,  as  well  as  a connecting  principle  for  all 
truths  of  the  same  description  previously  obtained  by  experiment. 

§ 7.  The  discoveries  which  change  the  method  of  a science  from  experi- 
mental to  deductive,  mostly  consist  in  establishing,  either  by  deduction  or 
by  direct  experiment,  that  the  varieties  of  a particular  phenomenon  uni- 
formly accompany  the  varieties  of  some  other  phenomenon  better  known. 
Thus  the  science  of  sound,  which  previously  stood  in  the  lowest  rank  of 
merely  experimental  science,  became  deductive  when  it  was  proved  by  ex- 
periment that  every  variety  of  sound  was  consequent  on,  and  therefore  a 
mark  of,  a distinct  and  definable  variety  of  oscillatory  motion  among  the 
particles  of  the  transmitting  medium.  When  this  was  ascertained,  it  fol- 
lowed that  every  relation  of  succession  or  co-existence  which  obtained  be- 
tween phenomena  of  the  more  known  class,  obtained  also  between  the 
phenomena  which  correspond  to  them  in  the  other  class.  Every  sound, 
being  a mark  of  a particular  oscillatory  motion,  became  a mark  of  every 
thing  which,  by  the  laws  of  dynamics,  was  known  to  be  inferable  from 
that  motion  ; and  every  thing  which  by  those  same  laws  was  a mark  of  any 
oscillatory  motion  among  the  particles  of  an  elastic  medium,  became  a mark 
of  the  corresponding  sound.  And  thus  many  truths,  not  before  suspected, 
concerning  sound,  become  deducible  from  the  known  laws  of  the  propaga- 
tion of  motion  through  an  elastic  medium;  while  facts  already  emjrirically 
known  respecting  sound,  become  an  indication  of  corresponding  properties 
of  vibrating  bodies,  previously  undiscovered. 

But  the  grand  agent  for  transforming  experimental  into  deductive  sci- 
ences, is  the  science  of  number.  The  proj)erties  of  number,  alone  among 
all  known  phenomena,  are,  in  the  most  rigorous  sense,  properties  of  all 
things  whatever.  All  things  are  not  colored,  or  ponderable,  or  even  ex- 
tended; but  all  things  are  numerable.  And  if  we  consider  this  science  in 
its  whole  extent,  from  common  arithmetic  up  to  the  calculus  of  variations, 
the  truths  already  ascertained  seem  all  but  infinite,  and  admit  of  indefinite 
extension. 

These  truths,  though  affirmable  of  all  things  whatever,  of  course  apply 
to  them  only  in  respect  of  their  quantity.  But  if  it  comes  to  be  discovered 
that  variations  of  quality  in  any  class  of  phenomena,  correspond  regularly 


TRAINS  OF  REASONING. 


167 


to  variations  of  quantity  either  in  those  same  or  in  some  other  phenomena; 
every  formula  of  mathematics  applicable  to  quantities  which  vary  in  that 
particular  manner,  becomes  a mark  of  a corresponding  general  truth  re- 
specting the  variations  in  quality  which  accompany  them:  and  the  sci- 
ence of  quantity  being  (as  far  as  any  science  can  be)  altogether  deductive, 
the  theory  of  that  particular  kind  of  qualities  becomes,  to  this  extent,  de- 
ductive likewise. 

The  most  striking  instance  in  point  which  history  affords  (though  not 
an  example  of  an  experimental  science  rendered  deductive,  but  of  an  un- 
paralleled extension  given  to  the  deductive  process  in  a science  which  was 
deductive  already),  is  the  revolution  in  geometry  which  originated  with 
Descartes,  and  was  completed  by  Clairaut.  These  great  mathematicians 
pointed  out  the  importance  of  the  fact,  that  to  every  variety  of  position  in 
points,  direction  in  lines,  or  form  in  curves  or  surfaces  (all  of  which  are 
Qualities),  there  corresponds  a peculiar  relation  of  quantity  between  either 
two  or  three  rectilineal  co-ordinates ; insomuch  that  if  the  law  were  known 
according  to  which  those  co-ordinates  vary  relatively  to  one  another,  every 
other  geometrical  property  of  the  line  or  surface  in  question,  whether  re- 
lating to  quantity  or  quality,  would  be  capable  of  being  inferred.  Hence 
it  followed  that  every  geometrical  question  could  be  solved,  if  the  corre- 
sponding algebraical  one  could ; and  geometry  received  an  accession  (act- 
ual or  potential)  of  new  truths,  corresponding  to  every  property  of  num- 
bers which  the  progress  of  the  calculus  had  brought,  or  might  in  future 
bring,  to  light.  In  the  same  general  manner,  mechanics,  astronomy,  and  in 
a less  degree,  every  branch  of  natural  philosophy  commonly  so  called,  have 
been  made  algebraical.  The  varieties  of  physical  phenomena  with  which 
those  sciences  are  conversant,  have  been  found  to  answer  to  determinable 
varieties  in  the  quantity  of  some  circumstance  or  other;  or  at  least  to  va- 
rieties of  form  or  position,  for  which  corresponding  equations  of  quantity 
had  already  been,  or  were  susceptible  of  being,  discovered  by  geometers. 

In  these  various  transformations,  the  propositions  of  the  science  of  num- 
ber do  but  fulfill  the  function  proper  to  all  propositions  forming  a train  of 
reasoning,  viz.,  that  of  enabling  us  to  arrive  in  an  indirect  method,  by 
marks  of  marks,  at  such  of  the  properties  of  objects  as  we  can  not  direct- 
ly ascertain  (or  not  so  conveniently)  by  experiment.  We  travel  from  a 
given  visible  or  tangible  fact,  through  the  truths  of  numbers,  to  the  facts 
sought.  The  given  fact  is  a mark  that  a certain  relation  subsists  between 
the  quantities  of  some  of  the  elements  concerned ; while  the  fact  sought 
presupposes  a certain  relation  between  the  quantities  of  some  other  ele- 
ments : now,  if  these  last  quantities  are  dependent  in  some  known  manner 
upon  the  former,  or  vicb  versa,  we  can  argue  from  the  numerical  relation 
between  the  one  set  of  quantities,  to  determine  that  which  subsists  be- 
tween the  other  set;  the  theorems  of  the  calculus  affording  the  intermedi- 
ate links.  And  thus  one  of  the  two  physical  facts  becomes  a mark  of  the 
other,  by  being  a mark  of  a mark  of  a mark  of  it. 


168 


REASONING. 


CHAPTER  Y. 

OP  DEMONSTRATION,  AND  NECESSARY  TRUTHS. 

§ 1.  Ip,  as  laid  down  in  the  two  preceding  chapters,  the  foundation  of 
all  sciences,  even  deductive  or  demonstrative  sciences,  is  Induction ; if 
every  step  in  the  ratiocinations  even  of  geometry  is  an  act  of  induction  ; 
and  if  a train  of  reasoning  is  but  bringing  many  inductions  to  bear  upon 
the  same  subject  of  inquiry,  and  drawing  a case  within  one  induction  by 
means  of  another ; wherein  lies  the  peculiar  certainty  always  ascribed  to 
the  sciences  which  are  entirely,  or  almost  entirely,  deductive  ? Why  are 
they  called  the  Exact  Sciences?  Why  are  mathematical  certainty, and  the 
evidence  of  demonstration,  common  phrases  to  express  the  very  highest 
degree  of  assurance  attainable  by  reason  ? Why  are  mathematics  by  al- 
most all  philosophers,  and  (by  some)  even  those  branches  of  natural  phi- 
losophy which,  through  the  medium  of  mathematics,  have  been  converted 
into  deductive  sciences,  considered  to  be  independent  of  the  evidence  of 
experience  and  observation,  and  characterized  as  systems  of  Necessary 
Truth  ? 

The  answer  I conceive  to  be,  that  this  character  of  necessity,  ascribed  to 
the  truths  of  mathematics,  and  (even  with  some  reservations  to  be  here- 
after made)  the  peculiar  certainty  attributed  to  them,  is  an  illusion  ; in  or- 
der to  sustain  which,  it  is  necessary  to  suppose  that  those  truths  relate  to, 
and  express  the  properties  of,  purely  imaginary  objects.  It  is  acknowl- 
edged that  the  conclusions  of  geometry  are  deduced,  partly  at  least,  from 
the  so-called  Definitions,  and  that  those  definitions  are  assumed  to  be  cor- 
rect representations,  as  far  as  they  go,  of  the  objects  With  which  geometry 
is  conversant.  Now  we  have  pointed  out  that,  from  a definition  as  such, 
no  proposition,  unless  it  be  on  a concerning  the  meaning  of  a word,  can  ever 
follow  ; and  that  what  apparently  follows  from  a definition,  follows  in  real- 
ity from  an  implied  assumption  that  there  exists  a real  thing  conformable 
thereto.  This  assumption,  in  the  case  of  the  definitions  of  geometry,  is  not 
strictly  true : there  exist  no  real  things  exactly  conformable  to  the  defini- 
tions. There  exist  no  points  without  magnitude ; no  lines  without  breadth, 
nor  perfectly  straight;  no  circles  with  all  their  radii  exactly  equal,  nor 
squares  with  all  their  angles  perfectly  right.  It  will  perhaps  be  said  that 
the  assumption  does  not  extend  to  the  actual,  but  only  to  the  possible,  exist- 
ence of  such  things.  I answer  that,  according  to  any  test  we  have  of  possi- 
bility, they  are  not  even  possible.  Their  existence,  so  far  as  we  can  form 
any  judgment,  would  seem  to  be  ir*consistent  with  the  physical  constitu- 
tion of  our  planet  at  least,  if  not  of  the  universe.  To  get  rid  of  this  diffi- 
culty, and  at  the  same  time  to  save  the  credit  of  the  supposed  system  of 
necessary  truth,  it  is  customary  to  say  that  the  points,  lines,  circles,  and 
squares  which  are  the  subject  of  geometry,  exist  in  our  conceptions  mere- 
ly, and  are  part  of  our  minds ; which  minds,  by  working  on  their  own  ma- 
terials, construct  an  a priori  science,  the  evidence  of  which  is  purely  men- 
tal, and  has  nothing  whatever  to  do  with  outward  experience.  By  how- 
soever high  authorities  this  doctrine  may  have  been  sanctioned,  it  appears 


DEMONSTRATION,  AND  NECESSARY  TRUTHS. 


169 


to  rue  psychologically  incorrect.  The  points,  lines,  circles,  and  squares 
which  any  one  has  in  his  mind,  are  (I  apprehend)  simply  copies  of  the 
points,  lines,  circles,  and  squares  which  he  has  known  in  his  experience. 
Our  idea  of  a point,  I apprehend  to  be  simply  our  idea  of  the  minimum 
visibile,  the  smallest  portion  of  surface  which  we  can  see.  A line,  as  de- 
fined by  geometers,  is  wholly  inconceivable.  We  can  reason  about  a line 
as  if  it  had  no  breadth ; because  we  have  a power,  which  is  the  foundation 
of  all  the  control  we  can  exercise  over  the  operations  of  our  minds;  the 
power,  when  a perception  is  present  to  our  senses,  or  a conception  to  our 
intellects,  of  attending  to  a part  only  of  that  perception  or  conception,  in- 
stead of  the  whole.  But  we  can  not  conceive  a line  without  breadth ; we 
can  form  no  mental  picture  of  such  a line : all  the  lines  which  we  have  in 
our  minds  are  lines  possessing  breadth.  If  any  one  doubts  this,  we  may 
refer  him  to  his  own  experience.  I much  question  if  any  one  who  fancies 
that  he  can  conceive  what  is  called  a mathematical  line,  thinks  so  from  the 
evidence  of  his  consciousness:  I suspect  it  is  rather  because  he  supposes 
that  unless  such  a conception  were  possible,  mathematics  could  not  exist  as 
a science : a supposition  which  there  will  be  no  difficulty  in  showing  to  be 
entirely  groundless. 

Since, then,  neither  in  nature,  nor  in  the  human  mind,  do  there  exist  any 
objects  exactly  corresponding  to  the  definitions  of  geometry,  while  yet  that 
science  can  not  be  supposed  to  be  conversant  about  nonentities;  nothing 
remains  but  to  consider  geometry  as  conversant  with  such  lines,  angles, 
and  figures,  as  really  exist;  and  the  definitions,  as  they  are  called,  must  be 
regarded  as  some  of  our  first  and  most  obvious  generalizations  concerning 
those  natural  objects.  The  correctness  of  those  generalizations,  os  gener- 
alizations, is  without  a flaw  : the  equality  of  all  the  radii  of  a circle  is  true 
of  all  circles,  so  far  as  it  is  true  of  any  one:  but  it  is  not  exactly  true  of 
any  circle  ; it  is  only  nearly  true ; so  nearly  that  no  error  of  any  impor- 
tance in  practice  will  be  incurred  by  feigning  it  to  be  exactly  true.  When 
we  have  occasion  to  extend  these  inductions,  or  their  consequences,  to  cases 
in  which  the  error  would  be  appreciable — to  lines  of  perceptible  breadth 
or  thickness,  parallels  which  deviate  sensibly  from  equidistance,  and  the 
like— we  correct  our  conclusions,  by  combining  with  them  a fresh  set  of 
propositions  relating  to  the  aberration;  just  as  we  also  take  in  proposi- 
tions relating  to  the  physical  or  chemical  properties  of  the  material,  if  those 
properties  happen  to  introduce  any  modification  into  the  result;  which 
they  easily  may,  even  with  respect  to  figure  and  magnitude,  as  in  the  case, 
for  instance,  of  expansion  by  heat.  So  long,  however,  as  there  exists  no 
practical  necessity  for  attending  to  any  of  the  properties  of  the  object  ex- 
cept its  geometrical  properties,  or  to  any  of  the  natural  irregularities  in 
those,  it  is  convenient  to  neglect  the  consideration  of  the  other  properties 
and  of  the  irregularities,  and  to  reason  as  if  these  did  not  exist : according- 
ly, we  formally  announce  in  the  definitions,  that  we  intend  to  proceed  on 
this  plan.  But  it  is  an  error  to  suppose,  because  we  resolve  to  confine  our 
attention  to  a certain  number  of  the  properties  of  an  object,  that  we  there- 
fore conceive,  or  have  an  idea  of,  the  object,  denuded  of  its  other  proper- 
ties. We  are  thinking,  all  the  time,  of  precisely  such  objects  as  we  have 
seen  and  touched,  and  with  all  the  properties  which  naturally  belong  to 
them ; but,  for  scientific  convenience,  we  feign  them  to  be  divested  of  all 
properties,  except  those  which  are  material  to  our  purpose,  and  in  regard 
to  which  we  design  to  consider  them. 

The  peculiar  accuracy,  supposed  to  be  characteristic  of  the  first  princi- 


170 


REASONING. 


pies  of  geometry,  thus  appears  to  be  fictitious.  The  assertions  on  which 
the  reasonings  of  the  science  are  founded,  do  not,  any  more  than  in  other 
sciences,  exactly  correspond  with  the  fact ; but  we  suppose  that  they  do 
so,  for  tlie  sake  of  tracing  the  consequences  which  follow  from  the  suppo- 
sition. The  opinion  of  Dugald  Stewart  respecting  the  foundations  of  ge- 
ometry, is,  I conceive,  substantially  correct ; that  it  is  built  on  hypotheses ; 
that  it  owes  to  this  alone  the  peculiar  certainty  supposed  to  distinguish  it; 
and  that  in  any  science  whatever,  by  reasoning  from  a set  of  hypotheses, 
we  may  obtain  a body  of  conclusions  as  certain  as  those  of  geometry,  that 
is,  as  strictly  in  accordance  with  the  hypotheses,  and  as  irresistibly  compel- 
ling assent,  on  condition  that  those  hypotheses  are  true.* 

When,  therefore,  it  is  affirmed  that  the  conclusions  of  geometry  are  nec- 
essary truths,  the  necessity  consists  in  reality  only  in  this,  that  they  cor- 
rectly follow  from  the  suppositions  from  which  they  are  deduced.  Those 
suppositions  are  so  far  from  being  necessary,  that  they  are  not  even  true ; 
they  purposely  depart,  more  or  less  widely, from  the  truth.  The  only  sense 
in  which  necessity  can  be  ascribed  to  the  conclusions  of  any  scientific  in- 
vestigation, is  that  of  legitimately  following  from  some  assumption,  which, 
by  the  conditions  of  the  inquiry,  is  not  to  be  questioned.  In  this  relation, 
of  course,  the  derivative  truths  of  every  deductive  science  must  stand  to 
the  inductions,  or  assumptions,  on  which  the  science  is  founded,  and  which, 
whether  true  or  untrue,  certain  or  doubtful  in  themselves,  are  always  sup- 
posed certain  for  the  purposes  of  the  particular  science.  And  therefore 
the  conclusions  of  all  deductive  sciences  were  said  by  the  ancients  to  be 
necessary  propositions.  Wo  have  observed  already  that  to  be  predicated 
necessarily  was  characteristic  of  the  predicable  Proprium,  and  that  a pro- 
prium  was  any  property  of  a thing  which  could  be  deduced  from  its  es- 
sence, that  is,  from  the  properties  included  in  its  definition. 

§ 2.  The  important  doctrine  of  Dugald  Stewart,  which  I have  endeav- 
ored to  enforce,  has  been  contested  by  Dr.  Whewell,  both  in  the  disserta- 
tion appended  to  his  excellent  Mechaniccd  Euclid , and  in  his  elaborate 
work  on  the  Philosophy  of  the  Inductive  Sciences  • in  which  last  he  also 
replies  to  an  article  in  the  Edinburgh  Review  (ascribed  to  a writer  of 
great  scientific  eminence),  in  which  Stewart’s  opinion  was  defended  against 
his  former  strictures.  The  supposed  refutation  of  Stewart  consists  in 
proving  against  him  (as  has  also  been  done  in  this  work)  that  the  premises 
of  geometry  are  not  definitions,  but  assumptions  of  the  real  existence  of 
things  corresponding  to  those  definitions.  This,  however,  is  doing  little  for 
Dr.  Whewell’s  purpose ; for  it  is  these  very  assumptions  which  are  as- 
serted to  be  hypotheses,  and  which  he,  if  he  denies  that  geometry  is  founded 

* It  is  justly  remarked  by  Professor  Bain  {Logic,  ii.,  134)  that  the  word  Hypothesis  is  here 
used  in  a somewhat  peculiar  sense.  An  hypothesis,  in  science,  usually  means  a supposition 
not  proved  to  be  true,  but  surmised  to  be  so,  because  if  true  it  would  account  for  certain 
known  facts  ; and  the  final  result  of  the  speculation  may  be  to  prove  its  truth.  The  hypothe- 
ses spoken  of  in  the  text  are  of  a different  character ; they  are  known  not  to  be  literally  true, 
while  as  much  of  them  as  is  true  is  not  hypothetical,  but  certain.  The  two  cases,  however, 
resemble  in  the  circumstance  that  in  both  we  reason,  not  from  a truth,  but  from  an  assump- 
tion, and  the  truth  therefore  of  the  conclusions  is  conditional,  not  categorical.  This  suffices 
to  justify,  in  point  of  logical  propriety,  Stewart’s  use  of  the  term.  It  is  of  course  needful  to 
bear  in  mind  that  the  hypothetical  element  in  the  definitions  of  geometry  is  the  assumption 
that  what  is  very  nearly  true  is  exactly  so.  This  unreal  exactitude  might  be  called  a fiction, 
as  properly  as  an  hypothesis ; but  that  appellation,  still  more  than  the  other,  would  fail  to 
point  out  the  close  relation  which  exists  between  the  fictitious  point  or  line  and  the  points 
and  lines  of  which  we  have  experience. 


DEMONSTRATION,  AND  NECESSARY  TRUTHS. 


171 


on  hypotheses,  must  show  to  be  absolute  truths.  All  he  does,  however,  is 
to  observe,  that  they,  at  any  rate,  are  not  arbitrary  hypotheses ; that  we 
should  not  be  at  liberty  to  substitute  other  hypotheses  for  them;  that  not 
only  “ a definition,  to  be  admissible,  must  necessarily  refer  to  and  agree 
witli  some  conception  which  we  can  distinctly  frame  in  our  thoughts,”  but 
that  the  straight  lines,  for  instance,  which  we  define,  must  be  “those  by 
which  angles  are  contained,  those  by  which  triangles  are  bounded,  those  of 
which  parallelism  may  be  predicated,  and  the  like.”*  And  this  is  true ; 
but  this  has  never  been  contradicted.  Those  who  say  that  the  premises 
of  geometry  are  hypotheses,  are  not  bound  to  maintain  them  to  be  hypoth- 
eses which  have  no  relation  whatever  to  fact.  Since  an  hypothesis  framed 
for  the  purpose  of  scientific  inquiry  must  relate  to  something  which  has 
real  existence  (for  there  can  be  no  science  respecting  nonentities),  it  fol- 
lows that  any  hypothesis  we  make  respecting  an  object,  to  facilitate  our 
study  of  it,  must  not  involve  any  thing  which  is  distinctly  false,  and  repug- 
nant to  its  real  nature:  we  must  not  ascribe  to  the  thing  any  property 
which  it  has  not;  our  liberty  extends  only  to  slightly  exaggerating  some 
of  those  which  it  has  (by  assuming  it  to  be  completely  what  it  really  is 
very  nearly),  and  suppressing  others,  under  the  indispensable  obligation  of 
restoring  them  whenever,  and  in  as  far  as,  their  presence  or  absence  would 
make  any  material  difference  in  the  truth  of  our  conclusions.  Of  this  na- 
ture, accordingly,  are  the  first  principles  involved  in  the  definitions  of  ge- 
ometry. That  the  hypotheses  should  be  of  this  particular  character,  is, 
however,  no  further  necessary,  than  inasmuch  as  no  others  could  enable  us 
to  deduce  conclusions  which,  with  due  corrections,  would  be  true  of  real 
objects : and  in  fact,  when  our  aim  is  only  to  illustrate  truths,  and  not  to 
investigate  them,  we  are  not  under  any  such  restriction.  We  might  sup- 
pose an  imaginary  animal,  and  work  out  by  deduction,  from  the  known 
laws  of  physiology,  its  natural  history ; or  an  imaginary  commonwealth, 
and  from  the  elements  composing  it,  might  argue  what  would  be  its  fate. 
And  the  conclusions  which  we  might  thus  draw  from  purely  arbitrary  hy- 
potheses, might  form  a highly  useful  intellectual  exercise  : but  as  they  could 
only  teach  us  what  tcould  be  the  properties  of  objects  which  do  not  really 
exist,  they  would  not  constitute  any  addition  to  our  knowledge  of  nature : 
while,  on  the  contrary,  if  the  hypothesis  merely  divests  a real  object  of 
some  portion  of  its  properties,  without  clothing  it  in  false  ones,  the  conclu- 
sions will  always  express,  under  known  liability  to  correction,  actual  truth. 

§ 3.  But  though  Dr.  Whewell  has  not  shaken  Stewart’s  doctrine  as  to 
the  hypothetical  character  of  that  portion  of  the  first  principles  of  geom- 
etry which  are  involved  in  the  so-called  definitions,  he  has,  I conceive,  great- 
ly the  advantage  of  Stewart  on  another  important  point  in  the  theory  of 
geometrical  reasoning ; the  necessity  of  admitting,  among  those  first  prin- 
ciples, axioms  as  well  as  definitions.  Some  of  the  axioms  of  Euclid  might, 
no  doubt,  be  exhibited  in  the  form  of  definitions,  or  might  be  deduced,  by 
reasoning,  from  propositions  similar  to  what  are  so  called.  Thus,  if  instead 
of  the  axiom,  Magnitudes  which  can  be  made  to  coincide  are  equal,  we  in- 
troduce a definition,  “ Equal  magnitudes  are  those  which  may  be  so  ap- 
plied to  one  another  as  to  coincide ;”  the  three  axioms  which  follow  (Mag- 
nitudes which  are  equal  to  the  same  are  equal  to  one  another — If  equals 
ai'e  added  to  equals,  the  sums  are  equal — If  equals  are  taken  from  equals, 


* Mechanical  Euclid,  pp.  149  et  seqq. 


172 


REASONING. 


the  remainders  are  equal),  may  be  proved  by  an  imaginary  superposition, 
resembling  that  by  which  the  fourth  proposition  of  the  first  book  of  Euclid 
is  demonstrated.  But  though  these  and  several  others  may  be  struck  out 
of  the  list  of  first  principles,  because,  though  not  requiring  demonstration, 
they  are  susceptible  of  it ; there  will  be  found  in  the  list  of  axioms  two  or 
three  fundamental  truths,  not  capable  of  being  demonstrated : among  which 
must  be  reckoned  the  proposition  that  two  straight  lines  can  not  inclose  a 
space  (or  its  equivalent,  Straight  lines  which  coincide  in  two  points  coin- 
cide altogether),  and  some  property  of  parallel  lines,  other  than  that  which 
constitutes  their  definition : one  of  the  most  suitable  for  the  purpose  being 
that  selected  by  Professor  Playfair:  “Two  straight  lines  which  intersect 
each  other  can  not  both  of  them  be  parallel  to  a third  straight  line.”* 

The  axioms,  as  well  those  which  are  indemonstrable  as  those  which  ad- 
mit of  being  demonstrated,  differ  from  that  other  class  of  fundamental 
principles  which  are  involved  in  the  definitions,  in  this,  that  they  are  true 
without  any  mixture  of  hypothesis.  That  things  which  are  equal  to  the 
same  thing  are  equal  to  one  another,  is  as  true  of  the  lines  and  figures  in 
nature,  as  it  would  be  of  the  imaginary  ones  assumed  in  the  definitions. 
In  this  respect,  however,  mathematics  are  only  on  a par  with  most  other 
sciences.  In  almost  all  sciences  there  are  some  general  propositions  which 
are  exactly  true,  while  the  greater  part  are  only  more  or  less  distant  ap- 
proximations to  the  truth.  Thus  in  mechanics,  the  first  law  of  motion  (the 
continuance  of  a movement  once  impressed,  until  stopped  or  slackened  by 
some  resisting  force)  is  true  without  qualification  or  error.  The  rotation 
of  the  earth  in  twenty-four  hours,  of  the  same  length  as  in  our  time,  has 
gone  on  since  the  first  accurate  observations,  without  the  increase  or  dim- 
inution of  one  second  in  all  that  period.  These  are  inductions  which 
require  no  fiction  to  make  them  be  received  as  accurately  true : but  along 
with  them  there  are  others,  as  for  instance  the  propositions  respecting  the 
figure  of  the  earth,  which  are  but  approximations  to  the  truth  ; and  in  or- 
der to  use  them  for  the  further  advancement  of  our  knowledge,  we  must 
feign  that  they  are  exactly  true,  though  they  really  want  something  of  be- 
ing so. 

§ 4.  It  remains  to  inquire,  what  is  the  ground  of  our  belief  in  axioms — 
what  is  the  evidence  on  which  they  rest  ? I answer,  they  are  experi- 
mental truths ; generalizations  from  observation.  The  proposition,  Two 
straight  lines  can  not  inclose  a space  — or,  in  other  words,  Two  straight 
lines  which  have  once  met,  do  not  meet  again,  but  continue  to  diverge — 
is  an  induction  from  the  evidence  of  our  senses. 

This  opinion  runs  counter  to  a scientific  prejudice  of  long  standing  and 
great  strength,  and  there  is  probably  no  proposition  enunciated  in  this 
work  for  which  a more  unfavorable  reception  is  to  be  expected.  It  is, 
however,  no  new  opinion  ; and  even  if  it  were  so,  would  be  entitled  to  be 
judged,  not  by  its  novelty,  but  by  the  strength  of  the  arguments  by  which 
it  can  be  supported.  I consider  it  very  fortunate  that  so  eminent  a cham- 

* We  might,  it  is  true,  insert  this  property  into  the  definition  of  parallel  lines,  framing  the 
definition  so  as  to  require,  both  that  when  produced  indefinitely  they  shall  never  meet,  and 
also  that  any  Straight  line  which  intersects  one  of  them  shall,  if  prolonged,  meet  the  other. 
But  by  doing  this  we  by  no  means  get  rid  of  the  assumption  ; we  are  still  obliged  to  take  for 
granted  the  geometrical  truth,  that  all  straight  lines  in  the  same  plane,  which  have  the  former 
of  these  properties,  have  also  the  latter.  For  if  it  were  possible  that  they  should  not,  that  is, 
if  any  straight  lines  in  the  same  plane,  other  than  those  which  are  parallel  according  to  the 
definition,  had  the  property  of  never  meeting  although  indefinitely  produced,  the  demonstra- 
tions of  the  subsequent  portions  of  the  theory  of  parallels  could  not  be  maintained. 


DEMONSTRATION,  AND  NECESSARY  TRUTHS. 


173 


pion  of  the  contrary  opinion  as  Dr.  Whewell  has  found  occasion  for  a most 
elaborate  treatment  of  the  whole  theory  of  axioms,  in  attempting  to  con- 
struct the  philosophy  of  the  mathematical  and  physical  sciences  on  the 
basis  of  the  doctrine  against  which  I now  contend.  Whoever  is  anxious 
that  a discussion  should  go  to  the  bottom  of  the  subject,  must  rejoice  to 
see  the  opposite  side  of  the  question  worthily  represented.  If  what  is 
said  by  Dr.  Whewell,  in  support  of  an  opinion  which  he  has  made  the 
foundation  of  a systematic  work,  can  be  shown  not  to  be  conclusive,  enough 
will  have  been  done,  without  going  elsewhere  in  quest  of  stronger  argu- 
ments and  a more  powerful  adversary. 

It  is  not  necessary  to  show  that  the  truths  which  we  call  axioms  are 
originally  suggested  by  observation,  and  that  we  should  never  have  known 
that  two  straight  lines  can  not  inclose  a space  if  wre  had  never  seen  a 
straight  line:  thus  much  being  admitted  by  Dr.  Whewell,  and  by  all,  in 
recent  times,  who  have  taken  his  view  of  the  subject.  But  they  contend, 
that  it  is  not  experience  which  proves  the  axiom;  but  that  its  truth  is  per- 
ceived a priori,  by  the  constitution  of  the  mind  itself,  from  the  first  mo- 
ment -when  the  meaning  of  the  proposition  is  apprehended  ; and  without 
any  necessity  for  verifying  it  by  repeated  trials,  as  is  requisite  in  the  case 
of  truths  really  ascertained  by  observation. 

They  can  not,  however,  but  allow  that  the  truth  of  the  axiom,  Two 
straight  lines  can  not  inclose  a space,  even  if  evident  independently  of  ex- 
perience, is  also  evident  from  experience.  Whether  the  axiom  needs  con- 
firmation or  not,  it  receives  confirmation  in  almost  every  instant  of  our 
lives ; since  we  can  not  look  at  any  two  straight  lines  which  intersect  one 
another,  without  seeing  that  from  that  point  they  continue  to  diverge  more 
and  more.  Experimental  proof  crowds  in  upon  us  in  such  endless  profu- 
sion, and  without  one  instance  in  which  there  can  be  even  a suspicion  of 
an  exception  to  the  rule,  that  we  should  soon  have  stronger  ground  for  be- 
lieving the  axiom,  even  as  an  experimental  truth,  than  we  have  for  almost 
any  of  the  general  truths  which  we  confessedly  learn  from  the  evidence  of 
our  senses.  Independently  of  a priori  evidence,  we  should  certainly  be- 
lieve it  with  an  intensity  of  conviction  far  greater  than  we  accord  to  any 
ordinary  physical  truth  : and  this  too  at  a time  of  life  much  earlier  than 
that  from  which  we  date  almost  any  part  of  our  acquired  knowledge,  and 
much  too  early  to  admit  of  our  retaining  any  recollection  of  the  history  of 
our  intellectual  operations  at  that  period.  Where  then  is  the  necessity  for 
assuming  that  our  recognition  of  these  truths  has  a different  origin  from 
the  rest  of  our  knowledge,  when  its  existence  is  perfectly  accounted  for  by 
supposing  its  origin  to  be  the  same  ? when  the  causes  which  produce  be- 
lief in  all  other  instances,  exist  in  this  instance,  and  in  a degree  of  strength 
as  much  superior  to  what  exists  in  other  cases,  as  the  intensity  of  the  be- 
lief itself  is  superior?  The  burden  of  proof  lies  on  the  advocates  of  the 
contrary  opinion : it  is  for  them  to  point  out  some  fact,  inconsistent  with 
the  supposition  that  this  part  of  our  knowdedge  of  nature  is  derived  from 
the  same  sources  as  every  other  part.* 

* Some  persons  find  themselves  prevented  from  believing  that  the  axiom,  Two  straight  lines 
can  not  inclose  a space,  could  ever  become  known  to  us  through  experience,  by  a difficulty 
which  may  be  stated  as  follows  : If  the  straight  lines  spoken  of  are  those  contemplated  in  the 
definition — lines  absolutely  without  breadth  and  absolutely  straight — that  such  are  incapable 
of  inclosing  a space  is  not  proved  by  experience,  for  lines  such  as  these  do  not  present  them- 
selves in  our  experience.  If,  on  the  other  hand,  the  lines  meant  are  such  straight  lines  as  we 
do  meet  with  in  experience,  lines  straight  enough  for  practical  purposes,  but  in  reality  slightly 
zigzag,  and  with  some,  however  trifling,  breadth;  as  applied  to  these  lines  the  axiom  is  not 


174 


REASONING. 


This,  for  instance,  they  would  be  able  to  do,  if  they  could  prove  chrono- 
logically that  we  had  the  conviction  (at  least  practically)  so  early  in  infan- 
cy as  to  be  anterior  to  those  impressions  on  the  senses,  upon  which,  on  the 
other  theory,  the  conviction  is  founded.  This,  however,  can  not  be  proved: 
the  jioint  being  too  far  back  to  be  within  the  reach  of  memory,  and  too  ob- 
scure for  external  observation.  The  advocates  of  the  a priori  theory  are 
obliged  to  have  recourse  to  other  arguments.  These  are  reducible  to  two, 
which  I shall  endeavor  to  state  as  clearly  and  as  forcibly  as  possible. 

§ 5.  In  the  first  place  it  is  said,  that  if  our  assent  to  the  proposition  that 
two  straight  lines  can  not  inclose  a space,  were  derived  from  the  senses, 
we  could  only  be  convinced  of  its  truth  by  actual  trial,  that  is,  by  seeing  or 
feeling  the  straight  lines ; whereas,  in  fact,  it  is  seen  to  be  true  by  merely 
thinking  of  them.  That  a stone  thrown  into  water  goes  to  the  bottom, 
may  be  perceived  by  our  senses,  but  mere  thinking  of  a stoue  thrown  into 
the  water  would  never  have  led  us  to  that  conclusion : not  so,  however, 
with  the  axioms  relating  to  straight  lines  : if  I could  be  made  to  conceive 
what  a straight  line  is,  without  having  seen  one,  I should  at  once  recognize 
that  two  such  lines  can  not  inclose  a space.  Intuition  is  “ imaginary  look- 
ing but  experience  must  be  real  looking:  if  we  see  a property  of 
straight  lines  to  be  true  by  merely  fancying  ourselves  to  be  looking  at 
them,  the  ground  of  our  belief  can  not  be  the  senses,  or  experience;  it 
must  be  something  mental. 

To  this  argument  it  might  be  added  in  the  case  of  this  particular  axiom 
(for  the  assertion  would  not  be  true  of  all  axioms),  that  the  evidence  of  it 
from  actual  ocular  inspection  is  not  only  unnecessary,  but  unattainable. 
What  says  the  axiom  ? That  two  straight  lines  can  not  inclose  a space ; 
that  after  having  once  intersected,  if  they  are  prolonged  to  infinity  they  do 
not  meet,  but  continue  to  diverge  from  one  another.  How  can  this,  in  any 
single  case,  be  proved  by  actual  observation?  We  may  follow  the  lines  to 
any  distance  we  please;  but  we  can  not  follow  them  to  infinity : for  aught 
our  senses  can  testify,  they  may,  immediately  beyond  the  farthest  point  to 
which  we  have  traced  them,  begin  to  approach,  and  at  last  meet.  Unless, 
therefore,  we  had  some  other  proof  of  the  impossibility  than  observation 
affords  us,  we  should  have  no  ground  for  believing  the  axiom  at  all. 

To  these  arguments,  which  1 trust  I can  not  be  accused  of  understating, 
a satisfactory  answer  will,  I conceive,  be  found,  if  we  advert  to  one  of  the 
characteristic  properties  of  geometrical  forms  — their  capacity  of  being 
painted  in  the  imagination  with  a distinctness  equal  to  reality : in  other 
words,  the  exact  resemblance  of  our  ideas  of  form  to  the  sensations  which 

true,  for  two  of  them  may,  and  sometimes  do,  inclose  a small  portion  of  space.  In  neither 
case,  therefore,  does  experience  prove  the  axiom. 

Those  who  employ  this  argument  to  show  that  geometrical  axioms  can  not  be  proved  by 
induction,  show  themselves  unfamiliar  with  a common  and  perfectly  valid  mode  of  inductive 
proof ; proof  by  approximation.  Though  experience  furnishes  us  with  no  lines  so  unim- 
peachably straight  that  two  of  them  are  incapable  of  inclosing  the  smallest  space,  it  presents 
us  with  gradations  of  lines  possessing  less  and  less  either  of  breadth  or  of  flexure,  of  which 
series  the  straight  line  of  the  definition  is  the  ideal  limit.  And  observation  shows  that  just  as 
much,  and  as  nearly,  as  the  straight  lines  of  experience  approximate  to  having  no  breadth  or 
flexure,  so  much  and  so  nearly  does  the  space-inclosing  power  of  any  two  of  them  approach 
to  zero.  The  inference  that  if  they  had  no  breadth  or  flexure  at  all,  they  would  inclose  no 
space  ;\t  all,  is  a correct  inductive  inference  from  these  facts,  conformable  to  one  of  the  four 
Inductive  Methods  hereinafter  characterized,  the  Method  of  Concomitant  Variations ; of 
which  the  mathematical  Doctrine  of  Limits  presents  the  extreme  case. 

* Whewell’s  History  of  Scientific  Ideas , i.,  140. 


DEMONSTRATION,  AND  NECESSARY  TRUTHS. 


175 


suggest  them.  This,  in  the  first  place,  enables  us  to  make  (at  least  with  a 
little  practice)  mental  pictures  of  all  possible  combinations  of  lines  and  an- 
gles, which  resemble  the  realities  quite  as  well  as  any  which  we  could  make 
on  paper ; and  in  the  next  place,  make  those  pictures  just  as  fit  subjects  of 
geometrical  experimentation  as  the  realities  themselves  ; inasmuch  as  pic- 
tures, if  sufficiently  accurate,  exhibit  of  course  all  the  properties  which 
would  be  manifested  by  the  realities  at  one  given  instant,  and  on  simple 
inspection  : and  in  geometry  we  are  concerned  only  with  such  properties, 
and  not  with  that  which  pictures  could  not  exhibit,  the  mutual  action  of 
bodies  one  upon  another.  The  foundations  of  geometry  would  therefore 
be  laid  in  direct  experience,  even  if  the  experiments  (which  in  this  case 
consist  merely  in  attentive  contemplation)  were  practiced  solely  upon 
what  we  call  our  ideas,  that  is,  upon  the  diagrams  in  our  minds,  and  not 
upon  outward  objects.  For  in  all  systems  of  experimentation  we  take 
some  objects  to  serve  as  representatives  of  all  which  resemble  them;  and 
in  the  present  case  the  conditions  which  qualify  a real  object  to  be  the  rep- 
resentative of  its  class,  are  completely  fulfilled  by  an  object  existing  only 
in  our  fancy.  Without  denying,  therefore,  the  possibility  of  satisfying  our- 
selves that  two  straight  lines  can  not  inclose  a space,  by  merely  thinking 
of  straight  lines  without  actually  looking  at  them;  I contend,  that  we  do 
not  believe  this  truth  on  the  ground  of  the  imaginary  intuition  simply,  but 
because  we  know  that  the  imaginary  lines  exactly  resemble  real  ones,  and 
that  we  may  conclude  from  them  to  real  ones  with  quite  as  much  certainty 
as  we  could  conclude  from  one  real  line  to  another.  The  conclusion,  there- 
fore, is  still  an  induction  from  observation.  And  we  should  not  be  author- 
ized to  substitute  observation  of  the  image  in  our  mind,  for  observation 
of  the  reality,  if  we  had  not  learned  by  long-continued  experience  that  the 
properties  of  the  reality  are  faithfully  represented  in  the  image;  just  as 
we  should  be  scientifically  warranted  in  describing  an  animal  which  we 
have  never  seen,  from  a picture  made  of  it  with  a daguerreotype ; but  not 
until  we  had  learned  by  ample  experience,  that  observation  of  such  a pic- 
ture is  precisely  equivalent  to  observation  of  the  original. 

These  considerations  also  remove  the  objection  arising  from  the  im- 
possibility of  ocularly  following  the  lines  in  their  prolongation  to  infinity. 
For  though,  in  order  actually  to  see  that  two  given  lines  never  meet,  it 
would  be  necessary  to  follow  them  to  infinity;  yet  without  doing  so  we 
may  know  that  if  they  ever  do  meet,  or  if,  after  diverging  from  one  anoth- 
er, they  begin  again  to  approach,  this  must  take  place  not  at  an  infinite, 
but  at  a finite  distance.  Supposing,  therefore,  such  to  be  the  case,  we  can 
transport  ourselves  thither  in  imagination,  and  can  frame  a mental  image 
of  the  appearance  which  one  or  both  of  the  lines  must  present  at  that  point, 
which  we  may  rely  on  as  being  precisely  similar  to  the  reality.  Now, 
whether  we  fix  our  contemplation  upon  this  imaginary  picture,  or  call  to 
mind  the  generalizations  we  have  had  occasion  to  make  from  former  ocular 
observation,  we  learn  by  the  evidence  of  experience,  that  a line  which,  after 
diverging  from  another  straight  line,  begins  to  approach  to  it,  produces 
the  impression  on  our  senses  which  we  describe  by  the  expression,  “ a bent 
line,”  not  by  the  expression,  “ a straight  line.”* 

* Dr.  Whewell  ( Philosophy  of  Discovery,  p.  289)  thinks  it  unreasonable  to  contend  that  we 
know  by  experience,  that  our  idea  of  a line  exactly  resembles  a real  line.  “ It  does  not  ap- 
pear,” he  says,  “ how  we  can  compare  our  ideas  with  the  realities,  since  we  know  the  realities 
only  by  our  ideas.”  We  know  the  realities  by  our  sensations.  Dr.  Whewell  surely  does  not 
hold  the  “doctrine  of  perception  by  means  of  ideas,”  which  Reid  gave  himself  so  much  trou- 
ble to  refute. 


17G 


REASONING. 


The  preceding  argument,  which  is,  to  my  mind  unanswerable,  merges, 
however,  in  a still  more  comprehensive  one,  which  is  stated  most  clearly 
and  conclusively  by  Professor  Bain.  The  psychological  reason  why  ax- 
ioms, and  indeed  many  propositions  not  ordinarily  classed  as  such,  may  be 
learned  from  the  idea  only  without  referring  to  the  fact,  is  that  in  the  proc- 
ess of  acquiring  the  idea  we  have  learned  the  fact.  The  proposition  is 
assented  to  as  soon  as  the  terms  are  understood,  because  in  learning  to  un- 
derstand the  terms  we  have  acquired  the  experience  which  proves  the  propo- 
sition to  be  true.  “We  required,”  says  Mr.  Bain,*  “concrete  experience  in 
the  first  instance,  to  attain  to  the  notion  of  whole  and  part ; but  the  notion, 
once  arrived  at,  implies  that  the  whole  is  greater.  In  fact,  we  could  not 

have  the  notion  without  an  experience  tantamount  to  this  conclusion 

When  we  have  mastered  the  notion  of  straightness,  we  have  also  mastered 
that  aspect  of  it  expressed  by  the  affirmation  that  two  straight  lines  can 
not  inclose  a space.  No  intuitive  or  innate  powers  or  perceptions  are 
needed  in  such  cases We  can  not  have  the  full  meaning  of  Straight- 

ness, without  going  through  a comparison  of  straight  objects  among  them- 
selves, and  with  their  opposites,  bent  or  crooked  objects.  The  result  of 
this  comparison  is,  inter  cilia,  that  straightness  in  two  lines  is  seen  to  be 
incompatible  with  inclosing  a space;  the  inclosure  of  space  involves  crook- 
edness in  at  least  one  of  the  lines.”  And  similarly,  in  the  case  of  every 
first  principle,!  “ the  same  knowledge  that  makes  it  understood,  suffices  to 
verify  it.”  The  more  this  observation  is  considered  the  more  (I  am  con- 
vinced) it  will  be  felt  to  go  to  the  very  root  of  the  controversy. 

§ 6.  The  first  of  the  two  arguments  in  support  of  the  theory  that  axioms 
are  a priori  truths,  having,  I think,  been  sufficiently  answered ; I proceed 
to  the  second,  which  is  usually  the  most  relied  on.  Axioms  (it  is  asserted) 

If  Dr.  Whewell  doubts  whether  we  compare  our  ideas  with  the  corresponding  sensations, 
and  assume  that  they  resemble,  let  me  ask  on  what  evidence  do  we  judge  that  a portrait  of  a 
person  not  present  is  like  the  original.  Surely  because  it  is  like  our  idea,  or  mental  image  of 
the  person,  and  because  our  idea  is  like  the  man  himself. 

Dr.  Whewell  also  says,  that  it  does  not  appear  why  this  resemblance  of  ideas  to  the  sensa- 
tions of  which  they  are  copies,  should  be  spoken  of  as  if  it  were  a peculiarity  of  one  class  of 
ideas,  those  of  space.  My  reply  is,  that  I do  not  so  speak  of  it.  The  peculiarity  I contend 
for  is  only  one  of  degree.  All  our  ideas  of  sensation  of  course  resemble  the  corresponding 
sensations,  but  they  do  so  with  very  different  degrees  of  exactness  and  of  reliability.  No  one, 
I presume,  can  recall  in  imagination  a color  or  an  odor  with  the  same  distinctness  and  ac- 
curacy with  which  almost  every  one  can  mentally  reproduce  an  image  of  a straight  line  or  a 
triangle.  To  the  extent,  however,  of  their  capabilities  of  accuracy,  our  recollections  of  colors 
or  of  odors  may  serve  as  subjects  of  experimentation,  as  well  as  those  of  lines  and  spaces,  and 
may  yield  conclusions  which  will  be  true  of  their  external  prototypes.  A person  in  whom, 
either  from  natural  gift  or  from  cultivation,  the  impressions  of  color  were  peculiarly  vivid  and 
distinct,  if  asked  which  of  two  blue  flowers  was  of  the  darkest  tinge,  though  he  might  never 
have  compared  the  two,  or  even  looked  at  them  together,  might  be  able  to  give  a confident 
answer  on  the  faith  of  his  distinct  recollection  of  the  colors ; that  is,  he  might  examine  his 
mental  pictures,  and  find  there  a property  of  the  outward  objects.  But  in  hardly  any  case 
except  that  of  simple  geometrical  forms,  could  this  be  done  by  mankind  generally,  with  a de- 
gree of  assurance  equal  to  that  which  is  given  by  a contemplation  of  the  objects  themselves. 
Persons  differ  most  widely  in  the  precision  of  their  recollection,  even  of  forms : one  person, 
when  he  has  looked  any  one  in  the  face  for  half  a minute,  can  draw  an  accurate  likeness  of 
him  from  memory ; another  may  have  seen  him  every  day  for  six  months,  and  hardly  know 
whether  his  nose  is  long  or  short.  But  every  body  has  a perfectly  distinct  mental  image  of  a 
Straight  line,  a circle,  or  a rectangle.  And  every  one  concludes  confidently  from  these  mental 
images  to  the  corresponding  outward  things.  The  truth  is,  that  we  may,  and  continually  do, 
study  nature  in  our  recollections,  when  the  objects  themselves  are  absent ; and  in  the  case  of 
geometrical  forms  we  can  perfectly,  but  in  most  other  cases  only  imperfectly,  trust  our  recol- 
lections. * Logic,  i.,  222.  t Ibid.,  226. 


DEMONSTRATION,  AND  NECESSARY  TRUTHS. 


m 

are  conceived  by  us  not  only  as  true,  but  as  universally  and  necessarily 
true.  Now,  experience  can  not  possibly  give  to  any  proposition  this  char- 
acter. I may  have  seen  snow  a hundred  times,  and  may  have  seen  that  it 
was  white,  but  this  can  not  give  me  entire  assurance  even  that  all  snow  is 
white ; much  less  that  snow  must  be  white.  “ However  many  instances 
we  may  have  observed  of  the  truth  of  a proposition,  there  is  nothing  to 
assure  us  that  the  next  case  shall  not  be  an  exception  to  the  rule.  If  it 
be  strictly  true  that  every  ruminant  animal  yet  known  has  cloven  hoofs, 
we  still  can  not  be  sure  that  some  creature  will  not  hereafter  be  discov- 
ered which  has  the  first  of  these  attributes,  without  having  the  other 

Experience  must  always  consist  of  a limited  number  of  observations;  and, 
however  numerous  these  may  be,  they  can  show  nothing  with  regard  to 
the  infinite  number  of  cases  in  which  the  experiment  has  not  been  made.” 
Besides,  Axioms  are  not  only  universal,  they  are  also  necessary.  Now  “ ex- 
perience can  not  offer  the  smallest  ground  for  the  necessity  of  a proposi- 
tion. Sire  can  observe  and  record  what  has  happened;  but  she  can  not 
find,  in  any  case,  or  in  any  accumulation  of  cases,  any  reason  for  what  must 
happen.  She  may  see  objects  side  by  side;  but  she  can  not  see  a reason 
why  they  must  ever  be  side  by  side.  She  finds  certain  events  to  occur  in 
succession  ; but  the  succession  supplies,  in  its  occurrence,  no  reason  for  its 
recurrence.  She  contemplates  external  objects;  but  she  can  not  detect  any 
internal  bond,  which  indissolubly  connects  the  future  with  the  past,  the  pos- 
sible with  the  real.  To  learn  a proposition  by  experience,  and  to  see  it  to 
be  necessarily  true,  are  two  altogether  different  processes  of  thought.”* 
And  Dr.  Whewell  adds,  “ If  any  one  does  not  clearly  comprehend  this  dis- 
tinction of  necessary  and  contingent  truths,  he  will  not  be  able  to  go  along 
with  us  in  our  researches  into  the  foundations  of  human  knowledge;  nor, 
indeed,  to  pursue  with  success  any  speculation  on  the  subject.”f 

In  the  following  passage,  we  are  told  what  the  distinction  is,  the  non- 
recognition of  which  incurs  this  denunciation.  “ Necessary  truths  are 
those  in  which  we  not  only  learn  that  the  proposition  is  true,  but  see  that 
it  must  be  true ; in  which  the  negation  of  the  truth  is  not  only  false,  but 
impossible ; in  which  we  can  not,  even  by  an  effort  of  imagination,  or  in 
a supposition,  conceive  the  reverse  of  that  which  is  asserted.  That  there 
are  such  truths  can  not  be  doubted.  We  may  take,  for  example,  all  rela- 
tions of  number.  Three  and  Two  added  together  make  Five.  We  can 
not  conceive  it  to  be  otherwise.  We  can  not,  by  any  freak  of  thought, 
imagine  Three  and  Two  to  make  Seven.”J 

Although  Dr.  Whewell  has  naturally  and  properly  employed  a variety 
of  phrases  to  bring  his  meaning  more  forcibly  home,  he  would,  I presume, 
allow  that  they  are  all  equivalent;  and  that  what  he  means  by  a necessary 
truth,  would  be  sufficiently  defined,  a proposition  the  negation  of  which  is 
not  only  false  but  inconceivable.  I am  unable  to  find  in  any  of  his  expres- 
sions, turn  them  what  way  you  will,  a meaning  beyond  this,  and  I do  not 
believe  he  would  contend  that  they  mean  any  thing  more. 

This,  therefore,  is  the  principle  asserted : that  propositions,  the  negation 
of  which  is  inconceivable,  or  in  other  words,  which  we  can  not  figure  to 
ourselves  as  being  false,  must  rest  on  evidence  of  a higher  aud  more  cogent 
description  than  any  which  experience  can  afford. 

Now  I can  not  but  wonder  that  so  much  stress  should  be  laid  on  the  cir- 
cumstance of  inconceivableness,  when  there  is  such  ample  experience  to 

* History  of  Scientific  Ideas,  i.,  65-67.  t Ibid.,  i.,  60.  t Ibid.,  58,  59. 

12 


178 


REASONING. 


show,  that  our  capacity  or  incapacity  of  conceiving  a thing  has  very  little 
to  do  with  the  possibility  of  the  thing  in  itself;  but  is  in  truth  very  much 
an  affair  of  accident,  and  depends  on  the  past  history  and  habits  of  our 
own  minds.  There  is  no  more  generally  acknowledged  fact  in  human  na- 
ture, than  the  extreme  difficulty  at  first  felt  in  conceiving  any  thing  as  pos- 
sible, which  is  in  contradiction  to  long  established  and  familiar  experience; 
or  even  to  old  familiar  habits  of  thought.  And  this  difficulty  is  a necessary 
result  of  the  fundamental  laws  of  the  human  mind.  When  we  have  often 
seen  and  thought  of  two  things  together,  and  have  never  in  any  one  in- 
stance either  seen  or  thought  of  them  separately,  there  is  by  the  primary 
law  of  association  an  increasing  difficulty,  which  may  in  the  end  become 
insuperable,  of  conceiving  the  two  things  apart.  This  is  most  of  all  con- 
spicuous in  uneducated  persons,  who  are  in  general  utterly  unable  to  sepa- 
rate any  two  ideas  which  have  once  become  firmly  associated  in  their 
minds;  and  if  persons  of  cultivated  intellect  have  any  advantage  on  the 
point,  it  is  only  because,  having  seen  and  heard  and  read  more,  and  being- 
more  accustomed  to  exercise  their  imagination,  they  have  experienced  then- 
sensations  and  thoughts  in  more  varied  combinations,  and  have  been  pre- 
vented from  forming  many  of  these  inseparable  associations.  But  this  ad- 
vantage has  necessarily  its  limits.  The  most  practiced  intellect  is  not  ex- 
empt from  the  universal  laws  of  our  conceptive  faculty.  If  daily  habit 
presents  to  any  one  for  a long  period  two  facts  in  combination,  and  if  he  is 
not  led  during  that  period  either  by  accident  or  by  his  voluntary  mental 
operations  to  think  of  them  apart,  he  will  probably  in  time  become  incapa- 
ble of  doing  so  even  by  the  strongest  effort;  and  the  supposition  that  the 
two  facts  can  be  separated  in  nature,  will  at  last  present  itself  to  his  mind 
with  all  the  characters  of  an  inconceivable  phenomenon.*  There  are  re- 
markable instances  of  this  in  the  history  of  science : instances  in  which  the 
most  instructed  men  rejected  as  impossible,  because  inconceivable,  things 
which  their  posterity,  by  earlier  practice  and  longer  perseverance  in  the  at- 
tempt, found  it  quite  easy  to  conceive,  and  which  every  body  now  knows 
to  be  true.  There  was  a time  when  men  of  the  most  cultivated  intellects, 
and  the  most  emancipated  from  the  dominion  of  early  prejudice,  could  not 
credit  the  existence  of  antipodes;  were  unable  to  conceive,  in  opposition 
to  old  association,  the  force  of  gravity  acting  upward  instead  of  downward. 
The  Cartesians  long  rejected  the  Newtonian  doctrine  of  the  gravitation  of 
all  bodies  toward  one  another,  on  the  faith  of  a general  proposition,  the  re- 
verse of  which  seemed  to  them  to  be  inconceivable — the  proposition  that  a 
body  can  not  act  where  it  is  not.  All  the  cumbrous  machinery  of  imagi- 
nary vortices,  assumed  without  the  smallest  particle  of  evidence,  appeared 
to  these  philosophers  a more  rational  mode  of  explaining  the  heavenly  mo- 
tions, than  one  which  involved  what  seemed  to  them  so  great  an  absurdity. f 


* “If  all  mankind  had  spoken  one  language,  we  can  not  doubt  that  there  would  have  been 
a powerful,  perhaps  a universal,  school  of  philosophers,  who  woidd  have  believed  in  the  in- 
herent connection  between  names  and  things,  who  would  have  taken  the  sound  man  to  be  the 
mode  of  agitating  the  air  which  is  essentially  communicative  of  the  ideas  of  reason,  cookery, 
bipedality,  etc.” — De  Morgan,  Formal  Logic,  p.  246. 

t It  would  be  difficult  to  name  a man  more  remarkable  at  once  for  the  greatness  and  the 
wide  range  of  his  mental  accomplishments,  than  Leibnitz.  Yet  this  eminent  man  gave  as  a 
reason  for  rejecting  Newton's  scheme  of  the  solar  system,  that  God  could  not  make  a body  re- 
volve round  a distant  centre,  unless  either  by  some  impelling  mechanism,  or  by  miracle: 
“ Tout  ce  qui  n’est  pas  explicable,”  says  he  in  a letter  to  the  Abbe'  Conti,  “ par  la  nature  des 
creatures,  est  miraculeux.  II  ne  suffit  pas  de  dire:  Dieu  a fait  une  telle  loi  de  nature  ; done 
la  chose  est  naturelle.  II  faut  que  la  loi  soit  exe'cutable  par  les  natures  des  creatures.  Si 


DEMONSTRATION,  AND  NECESSARY  TRUTHS. 


179 


And  they  no  doubt  found  it  as  impossible  to  conceive  that  a body  should 
act  upon  the  earth  from  the  distance  of  the  sun  or  moon,  as  we  find  it  to 
conceive  an  end  to  space  or  time,  or  two  straight  lines  inclosing  a space. 
Newton  himself  had  not  been  able  to  realize  the  conception,  or  we  should 
not  have  had  his  hypothesis  of  a subtle  ether,  the  occult  cause  of  gravita- 
tion ; and  his  writings  prove,  that  though  he  deemed  the  particular  nature 
of  the  intermediate  agency  a matter  of  conjecture,  the  necessity  of  some 
such  agency  appeared  to  him  indubitable. 

If,  then,  it  be  so  natural  to  the  human  mind,  even  in  a high  state  of  cul- 
ture, to  be  incapable  of  conceiving,  and  on  that  ground  to  believe  impossi- 
ble, what  is  afterward  not  only  found  to  be  conceivable  but  proved  to  be 
true ; what  wonder  if  in  cases  where  the  association  is  still  older,  more  con- 
firmed, and  more  familiar,  and  in  which  nothing  ever  occurs  to  shake  our 
conviction,  or  even  suggest  to  us  any  conception  at  variance  with  the  asso- 
ciation, the  acquired  incapacity  should  continue,  and  be  mistaken  for  a nat- 
ural incapacity  ? It  is  true,  our  experience  of  the  varieties  in  nature  ena- 
bles us,  within  certain  limits,  to  conceive  other  varieties  analogous  to  them. 
We  can  conceive  the  sun  or  moon  falling ; for  though  we  never  saw  them 
fall,  nor  ever,  perhaps,  imagined  them  falling,  we  have  seen  so  many  other 
things  fall,  that  we  have  innumerable  familiar  analogies  to  assist  the  con- 
ception ; which,  after  all,  we  should  probably  have  some  difficulty  in  fram- 
ing, were  we  not  well  accustomed  to  see  the  sun  and  moon  move  (or  ap- 
pear to  move),  so  that  we  are  only  called  upon  to  conceive  a slight  change 
in  the  direction  of  motion,  a circumstance  familiar  to  our  experience.  But 
when  experience  affords  no  model  on  which  to  shape  the  new  conception, 
how  is  it  possible  for  us  to  form  it  ? How,  for  example,  can  we  imagine 
an  end  to  space  or  time?  We  never  saw  any  object  without  something 
beyond  it,  nor  experienced  any  feeling  without  something  following  it. 
When,  therefore,  we  attempt  to  conceive  the  last  point  of  space,  we  have 
the  idea  irresistibly  raised  of  other  points  beyond  it.  When  we  try  to  im- 
agine the  last-  instant  of  time,  we  can  not  help  conceiving  another  instant 
after  it.  Nor  is  there  any  necessity  to  assume,  as  is  done  by  a modern 
school  of  metaphysicians,  a peculiar  fundamental  law  of  the  mind  to  ac- 
count for  the  feeling  of  infinity  inherent  in  our  conceptions  of  space  and 
time;  that  apparent  infinity  is  sufficiently  accounted  for  by  simpler  and 
universally  acknowledged  laws. 

Now,  in  the  case  of  a geometrical  axiom,  such,  for  example,  as  that  two 
straight  lines  can  not  inclose  a space — a truth  which  is  testified  to  us  by 
our  very  earliest  impressions  of  the  external  world — how  is  it  possible 
(whether  those  external  impressions  be  or  be  not  the  ground  of  our  belief) 
that  the  reverse  of  the  proposition  could  be  otherwise  than  inconceivable 
to  us?  What  analogy  have  we,  what  similar  order  of  facts  in  any  other 
branch  of  our  experience,  to  facilitate  to  us  the  conception  of  two  straight 
lines  inclosing  a space?  Nor  is  even  this  all.  I have  already  called  atten- 
tion to  the  peculiar  property  of  our  impressions  of  form,  that  the  ideas  or 
mental  images  exactly  resemble  their  prototypes,  and  adequately  represent 
them  for  the  purposes  of  scientific  observation.  From  this,  and  from  the 
intuitive  character  of  the  observation,  which  in  this  case  reduces  itself  to 

Dieu  donnait  cette  loi,  par  exemple,  a un  corps  libre,  de  tourner  a l’entour  d'un  certain  centre, 
il  faudrait  ou  qu'il  y joignit  d'autres  corps  qui  par  leur  impulsion  Vobligeassent  de  rester  tou- 
jours  dans  son  orbits  circulaire,  ou  qu'il  mit  un  ange  a ses  trousses,  ou  enjin  il  faudrait  qu'il  y 
concourut  extraordinairement ; car  naturellement  il  s’ecartera  par  la  tangente.” — Works  of 
Leibnitz,  ed.  Dntens,  iii.,  446. 


ISO 


REASONING. 


simple  inspection,  we  can  not  so  much  as  call  up  in  our  imagination  two 
straight  lines,  in  order  to  attempt  to  conceive  them  inclosing  a space,  with- 
out by  that  very  act  repeating  the  scientific  experiment  which  establishes 
the  contrary.  Will  it  really  be  contended  that  the  inconceivableness  of  the 
thing,  in  such  circumstances,  proves  any  thing  against  the  experimental  or- 
igin of  the  conviction  ? Is  it  not  clear  that  in  whichever  mode  our  belief 
in  the  proposition  may  have  originated,  the  impossibility  of  our  conceiving 
the  negative  of  it  must,  on  either  hypothesis,  be  the  same  ? As,  then,  Dr. 
Whewell  exhorts  those  who  have  any  difficulty  in  recognizing  the  distinc- 
tion held  by  him  between  necessary  and  contingent  truths,  to  study  geom- 
etry— a condition  which  I can  assure  him  I have  conscientiously  fulfilled — 
I,  in  return,  with  equal  confidence,  exhort  those  who  agree  with  him,  to 
study  the  general  laws  of  association;  being  convinced  that  nothing  more 
is  requisite  than  a moderate  familiarity  with  those  laws,  to  dispel  the  illu-- 
sion  which  ascribes  a peculiar  necessity  to  our  earliest  inductions  from  ex- 
perience, and  measures  the  possibility  of  things  in  themselves,  by  the  hu- 
man capacity  of  conceiving  them. 

I hope  to  be  pardoned  for  adding,  that  Dr.  Whewell  himself  has  both 
confirmed  by  his  testimony  the  effect  of  habitual  association  in  giving  to 
an  experimental  truth  the  appearance  of  a necessary  one,  and  afforded  a 
striking  instance  of  that  remarkable  law  in  his  own  person.  In  his  Philos- 
ophy  of  the  Inductive  Sciences  he  continually  asserts,  that  propositions 
which  not  only  are  not  self-evident,  but  which  we  know  to  have  been  dis- 
covered gradually,  and  by  great  efforts  of  genius  and  patience,  have,  wffien 
once  established,  appeared  so  self-evident  that,  but  for  historical  proof,  it 
would  have  been  impossible  to  conceive  that  they  had  not  been  recognized 
from  the  first  by  all  persons  in  a sound  state  of  their  faculties.  “We  now 
despise  those  who,  in  the  Copernican  controversy,  could  not  conceive  the 
apparent  motion  of  the  sun  on  the  heliocentric  hypothesis ; or  those  who, 
iu  opposition  to  Galileo,  thought  that  a uniform  force  might  be  that  which 
generated  a velocity  proportional  to  the  space;  or  those  who  held  there 
was  something  absurd  in  Newton’s  doctrine  of  the  different  refrangibility 
of  differently  colored  rays;  or  those  who  imagined  that  when  elements 
combine,  their  sensible  qualities  must  be  manifest  in  the  compound;  or 
those  who  were  reluctant  to  give  up  the  distinction  of  vegetables  into  herbs, 
shrubs,  and  trees.  We  can  not  help  thinking  that  men  must  have  been 
singularly  dull  of  comprehension,  to  find  a difficulty  in  admitting  what  is 
to  us  so  plain  and  simple.  We  have  a latent  persuasion  that  we  in  their 
place  should  have  been  wiser  and  more  clear-sighted ; that  we  should  have 
taken  the  right  side,  and  given  our  assent  at  once  to  the  truth.  Yet  in  re- 
ality such  a persuasion  is  a mere  delusion.  The  persons  who,  in  such  in- 
stances as  the  above,  were  on  the  losing  side,  were  very  far,  in  most  cases, 
from  being  persons  more  prejudiced,  or  stupid,  or  narrow-minded,  than  the 
greater  part  of  mankind  now  are;  and  the  cause  for  which  they  fought 
was  far  from  being  a manifestly  bad  one,  till  it  had  been  so  decided  by  the 

result  of  the  war So  complete  has  been  the  victory  of  truth  in  most 

of  these  instances,  that  at  present  we  can  hardly  imagine  the  struggle  to 
have  been  necessary.  The  very  essence  of  these  triumphs  is,  that  they  lead 
us  to  regard  the  views  we  reject  as  not  only  false  hut  inconceivable 

This  last  proposition  is  precisely  what  I contend  for ; and  I ask  no  more, 
iu  order  to  overthrow  the  whole  theory  of  its  author  on  the  nature  of  the 

* Novum  Organum  Renovatum,  pp.  32,  33. 


DEMONSTRATION,  AND  NECESSARY  TRUTHS. 


181 


evidence  of  axioms.  For  what  is  that  theory?  That  the  truth  of  axioms 
can  not  have  been  learned  from  experience,  because  their  falsity  is  incon- 
ceivable. But  Dr.  Whewell  himself  says,  that  we  are  continually  led,  by 
the  natural  progress  of  thought,  to  regard  as  inconceivable  what  our  fore- 
fathers not  only  conceived  but  believed,  nay  even  (he  might  have  added) 
were  unable  to  conceive  the  reverse  of.  He  can  not  intend  to  justify  this 
mode  of  thought : he  can  not  mean  to  say,  that  we  can  be  right  in  regard- 
ing as  inconceivable  what  others  have  conceived,  and  as  self-evident  what 
to  others  did  not  appear  evident  at  all.  After  so  complete  an  admis- 
sion that  inconceivableness  is  an  accidental  thing,  not  inherent  in  the  phe- 
nomenon itself,  but  dependent  on  the  mental  history  of  the  person  who 
tries  to  conceive  it,  how  can  he  ever  call  upon  us  to  reject  a proposition  as 
impossible  on  no  other  ground  than  its  inconceivableness?  Yet  he  not 
only  does  so,  but  has  unintentionally  afforded  some  of  the  most  remarkable 
examples  which  can  be  cited  of  the  very  illusion  which  he  has  himself  so 
clearly  pointed  out.  I select  as  specimens,  his  remarks  on  the  evidence  of 
the  three  laws  of  motion,  and  of  the  atomic  theory. 

With  respect  to  the  laws  of  motion,  Dr.  Whewell  says:  “No  one  can 
doubt  that,  in  historical  fact,  these  laws  were  collected  from  experience. 
That  such  is  the  case,  is  no  matter  of  conjecture.  We  know  the  time,  the 
persons,  the  circumstances,  belonging  to  each  step  of  each  discovery.”* 
After  this  testimony,  to  adduce  evidence  of  the  fact  would  be  superfluous. 
And  not  only  were  these  laws  by  no  means  intuitively  evident,  but  some 
of  them  were  originally  paradoxes.  The  first  law  was  especially  so.  That 
a body,  once  in  motion,  would  continue  forever  to  move  in  the  same  direc- 
tion with  undiminished  velocity  unless  acted  upon  by  some  new  force,  was 
a proposition  which  mankind  found  for  a long  time  the  greatest  difficulty 
in  crediting.  It  stood  opposed  to  apparent  experience  of  the  most  familiar 
kind,  which  taught  that  it  was  the  nature  of  motion  to  abate  gradually, 
and  at  last  terminate  of  itself.  Yet  when  once  the  contrary  doctrine  was 
firmly  established,  mathematicians,  as  Dr.  Whewell  observes,  speedily  be- 
gan to  believe  that  laws,  thus  contradictory  to  first  appearances,  and  which, 
even  after  full  proof  had  been  obtained,  it  had  required  generations  to  ren- 
der familiar  to  the  minds  of  the  scientific  world,  were  under  “ a demonstra- 
ble necessity,  compelling  them  to  be  such  as  they  are  and  no  other;”  and 
he  himself,  though  not  venturing  “absolutely  to  pronounce”  that  all  these 
laws  “ can  be  rigorously  traced  to  an  absolute  necessity  in  the  nature  of 
things,”!  does  actually  so  think  of  the  law  just  mentioned;  of  which  he 
says:  “Though  the  discovery  of  the  first  law  of  motion  was  made,  histor- 
ically speaking,  by  means  of  experiment,  we  have  now  attained  a point  of 
view  in  which  we  see  that  it  might  have  been  certainly  known  to  be  true, 
independently  of  experience.”!;  Can  there  be  a more  striking  exemplifi- 
cation than  is  here  afforded,  of  the  effect  of  association  which  we  have'de- 
seribed?  Philosophers,  for  generations,  have  the  most  extraordinary  diffi- 
culty in  putting  certain  ideas  together ; they  at  last  succeed  in  doing  so ; 
and  after  a sufficient  repetition  of  the  process,  they  first  fancy  a natural 
bond  between  the  ideas,  then  experience  a growing  difficulty,  which  at  last, 
by  the  continuation  of  the  same  progress,  becomes  an  impossibility,  of  sev- 
ering them  from  one  another.  If  such  be  the  progress  of  an  experimental 
conviction  of  which  the  date  is  of  yesterday,  and  which  is  in  opposition  to 
first  appearances,  how  must  it  fare  with  those  which  are  conformable  to 


History  of  Scientific  Ideas,  i.,  264. 


t Ibid.,  i.,  263. 


f Ibid.,  240. 


1S2 


REASONING. 


appearances  familiar  from  the  first  dawn  of  intelligence,  and  of  the  conclu- 
siveness of  which,  from  the  earliest  records  of  human  thought,  no  skeptic 
has  suggested  even  a momentary  doubt? 

The  other  instance  which  I shall  quote  is  a truly  astonishing  one,  and 
may  be  called  the  reductio  ad  absurdum  of  the  theory  of  inconceivableness. 
Speaking  of  the  laws  of  chemical  composition,  Dr.  Whewell  says:*  “That 
they  could  never  have  been  clearly  understood,  and  therefore  never  firmly 
established,  without  laborious  and  exact  experiments,  is  certain ; but  yet 
we  may  venture  to  say,  that  being  once  known,  they  possess  an  evidence 
beyond  that  of  mere  experiment.  For  how  hi  fact  can  we  conceive  combi- 
nations, otherwise  than  as  definite  in  kind  and  quality?  If  we  were  to 
suppose  each  element  ready  to  combine  with  any  other  indifferently,  and 
indifferently  in  any  quantity,  we  should  have  a world  in  which  all  would  be 
confusion  and  indefiniteness.  There  would  be  no  fixed  kinds  of  bodies. 
Salts,  and  stones,  and  ores,  would  approach  to  and  graduate  into  each  other 
by  insensible  degrees.  Instead  of  this,  we  know  that  the  world  consists  of* 
bodies  distinguishable  from  each  other  by  definite  differences,  capable  of 
being  classified  and  named,  and  of  having  general  propositions  asserted 
concerning  them.  And  as  ice  can  not  conceive  a world  in  which  this 
should  not  be  the  case,  it  would  appear  that  we  can  not  conceive  a state  of 
things  in  which  the  laws  of  the  combination  of  elements  should  not  be  of 
that  definite  and  measured  kind  which  we  have  above  asserted.” 

That  a philosopher  of  Dr.  Whcwell’s  eminence  should  gravely  assert 
that  we  can  not  conceive  a world  in  which  the  simple  elements  should  com- 
bine in  other  than  definite  proportions;  that  by  dint  of  meditating  on  a 
scientific  truth,  the  original  discoverer  of  which  was  still  living,  he  should 
have  rendered  the  association  in  his  own  mind  between  the  idea  of  combi- 
nation and  that  of  constant  proportions  so  familiar  and  intimate  as  to  be 
unable  to  conceive  the  one  fact  without  the  other;  is  so  signal  an  instance 
of  the  mental  law  for  which  I am  contending,  that  one  word  more  in  illus- 
tration must  be  superfluous. 

In  the  latest  and  most  complete  elaboration  of  his  metaphysical  system 
(the  Philosophy  of  Discovery'),  as  well  as  in  the  earlier  discourse  on  the 
Fundamental  Antithesis  of  Philosophy,  reprinted  as  an  appendix  to  that 
work,  Dr.  Whewell,  while  very  candidly  admitting  that  his  language  was 
open  to  misconception,  disclaims  having  intended  to  say  that  mankind  in 
general  can  now  perceive  the  law  of  definite  proportions  in  chemical  com- 
bination to  be  a necessary  truth.  All  he  meant  was  that  philosophical 
chemists  in  a future  generation  may  possibly  see  this.  “Some  truths  may 
be  seen  by  intuition,  but  yet  the  intuition  of  them  may  be  a rare  and  a dif- 
ficult attainment.”!  And  he  explains  that  the  inconceivableness  which,  ac- 
cording to  his  theory,  is  the  test  of  axioms,  “ depends  entirely  upon  the 
clearness  of  the  Ideas  which  the  axioms  involve.  So  long  as  those  ideas 
are  vague  and  indistinct,  the  contrary  of  an  axiom  may  be  assented  to, 
though  it  can  not  be  distinctly  conceived.  It  may  be  assented  to,  not  be- 
cause it  is  possible,  but  because  we  do  not  see  clearly  what  is  possible.  To 
a person  who  is  only  beginning'to  think  geometrically,  there  may  appear 
nothing  absurd  in  the  assertion  that  two  straight  lines  may  inclose  a space. 
And  in  the  same  manner,  to  a person  who  is  only  beginning  to  think  of 
mechanical  truths,  it  may  not  appear  to  be  absurd,  that  in  mechanical  proc- 
esses, Reaction  should  be  greater  or  less  than  Action ; and  so,  again,  to  a 


Hist.  Scientific  Ideas , ii. , 25,  26. 


t Phil,  of  Disc.,  p.  339. 


DEMONSTRATION,  AND  NECESSARY  TRUTHS. 


183 


person  who  has  not  thought  steadily  about  Substance,  it  may  not  appear 
inconceivable,  that  by  chemical  operations,  we  should  generate  new  matter, 
or  destroy  matter  which  already  exists.”*  Necessary  truths,  therefore,  are 
not  those  of  which  we  can  not  conceive,  but  “those  of  which  we  can  not 
distinctly  conceive,  the  contrary.”!  So  long  as  our  ideas  are  indistinct  al- 
together, we  do  not  know  what  is  or  is  not  capable  of  being  distinctly 
conceived;  but,  by  the  ever  increasing  distinctness  with  which  scientific 
men  apprehend  the  general  conceptions  of  science,  they  in  time  come  to 
perceive  that  there  are  certain  laws  of  nature,  which,  though  historically 
and  as  a matter  of  fact  they  were  learned  from  experience,  we  can  not, 
now  that  we  know  them,  distinctly  conceive  to  be  other  than  they  are-. 

The  account  which  I should  give  of  this  progress  of  the  scientific  mind 
is  somewhat  different.  After  a general  law  of  nature  has  been  ascertained, 
men’s  minds  do  not  at  first  acquire  a complete  facility  of  familiarly  repre- 
senting to  themselves  the  phenomena  of  nature  in  the  character  which  that 
law  assigns  to  them.  The  habit  which  constitutes  the  scientific  cast  of 
mind,  that  of  conceiving  facts  of  all  descriptions  conformably  to  the  laws 
which  regulate  them — phenomena  of  all  descriptions  according  to  the  re- 
lations which  have  been  ascertained  really  to  exist  between  them;  this  hab- 
it, in  the  case  of  newly-discovered  relations,  comes  only  by  degrees.  So 
long  as  it  is  not  thoroughly  formed,  no  necessary  character  is  ascribed  to 
the  new  truth.  But  in  time,  the  philosopher  attains  a state  of  mind  in 
which  his  mental  picture  of  nature  spontaneously  represents  to  him  all  the 
phenomena  with  which  the  new  theory  is  concerned,  in  the  exact  light  in 
which  the  theory  regards  them : all  images  or  conceptions  derived  from 
any  other  theory,  or  from  the  confused  view  of  the  facts  which  is  anterior 
to  any  theory,  having  entirely  disappeared  from  his  mind.  The  mode  of 
representing  facts  which  results  from  the  theory,  has  now  become,  to  his 
faculties,  the  only  natural  mode  of  conceiving  them.  It  is  a known  truth, 
that  a prolonged  habit  of  arranging  phenomena  in  certain  groups,  and  ex- 
plaining them  by  means  of  certain  principles,  makes  any  other  arrangement 
or  explanation  of  these  facts  be  felt  as  unnatural : and  it  may  at  last  be- 
come as  difficult  to  him  to  represent  the  facts  to  himself  in  any  other  mode, 
as  it  often  was,  originally,  to  represent  them  in  that  mode. 

But,  further  (if  the  theory  is  true,  as  we  are  supposing  it  to  be),  any 
other  mode  in  which  he  tries,  or  in  which  he  was  formerly  accustomed, 
to  represent  the  phenomena,  will  be  seen  by  him  to  be  inconsistent  with 
the  facts  that  suggested  the  new  theory — facts  which  now  form  a part  of 
his  mental  picture  of  nature.  And  since  a contradiction  is  always  incon- 
ceivable, his  imagination  rejects  these  false  theories,  and  declares  itself  in- 
capable of  conceiving  them.  Their  inconceivableness  to  him  does  not,  how- 
ever, result  from  any  thing  in  the  theories  themselves,  intrinsically  and  a 
priori  repugnant  to  the  human  faculties  ; it  results  from  the  repugnance 
between  them  and  a portion  of  the  facts;  which  facts  as  long  as  he  did 
not  know,  or  did  not  distinctly  realize  in  his  menial  representations,  the 
false  theory  did  not  appear  other  than  conceivable;  it  becomes  inconceiv- 
able, merely  from  the  fact  that  contradictory  elements  can  not  be  combined 
in  the  same  conception.  Although,  then,  his  real  reason  for  rejecting  theo- 
ries at  variance  with  the  true  one,  is  no  other  than  that  they  clash  with  his 
experience,  he  easily  falls  into  the  belief,  that  he  rejects  them  because  they 
are  inconceivable,  and  that  he  adopts  the  true  theory  because  it  is  self-evi- 
dent, and  does  not  need  the  evidence  of  experience  at  all. 

* Phil,  of  Disc.,  p.  338.  t Ibid.,  p.  468. 


184 


REASONING. 


This  I take  to  be  the  real  and  sufficient  explanation  of  tbe  paradoxical 
truth,  on  which  so  much  stress  is  laid  by  Dr.  Whewell,  that  a scientifically 
cultivated  mind  is  actually,  in  virtue  of  that  cultivation,  unable  to  conceive 
suppositions  which  a common  man  conceives  without  the  smallest  difficul- 
ty. For  there  is  nothing  inconceivable  in  the  suppositions  themselves;  the 
impossibility  is  in  combining  them  with  facts  inconsistent  with  them,  as 
part  of  the  same  mental  picture ; an  obstacle  of  course  only  felt  by  those 
who  know  the  facts,  and  are  able  to  perceive  the  inconsistency.  As  far  as 
the  suppositions  themselves  are  concerned,  in  the  case  of  many  of  Dr.  Whe- 
well’s  necessary  truths  the  negative  of  the  axiom  is,  and  probably  will  be 
as  long  as  the  human  race  lasts,  as  easily  conceivable  as  the  affirmative. 
There  is  no  axiom  (for  example)  to  which  Dr.  Whewell  ascribes  a more 
thorough  character  of  necessity  and  self-evidence,  than  that  of  the  inde- 
structibility of  matter.  That  this  is  a true  law  of  nature  I fully  admit; 
but  I imagine  there  is  no  human  being  to  whom  the  opposite  supposition 
is  inconceivable — who  has  any  difficulty  in  imagining  a portion  of  matter 
annihilated:  inasmuch  as  its  apparent  annihilation,  in  no  respect  distin- 
guishable from  real  by  our  unassisted  senses,  takes  place  every  time  that 
water  dries  up,  or  fuel  is  consumed.  Again,  the  law  that  bodies  combine 
chemically  in  definite  proportions  is  undeniably  true;  but  few  besides  Dr. 
Whewell  have  reached  the  point  which  he  seems  personally  to  have  arrived 
at  (though  he  only  dares  prophesy  similar  success  to  the  multitude  after 
the  lapse  of  generations),  that  of  being  unable  to  conceive  a world  in  which 
the  elements  are  ready  to  combine  with  one  another  “ indifferently  in  any 
quantity  ;”  nor  is  it  likely  that  we  shall  ever  rise  to  this  sublime  height  of 
inability,  so  long  as  all  the  mechanical  mixtures  in  our  planet,  whether  sol- 
id, liquid,  or  aeriform,  exhibit  to  our  daily  observation  the  very  phenomenon 
declared  to  be  inconceivable. 

According  to  Dr.  Whewell,  these  and  similar  laws  of  nature  can  not  be 
drawn  from  experience,  inasmuch  as  they  are,  on  the  contrary,  assumed  in 
the  interpretation  of  experience.  Our  inability  to  “add  to  or  diminish  the 
quantity  of  matter  in  the  world,”  is  a truth  which  “neither  is  nor  can  be 
derived  from  experience;  for  the  experiments  which  we  make  to  verify  it 
presuppose  its  truth When  men  began  to  use  the  balance  in  chem- 

ical analysis,  they  did  not  prove  by  trial,  but  took  for  granted,  as  self-evi- 
dent, that  the  weight  of  the  whole  must  be  found  in  the  a^ereo-ate  weight 
of  the  elements.”*  True,  it  is  assumed ; but,  I apprehend,  no  otherwise 
than  as  all  experimental  inquiry  assumes  provisionally  some  theory  or  hy- 
pothesis, which  is  to  be  finally  held  true  or  not,  according  as  the  experi- 
ments decide.  The  hypothesis  chosen  for  this  purpose  will  naturally  be 
one  which  groups  together  some  considerable  number  of  facts  already 
known.  The  proposition  that  the  material  of  the  world,  as  estimated  by 
weight,  is  neither  increased  nor  diminished  by  any  of  the  processes  of  na- 
ture or  art,  had  many  appearances  in  its  favor  to  begin  with.  It  expressed 
truly  a great  number  of  familiar  facts.  There  were  other  facts  which  it 
had  the  appearance  of  conflicting  with,  and  which  made  its  truth,  as  a 
universal  law  of  nature,  at  first  doubtful.  Because  it  was  doubtful,  exper- 
iments were  devised  to  verify  it.  Men  assumed  its  truth  hypothetically, 
and  proceeded  to  try  whether,  on  more  careful  examination,  the  phenomena 
which  apparently  pointed  to  a different  conclusion,  would  not  be  found  to 
be  consistent  with  it.  This  turned  out  to  be  the  case;  and  from  that  time 


Phil,  of  Disc.,  pp.  472,  473. 


DEMONSTRATION,  and  necessary  truths. 


1S5 


the  doctrine  took  its  place  as  a universal  truth,  but  as  one  proved  to  be 
such  by  experience.  That  the  theory  itself  preceded  the  proof  of  its  truth 
— that  it  had  to  be  conceived  before  it  could  be  proved,  and  in  order  that 
it  might  be  proved — does  not  imply  that  it  was  self-evident,  and  did  not 
need  proof.  Otherwise  all  the  true  theories  in  the  sciences  are  necessary 
and  self-evident;  for  no  one  knows  better  than  Dr.  Whewell  that  they  all 
began  by  being  assumed,  for  the  purpose  of  connecting  them  by  deduc- 
tions with  those  facts  of  experience  on  which,  as  evidence,  they  now  con- 
fessedly rest.* 

* The  Quarterly  Review  for  June,  1841,  contained  an  article  of  great  ability  on  Dr.  Whe- 
well’s  two  great  works  (since  acknowledged  and  reprinted  in  Sir  John  Herschel's  Essays) 
which  maintains,  on  the  subject  of  axioms,  the  doctrine  advanced  in  the  text,  that  they  are 
generalizations  from  experience,  and  supports  that  opinion  by  a line  of  argument  strikingly 
coinciding  with  mine.  When  I state  that  the  whole  of  the  present  chapter. (except  the  last 
four  pages,  added  in  the  fifth  edition)  was  written  before  I had  seen  the  article  (the  greater 
part,  indeed,  before  it  was  published),  it  is  not  my  object  to  occupy  the  reader's  attention  with 
a matter  so  unimportant  as  the  degree  of  originality  which  may  or  may  not  belong  to  any  por- 
tion of  my  own  speculations,  but  to  obtain  for  an  opinion  which  is  opposed  to  reigning  doc- 
trines, the  recommendation  derived  from  a striking  concurrence  of  sentiment  between  two 
inquirers  entirely  independent  of  one  another.  I embrace  the  opportunity  of  citing  from  a 
writer  of  the  extensive  acquirements  in  physical  and  metaphysical  knowledge  and  the  capacity 
of  systematic  thought  which  the  article  evinces,  passages  so  remarkably  in  unison  with  my 
own  views  as  the  following : 

“ The  truths  of  geometry  are  summed  up  and  embodied  in  its  definitions  and  axioms 

Let  us  turn  to  the  axioms,  and  what  do  we  find  ? A string  of  propositions  concerning  mag- 
nitude in  the  abstract,  which  are  equally  true  of  space,  time,  force,  number,  and  every  other 
magnitude  susceptible  of  aggregation  and  subdivision.  Such  propositions,  where  they  are 
not  mere  definitions,  as  some  of  them  are,  carry  their  inductive  origin  on  the  face  of  their 

enunciation Those  which  declare  that  two  straight  lines  can  not  inclose  a space,  and 

that  two  straight  lines  which  cut  one  another  can  not  both  be  parallel  to  a third,  are  in  reality 
the  only  ones  which  express  characteristic  properties  of  space,  and  these  it  will  be  worth  while 
to  consider  more  nearly.  Now  the  only  clear  notion  we  can  form  of  straightness  is  uniform- 
ity of  direction,  for  space  in  its  ultimate  analysis  is  nothing  but  an  assemblage  of  distances 
and  directions.  And  (not  to  dwell  on  the  notion  of  continued  contemplation,  i.  e.,  mental  ex- 
perience, as  included  in  the  very  idea  of  uniformity ; nor  on  that  of  transfer  of  the  contem- 
plating being  from  point  to  point,  and  of  experience,  during  such  transfer,  of  the  homogeneity 
of  the  interval  passed  over)  we  can  not  even  propose  the  proposition  in  an  intelligible  form  to 
any  one  whose  experience  ever  since  he  was  born  has  not  assured  him  of  the  fact.  The  unity 
of  direction,  or  that  we  can  not  march  from  a given  point  by  more  than  one  path  direct  to  the 
same  object,  is  matter  of  practical  experience  long  before  it  can  by  possibility  become  matter 
of  abstract  thought.  We  can  not  attempt  mentally  to  exemplify  the  conditions  of  the  assertion 
in  an  imaginary  case  opposed  to  it,  without  violating  our  habitual  recollection  of  this  experi- 
ence, and  defacing  our  mental  picture  of  space  as  grounded  on  it.  What  but  experience,  we 
may  ask,  can  possibly  assure  us  of  the  homogeneity  of  the  parts  of  distance,  time,  force,  and 
measurable  aggregates  in  general,  on  which  the  truth  of  the  other  axioms  depends  ? As  re- 
gards the  latter  axiom,  after  what  has  been  said  it  must  be  clear  that  the  very  same  course  of 
remarks  equally  applies  to  its  case,  and  that  its  truth  is  quite  as  much  forced  on  the  mind  as 

that  of  the  former  by  daily  and  hourly  experience, including  always,  be  it  observed,  in 

our  notion  of  experience,  that  which  is  gained  by  contemplation  of  the  inward  picture  which  the 
; mind  forms  to  itself  in  any  proposed  case,  or  which  it  arbitrarily  selects  as  an  example — such 
picture,  in  virtue  of  the  extreme  simplicity  of  these  primary  relations,  being  called  up  by  the 
imagination  with  as  much  vividness  and  clearness  as  could  be  done  by  any  external  impression , 
which  is  the  only  meaning  we  can  attach  to  the  word  intuition,  as  applied  to  such  relations .” 

And  again,  of  the  axioms  of  mechanics:  “As  we  admit  no  such  propositions,  other  than 
as  truths  inductively  collected  from  observation,  even  in  geometry  itself,  it  can  hardly  be  ex- 
pected that,  in  a science  of  obviously  contingent  relations,  we  should  acquiesce  in  a contrary 
view.  Let  us  take  one  of  these  axioms  and  examine  its  evidence : for  instance,  that  equal 
forces  perpendicularly  applied  at  the  opposite  ends  of  equal  arms  of  a straight  lever  will  bal- 
ance each  other.  What  but  experience,  we  may  ask,  in  the  first  place,  can  possible  inform  us 
that  a force  so  applied  will  have  any  tendency  to  turn  the  lever  on  its  centre  at  all  ? or  that 
force  can  be  so  transmitted  along  a rigid  line  perpendicular  to  its  direction,  as  to  act  elsewhere 
in  space  than  along  its  own  line  of  action  ? Surely  this  is  so  far  from  being  self-evident  that 


186 


REASONING. 


it  lias  even  a paradoxical  appearance,  which  is  only  to  be  removed  by  giving  our  lever  thick- 
ness, material  composition,  and  molecular  powers.  Again,  we  conclude,  that  the  two  forces, 
being  equal  and  applied  under  precisely  similar  circumstances,  must,  if  they  exert  any  effort 
at  all  to  turn  the  lever,  exert  equal  and  opposite  efforts  : but  what  a priori  reasoning  can  pos- 
sibly assure  us  that  they  do  act  under  precisely  similar  circumstances  ? that  points  which  dif- 
fer in  place  are  similarly  circumstanced  as  regards  the  exertion  of  force?  that  universal  space 
may  not  have  relations  to  universal  force — or,  at  all  events,  that  the  organization  of  the  ma- 
terial universe  may  not  be  such  as  to  place  that  portion  of  space  occupied  by  it  in  such  rela- 
tions to  the  forces  exerted  in  it,  as  may  invalidate  the  absolute  similarity  of  circumstances  as- 
sumed ? Or  we  may  argue,  what  have  we  to  do  with  the  notion  of  angular  movement  in  the 
lever  at  all  ? The  case  is  one  of  rest,  and  of  quiescent  destruction  of  force  by  force.  Now 
how  is  this  destruction  effected  ? Assuredly  by  the  counter-pressure  which  supports  the  ful- 
crum. But  would  not  this  destruction  equally  arise,  and  by  the  same  amount  of  counteract- 
ing force,  if  each  force  simply  pressed  its  own  half  of  the  lever  against  the  fulcrum  ? And 
what  can  assure  us  that  it  is  not  so,  except  removal  of  one  or  other  force,  and  consequent  tilt- 
ing of  the  lever?  The  other  fundamental  axiom  of  statics,  that  the  pressure  on  the  point  of 

support  is  the  sum  of  the  weights is  merely  a scientific  transformation  and  more  refined 

mode  of  stating  a coarse  and  obvious  result  of  universal  experience,  viz.,  that  t he  weight  of  a 
rigid  body  is  the  same,  handle  it  or  suspend  it  in  what  position  or  by  what  point  we  will,  and 
that  whatever  sustains  it  sustains  its  total  weight.  Assuredly,  as  Mr.  Whewell  justly  remarks, 
‘No  one  probably  ever  made  a trial  for  the  purpose  of  showing  that  the  pressure  on  the  sup- 
port is  equal  to  the  sum  of  the  weights.’ But  it  is  precisely  because  in  every  actiun 

of  his  life  from  earliest  infancy  he  has  been  continually  making  the  trial,  and  seeing  it  made 
by  every  other  living  being  about  him,  that  he  never  dreams  of  staking  its  result  on  one  addi- 
tional attempt  made  with  scientific  accuracy.  This  would  he  as  if  a man  should  resolve  to 
decide  by  experiment  whether  his  eyes  were  useful  for  the  purpose  of  seeing,  by  hermetically 
sealing  himself  up  for  half  an  hour  in  a metal  case.” 

On  the  “paradox  of  universal  propositions  obtained  by  experience,”  the  same  writer  says: 
“If  there  be  necessary  and  universal  truths  expressible  in  propositions  of  axiomatic  simplicity 
and  obviousness,  and  having  for  their  subject-matter  the  elements  of  all  our  experience  and 
all  our  knowledge,  surely  these  are  the  truths  which,  if  experience  suggest  to  us  any  truths  at 
all,  it  ought  to  suggest  most  readily,  clearly,  and  unceasingly.  If  it  were  a truth,  universal 
and  necessary,  that  a net  is  spread  over  the  whole  surface  of  every  planetary  globe,  we  should 
not  travel  far  on  our  own  without  getting  entangled  in  its  meshes,  and  making  the  necessity 
of  some  means  of  extrication  an  axiom  of  locomotion There  is,  therefore,  nothing  par- 

adoxical, but  the  reverse,  in  our  being  led  by  observation  to  a recognition  of  such  truths,  as 
general  propositions,  co-extensive  at  least  with  all  human  experience.  That  they  pervade  all 
the  objects  of  experience,  must  insure  their  continual  suggestion  by  experience;  that  they  are 
true,  must  insure  that  consistency  of  suggestion,  that  iteration  of  uncontradicted  assertion, 
which  commands  implicit  assent,  and  removes  all  occasion  of  exception  ; that  they  are  simple, 
and  admit  of  no  misunderstanding,  must  secure  their  admission  by  every  mind.” 

“A  truth,  necessary  and  universal,  relative  to  any  object  of  our  knowledge,  must  verify  it- 
self in  every  instance  where  that  object  is  before  our  contemplation,  and  if  at  the  same  time  it 
be  simple  and  intelligible,  its  verification  must  be  obvious.  The  sentiment  of  such  a truth 
can  not,  therefore,  but  be  present  to  our  minds  whenever  that  object  is  contemplated,  and  must 
therefore  make  a part  of  the  mental  picture  or  idea  of  that  object  which  ive  may  on  any  occa- 
sion summon  before  our  imagination All  propositions,  therefore,  become  not  only  untrue 

but  inconceivable,  if axioms  be  violated  in  their  enunciation.” 

Another  eminent  mathematician  had  previously  sanctioned  by  bis  authority  the  doctrine  of 
the  origin  of  geometrical  axioms  in  experience.  “Geometry  is  thus  founded  likewise  on 
observation  ; but  of  a kind  so  familiar  and  obvious,  that  the  primary  notions  which  it  fur- 
nishes might  seem  intuitive.” — Sir  John  Leslie,  quoted  by  Sir  William  Hamilton,  Discourses, 
etc.,  p.  272. 


DEMONSTRATION,  AND  NECESSARY  TRUTHS. 


187 


CHAPTER  VI. 

THE  SAME  SUBJECT  CONTINUED. 

§ 1.  In  the  examination  which  formed  the  subject  of  the  last  chapter, 
into  the  nature  of  the  evidence  of  those  deductive  sciences  which  are  com- 
monly represented  to  be  systems  of  necessary  truth,  we  have  been  led  to 
the  following  conclusions.  The  results  of  those  sciences  are  indeed  nec- 
essary, in  the  sense  of  necessarily  following  from  certain  first  principles, 
commonly  called  axioms  and  definitions;  that  is,  of  being  certainly  true 
if  those  axioms  and  definitions  are  so;  for  the  word  necessity,  even  in  this 
acceptation  of  it,  means  no  more  than  certainty.  But  their  claim  to  the 
character  of  necessity  in  any  sense  beyond  this,  as  implying  an  evidence 
independent  of  and  superior  to  observation  and  experience,  must  depend 
on  the  previous  establishment  of  such  a claim  in  favor  of  the  definitions 
and  axioms  themselves.  With  regard  to  axioms,  we  found  that,  consid- 
ered as  experimental  truths,  they  rest  on  superabundant  and  obvious  ev- 
idence. We  inquired,  whether,  since  this  is  the  case,  it  be  imperative  to 
suppose  any  other  evidence  of  those  truths  than  experimental  evidence,  any 
other  origin  for  our  belief  of  them  than  an  experimental  origin.  We  de- 
cided, that  the  burden  of  proof  lies  with  those  who  maintain  the  affirma- 
tive, and  we  examined,  at  considerable  length,  such  arguments  as  they  have 
produced.  The  examination  having  led  to  the  rejection  of  those  arguments, 
we  have  thought  ourselves  warranted  in  concluding  that  axioms  are  but  a 
class,  the  most  universal  class,  of  inductions  from  experience;  the  simplest 
and  easiest  cases  of  generalization  from  the  facts  furnished  to  us  by  our 
senses  or  by  our  internal  consciousness. 

While  the  axioms  of  demonstrative  sciences  thus  appeared  to  be  exper- 
imental truths,  the  definitions,  as  they  are  incorrectly  called,  in  those  sci- 
ences, were  found  by  us  to  be  generalizations  from  experience  which  are 
not  even,  accurately  speaking,  truths ; being  propositions  in  which,  while 
we  assert  of  some  kind  of  object,  some  property  or  properties  which  ob- 
servation shows  to  belong  to  it,  we  at  the  same  time  deny  that  it  possesses 
any  other  properties,  though  in  truth  other  properties  do  in  every  individ- 
ual instance  accompany,  and  in  almost  all  instances  modify,  the  property 
thus  exclusively  predicated.  The  denial,  therefore,  is  a mere  fiction,  or  sup- 
position, made  for  the  purpose  of  excluding  the  consideration  of  those  mod- 
ifying circumstances,  when  their  influence  is  of  too  trifling  amount  to  be 
worth  considering,  or  adjourning  it,  when  important  to  a more  convenient 
moment. 

From  these  considerations  it  would  appear  that  Deductive  or  Demon- 
strative Sciences  are  all,  without  exception,  Inductive  Sciences  ; that  their 
evidence  is  that  of  experience;  but  that  they  are  also,  in  virtue  of  the  pe- 
culiar character  of  one  indispensable  portion  of  the  general  formulae  ac- 
cording to  which  their  inductions  are  made,  Hypothetical  Sciences.  Their 
conclusions  are  only  true  on  certain  suppositions,  which  are,  or  ought  to 
be,  approximations  to  the  truth,  but  are  seldom,  if  ever,  exactly  true ; and 
to  this  hypothetical  character  is  to  be  ascribed  the  peculiar  certainty,  which 
is  supposed  to  be  inherent  in  demonstration. 


18S 


REASONING. 


What  we  have  now  asserted,  however,  can  not  be  received  as  universally 
true  of  Deductive  or  Demonstrative  Sciences,  until  verified  by  being  ap- 
plied to  the  most  remarkable  of  all  those  sciences,  that  of  Numbers;  the 
theory  of  the  Calculus;  Arithmetic  and  Algebra.  It  is  harder  to  believe 
of  the  doctrines  of  this  science  than  of  any  other,  either  that  they  are  not 
truths  a ‘priori , but  experimental  truths,  or  that  their  peculiar  certainty  is 
owing  to  their  being  not  absolute  but  only  conditional  truths.  This,  there- 
fore, is  a case  which  merits  examination  apart ; and  the  more  so,  because 
on  this  subject  we  have  a double  set  of  doctrines  to  contend  with ; that  of 
the  a priori  philosophers  on  one  side;  and  on  the  other,  a theory  the  most 
opposite  to  theirs,  which  was  at  one  time  very  generally  received,  and  is 
still  far  from  being  altogether  exploded,  among  metaphysicians. 

§ 2.  This  theory  attempts  to  solve  the  difficulty  apparently  inherent  in 
the  case,  by  representing  the  propositions  of  the  science  of  numbers  as 
merely  verbal,  and  its  processes  as  simple  transformations  of  language,  sub- 
stitutions of  one  expression  for  another.  The  proposition,  Two  and  one  is 
equal  to  three,  according  to  these  writers,  is  not  a truth,  is  not  the  assertion 
of  a really  existing  fact,  but  a definition  of  the  word  three ; a statement 
that  mankind  have  agreed  to  use  the  name  three  as  a sign  exactly  equiva- 
lent to  two  and  one ; to  call  by  the  former  name  whatever  is  called  by  the 
other  more  clumsy  phrase.  According  to  this  doctrine,  the  longest  process 
in  algebra  is  but  a succession  of  changes  in  terminology,  by  which  equiva- 
lent expressions  are  substituted  one  for  another ; a series  of  translations  of 
the  same  fact,  from  one  into  another  language ; though  how,  after  such  a 
series  of  translations,  the  fact  itself  comes  out  changed  (as  when  we  de- 
monstrate a new  geometrical  theorem  by  algebra),  they  have  not  explain- 
ed ; and  it  is  a difficulty  which  is  fatal  to  their  theory. 

It  must  be  acknowledged  that  there  are  peculiarities  in  the  processes  of 
arithmetic  and  algebra  which  render  the  theory  in  question  very  plausible, 
and  have  not  unnaturally  made  those  sciences  the  stronghold  of  Nominal- 
ism. The  doctrine  that  we  can  discover  facts,  detect  the  hidden  processes 
of  nature,  by  an  artful  manipulation  of  language,  is  so  contrary  to  common 
sense,  that  a person  must  have  made  some  advances  in  philosophy  to  be- 
lieve it : men  fly  to  so  paradoxical  a belief  to  avoid,  as  they  think,  some 
even  greater  difficulty,  which  the  vulgar  do  not  see.  What  has  led  many 
to  believe  that  reasoning  is  a mere  verbal  process,  is,  that  no  other  theory 
seemed  reconcilable  with  the  nature  of  the  Science  of  Numbers.  For  we 
do  not  carry  any  ideas  along  with  us  when  we  use  the  symbols  of  arithme- 
tic or  of  algebra.  In  a geometrical  demonstration  we  have  a mental  dia- 
gram, if  not  one  on  paper ; AB,  AC,  are  present  to  our  imagination  as  lines, 
intersecting  other  lines,  forming  an  angle  with  one  another,  and  the  like ; 
but  not  so  a and  b.  These  may  represent  lines  or  any  other  magnitudes, 
but  those  magnitudes  are  never  thought  of;  nothing  is  realized  in  our  im- 
agination but  a and  b.  The  ideas  which,  on  the  particular  occasion,  they 
happen  to  represent,  are  banished  from  the  mind  during  every  intermediate 
part  of  the  process,  between  the  beginning,  when  the  premises  are  trans- 
lated from  things  into  signs,  and  the  end,  when  the  conclusion  is  translated 
back  from  signs  into  things.  Nothing,  then,  being  in  the  reasoner’s  mind 
but  the  symbols,  what  can  seem  more  inadmissible  than  to  contend  that  the 
reasoning  process  has  to  do  with  any  thing  more?  We  seem  to  have  come 
to  one  of  Bacon’s  Prerogative  Instances ; an  experimentimi  crucis  on  the 
nature  of  reasoning  itself. 


DEMONSTRATION,  AND  NECESSARY  TRUTHS 


189 


Nevertheless,  it  will  appear  on  consideration,  that  this  apparently  so  de- 
cisive instance  is  no  instance  at  all ; that  there  is  in  every  step  of  an  arith- 
metical or  algebraical  calculation  a real  induction,  a real  inference  of  facts 
from  facts ; and  that  what  disguises  the  induction  is  simply  its  compre- 
hensive nature,  and  the  consequent  extreme  generality  of  the  language. 
All  numbers  must  be  numbers  of  something:  there  are  no  such  things  as 
numbers  in  the  abstract,  len  must  mean  ten  bodies,  or  ten  sounds,  or  ten 
beatings  of  the  pulse.  But  though  numbers  must  be  numbers  of  some- 
thing, they  may  be  numbers  of  any  thing.  Propositions,  therefore,  con- 
cerning numbers,  have  the  remarkable  peculiarity  that  they  are  proposi- 
tions concerning  all  things  whatever;  all  objects,  all  existences  of  every 
kind,  known  to  our  experience.  All  things  possess  quantity  ; consist  of 
parts  which  can  be  numbered ; and  in  that  character  possess  all  the  prop- 
erties which  are  called  properties  of  numbers.  That  half  of  four  is  two, 
must  be  true  w'hatever  the  word  four  represents,  whether  four  hours,  four 
miles,  or  four  pounds  weight.  We  need  only  conceive  a thing  divided  into 
four  equal  parts  (and  all  things  may  be  conceived  as  so  divided),  to  be  able 
to  predicate  of  it  every  property  of  the  number  four,  that  is,  every  arith- 
metical proposition  in  which  the  number  four  stands  on  one  side  of  the 
equation.  Algebra  extends  the  generalization  still  farther:  every  number 
represents  that  particular  number  of  all  things  without  distinction,  but  ev- 
ery algebraical  symbol  does  more,  it  represents  all  numbers  without  dis- 
tinction. As  soon  as  we  conceive  a thing  divided  into  equal  parts,  without 
knowing  into  what  number  of  parts,  we  may  call  it  a or  x,  and  apply  to  it, 
without  danger  of  error,  every  algebraical  formula  in  the  books.  The 
proposition,  2 (a  + b)  = 2 a + 2 b,  is  a truth  co-extensive  with  all  nature. 
Since  then  algebraical  truths  are  true  of  all  things  whatever,  and  not,  like 
those  of  geometry,  true  of  lines  only  or  of  angles  only,  it  is  no  wonder  that 
the  symbols  should  not  excite  in  our  minds  ideas  of  any  things  in  particu- 
lar. When  we  demonstrate  the  forty-seventh  proposition  of  Euclid,  it  is 
not  necessary  that  the  words  should  raise  in  us  an  image  of  all  right-angled 
triangles,  but  only  of  some  one  right-angled  triangle : so  in  algebra  we 
need  not,  under  the  symbol  a,  picture  to  ourselves  all  things  whatever,  but 
only  some  one  thing;  why  not,  then,  the  letter  itself?  The  mere  written 
characters,  a,  b,  x,  y , z,  serve  as  well  for  representatives  of  Things  in  general, 
as  any  more  complex  and  apparently  more  concrete  conception.  That  we 
are  conscious  of  them,  however,  in  their  character  of  things,  and  not  of  mere 
signs,  is  evident  from  the  fact  that  our  whole  process  of  reasoning  is  car- 
ried on  by  predicating  of  them  the  properties  of  things.  In  resolving  an 
algebraic  equation,  by  what  rules  do  we  proceed  ? By  applying  at  each 
step  to  a,  b,  and  x,  the  proposition  that  equals  added  to  equals  make  equals ; 
that  equals  taken  from  equals  leave  equals ; and  other  propositions  founded 
on  these  two.  These  are  not  properties  of  language,  or  of  signs  as  such, 
but  of  magnitudes,  which  is  as  much  as  to  say,  of  all  things.  The  infer- 
ences, therefore,  which  are  successively  drawn,  are  inferences  concerning 
things, not  symbols;  though  as  any  Things  whatever  will  serve  the  turn, 
there  is  no  necessity  for  keeping  the  idea  of  the  Thing  at  all  distinct,  and 
consequently  the  process  of  thought  may,  in  this  case,  be  allowed  without 
danger  to  do  what  all  processes  of  thought,  when  they  have  been  performed 
often,  will  do  if  permitted,  namely,  to  become  entirely  mechanical.  Hence 
the  general  language  of  algebra  comes  to  be  used  familiarly  without  excit- 
ing ideas,  as  all  other  general  language  is  prone  to  do  from  mere  habit, 
though  in  no  other  case  than  this  can  it  be  done  with  complete  safety. 


190 


REASONING. 


But  when  we  look  back  to  see  from  whence  the  probative  force  of  the 
process  is  derived,  we  find  that  at  every  single  step,  unless  we  suppose  our- 
selves to  be  thinking  and  talking  of  the  things,  and  not  the  mere  symbols, 
the  evidence  fails. 

There  is  another  circumstance,  which,  still  more  than  that  which  we  have 
now  mentioned,  gives  plausibility  to  the  notion  that  the  propositions  of 
arithmetic  and  algebra  are  merely  verbal.  That  is,  that  when  considered 
as  propositions  respecting  Things,  they  all  have  the  appearance  of  being 
identical  propositions.  The  assertion,  Two  and  one  is  equal  to  three,  con- 
sidered as  an  assertion  respecting  objects,  as  for  instance,  “ Two  pebbles 
and  one  pebble  are  equal  to  three  pebbles,”  does  not  affirm  equality  be- 
tween two  collections  of  pebbles,  but  absolute  identity.  It  affirms  that  if 
we  put  one  pebble  to  two  pebbles,  those  very  pebbles  are  three.  The  ob- 
jects, therefore,  being  the  very  same,  and  the  mere  assertion  that  “objects 
are  themselves”  being  insignificant,  it  seems  but  natural  to  consider  the 
proposition,  Two  and  one  is  equal  to  three,  as  asserting  mere  identity  of 
signification  between  the  two  names. 

This,  however,  though  it  looks  so  plausible,  will  not  bear  examination. 
The  expression  “two  pebbles  and  one  pebble,”  and  the  expression  “three 
pebbles,”  stand  indeed  for  the  same  aggregation  of  objects,  but  they  by  no 
means  stand  for  the  same  physical  fact.  They  are  names  of  the  same  ob- 
jects, but  of  those  objects  in  two  different  states:  though  they  denote  the 
same  things,  their  connotation  is  different.  Three  pebbles  in  two  separate 
parcels,  and  three  pebbles  in  one  parcel,  do  not  make  the  same  impression 
on  our  senses ; and  the  assertion  that  the  very  same  pebbles  may  by  an  al- 
teration of  place  and  arrangement  be  made  to  produce  either  the  one  set  of 
sensations  or  the  other,  though  a very  familiar  proposition,  is  not  an  iden- 
tical one.  It  is  a truth  known  to  us  by  early  and  constant  experience : an 
inductive  truth  ; and  such  truths  are  the  foundation  of  the  science  of  Num- 
ber. The  fundamental  truths  of  that  science  all  rest  on  the  evidence  of 
sense ; they  are  proved  by  showing  to  our  eyes  and  our  fingers  that  any 
given  number  of  objects — ten  balls,  for  example — may  by  separation  and 
re-arrangement  exhibit  to  our  senses  all  the  different  sets  of  numbers  the 
sums  of  which  is  equal  to  ten.  All  the  improved  methods  of  teaching 
arithmetic  to  children  proceed  on  a knowledge  of  this  fact.  All  who  wish 
to  carry  the  child’s  mind  along  with  them  in  learning  arithmetic;  all  who 
wish  to  teach  numbers,  and  not  mere  ciphers — now  teach  it  through  the  ev- 
idence of  the  senses,  in  the  manner  we  have  described. 

We  may,  if  we  please,  call  the  proposition,  “Three  is  two  and  one,”  a 
definition  of  the  number  three,  and  assert  that  arithmetic,  as  it  has  been 
asserted  that  geometry,  is  a science  founded  on  definitions.  But  they  are 
definitions  in  the  geometrical  sense,  not  the  logical;  asserting  not  the  mean- 
ing of  a term  only,  but  along  with  it  an  observed  matter  of  fact.  The 
proposition,  “A  circle  is  a figure  bounded  by  a line  which  has  all  its  points 
equally  distant  from  a point  within  it,”  is  called  the  definition  of  a circle; 
but  the  proposition  from  which  so  many  consequences  follow,  and  which 
is  really  a first  principle  in  geometry,  is,  that  figures  answering  to  this  de- 
scription exist.  And  thus  we  may  call  “Three  is  two  and  one”  a defini- 
tion of  three ; but  the  calculations  which  depend  on  that  proposition  do 
not  follow  from  the  definition  itself,  but  from  an  arithmetical  theorem  pre- 
supposed in  it,  namely,  that  collections  of  objects  exist,  which  while  they 
impress  the  senses  thus,  °0°,  may  be  separated  into  two  parts,  thus,  00  o- 
This  proposition  being  granted,  we  term  all  such  parcels  Threes,  after 


DEMONSTRATION,  AND  NECESSARY  TRUTHS. 


191 


which  the  enunciation  of  the  above-mentioned  physical  fact  will  serve  also 
for  a definition  of  the  word  Three. 

The  Science  of  Number  is  thus  no  exception  to  the  conclusion  we  pre- 
viously arrived  at,  that  the  processes  even  of  deductive  sciences  are  alto- 
gether inductive,  and  that  their  first  principles  are  generalizations  from  ex- 
perience. It  remains  to  be  examined  whether  this  science  resembles  geom- 
etry in  the  further  circumstance,  that  some  of  its  inductions  are  not  exactlv 
true  ; and  that  the  peculiar  certainty  ascribed  to  it,  on  account  of  which  its 
propositions  are  called  Necessary  Truths,  is  fictitious  and  hypothetical,  be- 
ing true  in  no  other  sense  than  that  those  propositions  legitimately  follow 
from  the  hypothesis  of  the  truth  of  premises  which  are  avowedly  mere  ap- 
proximations to  truth. 

§ 3.  The  inductions  of  arithmetic  are  of  two  sorts : first,  those  which  we 
have  just  expounded,  such  as  One  and  one  are  two, Two  and  one  are  three, 
etc.,  which  may  be  called  the  definitions  of  the  various  numbers,  in  the  im- 
proper or  geometrical  sense  of  the  word  Definition ; and  secondly,  the  two 
following  axioms : The  sums  of  equals  are  equal,  The  differences  of  equals 
are  equal.  These  two  are  sufficient;  for  the  corresponding  propositions  re- 
specting unequals  may  be  proved  from  these  by  a reductio  ad  absurdum. 

These  axioms,  and  likewise  the  so-called  definitions,  are,  as  has  already 
been  said,  results  of  induction;  true  of  all  objects  whatever,  and,  as  it  may 
seem,  exactly  true,  without  the  hypothetical  assumption  of  unqualified  truth 
where  an  approximation  to  it  is  all  that  exists.  The  conclusions,  therefore, 
it  will  naturally  be  inferred,  are  exactly  true,  and  the  science  of  number  is 
an  exception  to  other  demonstrative  sciences  in  this,  that  the  categorical 
certainty  which  is  predicable  of  its  demonstrations  is  independent  of  all 
hypothesis. 

On  more  accurate  investigation,  however,  it  will  be  found  that,  even  in 
this  case,  there  is  one  hypothetical  element  in  the  ratiocination.  In  all 
propositions  concerning  numbers,  a condition  is  implied,  without  which 
none  of  them  would  be  true;  and  that  condition  is  an  assumption  which 
may  be  false.  The  condition  is,  that  1 = 1 ; that  all  the  numbers  are  num- 
bers of  the  same  or  of  equal  units.  Let  this  be  doubtful,  and  not  one  of 
the  propositions  of  arithmetic  will  hold  true.  How  can  we  know  that  one 
pound  and  one  pound  make  two  pounds,  if  one  of  the  pounds  may  be  troy, 
and  the  other  avoirdupois?  They  may  not  make  two  pounds  of  either,  or 
of  any  weight.  How  can  we  know  that  a forty-horse  power  is  always  equal 
to  itself,  unless  we  assume  that  all  horses  are  of  equal  strength  ? It  is  cer- 
tain that  1 is  always  equal  in  number  to  1 ; and  where  the  mere  number  of 
objects,  or  of  the  parts  of  an  object,  without  supposing  them  to  be  equiv- 
alent in  any  other  respect,  is  all  that  is  material,  the  conclusions  of  arith- 
metic, so  far  as  they  go  to  that  alone,  are  true  without  mixture  of  hypoth- 
esis. There  are  such  cases  in  statistics ; as,  for  instance,  an  inquiry  into 
the  amount  of  the  population  of  any  country.  It  is  indifferent  to  that  in- 
quiry whether  they  are  grown  people  or  children,  strong  or  weak,  tall  or 
short;  the  only  thing  we  want  to  ascertain  is  their  number.  But  when- 
ever, from  equality  or  inequality  of  number,  equality  or  inequality  in  any 
other  respect  is  to  be  inferred,  arithmetic  carried  into  such  inquiries  be- 
comes as  hypothetical  a science  as  geometry.  All  units  must  be  assumed 
to  be  equal  in  that  other  respect;  and  this  is  never  accurately  true,  for  one 
actual  pound  weight  is  not  exactly  equal  to  another,  nor  one  measured  mile’s 
length  to  another ; a nicer  balance,  or  more  accurate  measuring  instruments, 
would  always  detect  some  difference. 


192 


REASONING. 


W1  nt  is  commonly  called  mathematical  certainty,  therefore,  which  com- 
prises the  twofold  conception  of  unconditional  truth  and  perfect  accuracy, 
is  not  an  attribute  of  all  mathematical  truths,  but  of  those  only  which  re- 
late to  pure  Number,  as  distinguished  from  Quantity  in  the  more  enlarged 
sense ; and  only  so  long  as  we  abstain  from  supposing  that  the  numbers 
are  a precise  index  to  actual  quantities.  The  certainty  usually  ascribed  to 
the  conclusions  of  geometry,  and  even  to  those  of  mechanics,  is  nothing 
whatever  but  certainty  of  inference.  We  can  have  full  assurance  of  par- 
ticular results  under  particular  suppositions,  but  we  can  not  have  the  same 
assurance  that  these  suppositions  are  accurately  true,  nor  that  they  include 
all  the  data  which  may  exercise  an  influence  over  the  result  in  any  given 
instance. 

§ 4.  It  appears,  therefore,  that  the  method  of  all  Deductive  Sciences  is 
hypothetical.  They  proceed  by  tracing  the  consequences  of  certain  as- 
sumptions ; leaving  for  separate  consideration  whether  the  assumptions 
are  true  or  not,  and  if  not  exactly  true,  whether  they  are  a sufficiently  near 
approximation  to  the  truth.  The  reason  is  obvious.  Since  it  is  only  in 
questions  of  pure  number  that  the  assumptions  are  exactly  true,  and  even 
there  only  so  long  as  no  conclusions  except  purely  numerical  ones  are  to 
be  founded  on  them;  it  must,  in  all  other  cases  of  deductive  investigation, 
form  a part  of  the  inquiry,  to  determine  how  much  the  assumptions  want 
of  being  exactly  true  in  the  case  in  hand.  This  is  generally  a matter  of 
observation,  to  be  repeated  in  every  fresh  case ; or  if  it  has  to  be  settled 
by  argument  instead  of  observation,  may  require  in  every  different  case 
different  evidence,  and  present  every  degree  of  difficulty,  from  the  lowest 
to  the  highest.  But  the  other  part  of  the  process — namely,  to  determine 
what  else  may  be  concluded  if  we  find,  and  in  proportion  as  we  find,  the 
assumptions  to  be  true — may  be  performed  once  for  all,  and  the  results 
held  ready  to  be  employed  as  the  occasions  turn  up  for  use.  We  thus  do 
all  beforehand  that  can  be  so  done,  and  leave  the  least  possible  work  to  be 
performed  when  cases  arise  and  press  for  a decision.  This  inquiry  into  the 
inferences  which  can  be  drawn  from  assumptions,  is  what  properly  consti- 
tutes Demonstrative  Science. 

It  is  of  course  quite  as  practicable  to  arrive  at  new  conclusions  from 
facts  assumed,  as  from  facts  observed ; from  fictitious,  as  from  real,  induc- 
tions. Deduction,  as  we  have  seen,  consists  of  a series  of  inferences  in  this 
form — a is  a mark  of  b,  b of  c,  c of  d,  therefore  a is  a mark  of  d,  which 
last  may  be  a truth  inaccessible  to  direct  observation.  In  like  manner  it 
is  allowable  to  say,  suppose  that  a were  a mark  of  b,  b of  c,  and  c of  d,  a 
would  be  a mark  of  d,  which  last  conclusion  was  not  thought  of  by  those 
who  laid  down  the  premises.  A system  of  propositions  as  complicated  as 
geometry  might  be  deduced  from  assumptions  which  are  false;  as  was 
done  by  Ptolemy,  Descartes,  and  others,  in  their  attempts  to  explain  syn- 
thetically the  phenomena  of  the  solar  system  on  the  supposition  that  the 
apparent  motions  of  the  heavenly  bodies  were  the  real  motions,  or  were 
produced  in  some  way  more  or  less  different  from  the  true  one.  Some- 
times the  same  thing  is  knowingly  done,  for  the  purpose  of  showing  the 
falsity  of  the  assumption  ; which  is  called  a reductio  ad  absurdum.  In 
such  cases,  the  reasoning  is  as  follows:  a is  a mark  of  b,  and  b of  c;  now 
if  c were  also  a mark  of  d,  a would  be  a mark  of  d ; but  d is  known  to  be 
a mark  of  the  absence  of  a ; consequently  a would  be  a mark  of  its  own 
absence,  which  is  a contradiction  ; therefore  c is  not  a mark  of  d. 


THEORIES  CONCERNING  AXIOMS. 


193 


§ 5.  It  has  even  been  held  by  some  writers,  that  all  ratiocination  rests 
in  the  last  resort  on  a reductio  ad  absurdum ; since  the  way  to  enforce  as- 
sent to  it,  in  case  of  obscurity,  would  be  to  show  that  if  the  conclusion  be 
denied  we  must  deny  some  one  at  least  of  the  premises,  which,  as  they  are 
all  supposed  true,  would  be  a contradiction.  And  in  accordance  with  this, 
many  have  thought  that  the  peculiar  nature  of  the  evidence  of  ratiocina- 
tion consisted  in  the  impossibility  of  admitting  the  premises  and  rejecting 
the  conclusion  without  a contradiction  in  terms.  This  theory,  however,  is 
inadmissible  as  an  explanation  of  the  grounds  on  which  ratiocination  itself 
rests.  If  any  one  denies  the  conclusion  notwithstanding  his  admission  of 
the  premises,  he  is  not  involved  in  any  direct  and  express  contradiction  un- 
til he  is  compelled  to  deny  some  premise;  and  he  can  only  be  forced  to  do 
this  by  a reductio  ad  absurdum , that  is,  by  another  ratiocination : now,  if 
he  denies  the  validity  of  the  reasoning  process  itself,  he  can  no  more  be 
forced  to  assent  to  the  second  syllogism  than  to  the  first.  In  truth,  there- 
fore, no  one  is  ever  forced  to  a contradiction  in  terms:  he  can  only  be 
forced  to  a contradiction  (or  rather  an  infringement)  of  the  fundamental 
maxim  of  ratiocination,  namely,  that  whatever  has  a mark,  has  what  it  is 
a mark  of;  or  (in  the  case  of  universal  propositions),  that  whatever  is  a 
mark  of  any  thing,  is  a mark  of  whatever  else  that  thing  is  a mark  of.  For 
in  the  case  of  every  correct  argument,  as  soon  as  thrown  into  the  syllogis- 
tic form,  it  is  evident  without  the  aid  of  any  other  syllogism,  that  he  who, 
admitting  the  premises,  fails  to  draw  the  conclusion,  does  not  conform  to 
the  above  axiom. 

We  have  now  proceeded  as  far  in  the  theory  of  Deduction  as  we  can  ad- 
vance in  the  present  stage  of  our  inquiry.  Any  further  insight  into  the 
subject  requires  that  the  foundation  shall  have  been  laid  of  the  philosophic 
theory  of  Induction  itself;  in  which  theory  that  of  Deduction,  as  a mode 
of  Induction,  which  we  have  now  shown  it  to  be,  will  assume  spontaneous- 
ly the  place  which  belongs  to  it,  and  will  receive  its  share  of  whatever  light 
may  be  thrown  upon  the  great  intellectual  operation  of  which  it  forms  so 
important  a part. 


CHAPTER  VII. 

EXAMINATION  OP  SOME  OPINIONS  OPPOSED  TO  TIIE  PRECEDING  DOCTRINES. 

§ 1.  Polemical  discussion  is  foreign  to  the  plan  of  this  work.  But  an 
opinion  which  stands  in  need  of  much  illustration,  can  often  receive  it  most 
effectually,  and  least  tediously,  in  the  form  of  a defense  against  objections. 
And  on  subjects  concerning  which  speculative  minds  are  still  divided,  a 
writer  does  but  half  his  duty  by  stating  his  own  doctrine,  if  he  does  not 
also  examine,  and  to  the  best  of  his  ability  judge,  those  of  other  thinkers. 

In  the  dissertation  which  Mr.  Herbert  Spencer  has  prefixed  to  his,  in 
many  respects,  highly  philosophical  treatise  on  the  Mind,*  he  criticises  some 
of  the  doctrines  of  the  two  preceding  chapters,  and  propounds  a theory  of 
his  own  on  the  subject  of  first  principles.  Mr.  Spencer  agrees  with  me  in 
considering  axioms  to  be  “ simply  our  earliest  inductions  from  experience.” 
But  he  differs  from  me  “widely  as  to  the  worth  of  the  test  of  incoriceiva- 


Principles  of  Psychology. 

)3 


194 


REASONING. 


bleness.”  He  thinks  that  it  is  the  ultimate  test  of  all  beliefs.  He  arrives 
at  this  conclusion  by  two  steps.  First,  vve  never  can  have  any  stronger 
ground  for  believing  any  thing,  than  that  the  belief  of  it  “ invariably  exists.” 
Whenever  any  fact  or  proposition  is  invariably  believed ; that  is,  if  I un- 
derstand Mr.  Spencer  rightly,  believed  by  all  persons,  and  by  one’s  self  at  all 
times ; it  is  entitled  to  be  received  as  one  of  the  primitive  truths,  or  orig- 
inal premises  of  our  knowledge.  Secondly,  the  criterion  by  which  we  de- 
cide whether  any  thing  is  invariably  believed  to  be  true,  is  our  inability  to 
conceive  it  as  false.  “The  inconceivability  of  its  negation  is  the  test  by 
which  we  ascertain  whether  a given  belief  invariably  exists  or  not.”  “For 
our  primary  beliefs,  the  fact  of  invariable  existence,  tested  by  an  abortive 
effort  to  cause  their  non-existence,  is  the  only  reason  assignable.”  He 
thinks  this  the  sole  ground  of  our  belief  in  our  own  sensations.  If  I believe 
that  I feel  cold,  I only  receive  this  as  true  because  I can  not  conceive  that 
I am  not  feeling  cold.  “ While  the  proposition  remains  true,  the  negation 
of  it  remains  inconceivable.”  There  are  numerous  other  beliefs  which  Mr. 
Spencer  considers  to  rest  on  the  same  basis;  being  chiefly  those,  or  a part 
of  those,  which  the  metaphysicians  of  the  Reid  and  Stewart  school  con- 
sider as  truths  of  immediate  intuition.  That  there  exists  a material  world; 
that  tins  is  the  very  world  which  vve  directly  and  immediately  perceive, 
and  not  merely  the  hidden  cause  of  our  perceptions;  that  Space,  Time, 
Force,  Extension,  Figure,  are  not  modes  of  our  consciousness,  but  objective 
realities ; are  regarded  by  Mr.  Spencer  as  truths  known  by  the  inconceiva- 
bleness of  their  negatives.  We  can  not,  he  says,  by  any  effort,  conceive 
these  objects  of  thought  as  mere  states  of  our  mind;  as  not  having  an  ex- 
istence external  to  us.  Their  real  existence  is,  therefore,  as  certain  as  our 
sensations  themselves.  The  truths  which  are  the  subject  of  direct  knowl- 
edge, being,  according  to  this  doctrine,  known  to  be  truths  only  by  the  in- 
conceivability of  their  negation ; and  the  truths  which  are  not  the  object 
of  direct  knowledge,  being  known  as  inferences  from  those  which  are;  and 
those  inferences  being  believed  to  follow  from  the  premises,  only  because 
we  can  not  conceive  them  not  to  follow ; inconceivability  is  thus  the  ulti- 
mate ground  of  all  assured  beliefs. 

Thus  far,  there  is  no  very  wide  difference  between  Mr.  Spencer’s  doctrine 
and  the  ordinary  one  of  philosophers  of  the  intuitive  school,  from  Descartes 
to  Dr.  Whewell;  but  at  this  point  Mr.  Spencer  diverges  from  them.  For 
he  does  not,  like  them,  set  up  the  test  of  inconceivability  as  infallible.  On 
the  contrary,  he  holds  that  it  may  be  fallacious,  not  from  any  fault  in  the 
test  itself,  but  because  “ men  have  mistaken  for  inconceivable  things,  some 
things  which  were  not  inconceivable.”  And  he  himself,  in  this  very  book, 
denies  not  a few  propositions  usually  regarded  as  among  the  most  marked 
examples  of  truths  whose  negations  are  inconceivable.  But  occasional  fail- 
ure, he  says,  is  incident  to  all  tests.  If  such  failure  vitiates  “ the  test  of  in- 
conceivableness,” it  “must  similarly  vitiate  all  tests  whatever.  We  con- 
sider an  inference  logically  drawn  from  established  premises  to  be  true. 
Yet  in  millions  of  cases  men  have  been  wrong  in  the  inferences  they  have 
thought  thus  drawn.  Do  we  therefore  argue  that  it  is  absurd  to  consider 
an  inference  true  on  no  other  ground  than  that  it  is  logically  drawn  from 
established  premises?  No:  we  say  that  though  men  may  have  taken  for 
logical  inferences,  inferences  that  were  not  logical,  there  nevertheless  are 
logical  inferences,  and  that  we  are  justified  in  assuming  the  truth  of  what 
seem  to  us  such,  until  better  instructed.  Similarly,  though  men  may  have 
thought  some  things  inconceivable  which  were  not  so,  there  may  still  be  in- 


THEORIES  CONCERNING  AXIOMS.  195 

conceivable  things ; and  the  inability  to  conceive  the  negation  of  a thing, 
may  still  be  ouv  best  warrant  for  believing  it Though  occasional- 


ly it  may  prove  an  imperfect  test,  yet,  as  our  most  certain  beliefs  are  capa- 
ble of  no  better,  to  doubt  any  one  belief  because  we  have  no  higher  guar- 
antee for  it,  is  really  to  doubt  all  beliefs.”  Mr.  Spencer’s  doctrine,  there- 
fore, does  not  erect  the  curable,  but  only  the  incurable  limitations  of  the 
human  conceptive  faculty,  into  laws  of  the  outward  universe. 

§ 2.  The  doctrine,  that  “ a belief  which  is  proved  by  the  inconceivable- 
ness of  its  negation  to  invariably  exist,  is  true,”  Mr.  Spencer  enforces  by 
two  arguments,  one  of  which  may  be  distinguished  as  positive,  and  the 
other  as  negative. 

The  positive  argument  is,  that  every  such  belief  represents  the  aggregate 
of  all  past  experience.  “Conceding  the  entire  truth  of”  the  “position, 
that  during  any  phase  of  human  progress,  the  ability  or  inability  to  form 
a specific  conception  wholly  depends  on  the  experiences  men  have  had ; 
and  that,  by  a widening  of  their  experiences,  they  may,  by  and  by,  be  en- 
abled to  conceive  things  before  inconceivable  to  them,  it  may  still  be  argued 
that  as,  at  any  time,  the  best  warrant  men  can  have  for  a belief  is  the  per- 
fect agreement  of  all  pre-existing  experience  in  support  of  it,  it  follows  that, 
at  any  time,  the  inconceivableness  of  its  negation  is  the  deepest  test  any 

belief  admits  of Objective  facts  are  ever  impressing  themselves  upon 

us;  our  experience  is  a register  of  these  objective  facts;  and  the  incon- 
ceivableness of  a thing  implies  that  it  is  wholly  at  variance  with  the  regis- 
ter. Even  were  this  all,  it  is  not  clear  how,  if  every  truth  is  primarily  in- 
ductive, any  better  test  of  truth  could  exist.  But  it  must  be  remembered 
that  while  many  of  these  facts,  impressing  themselves  upon  us,  are  occa- 
sional ; while  others  again  are  very  general ; some  are  universal  and  un- 
changing. These  universal  and  unchanging  facts  are,  by  the  hypothesis, 
certain  to  establish  beliefs  of  which  the  negations  are  inconceivable;  while 
the  others  are  not  certain  to  do  this ; and  if  they  do,  subsequent  facts  will 
reverse  their  action.  Hence  if,  after  an  immense  accumulation  of  experi- 
ences, there  remain  beliefs  of  which  the  negations  are  still  inconceivable, 
most,  if  not  all  of  them,  must  correspond  to  universal  objective  facts;  If 
there  be  ....  certain  absolute  uniformities  in  nature ; if  these  uniform- 
ities produce,  as  they  must,  absolute  uniformities  in  our  experience ; and 
if  ....  these  absolute  uniformities  in  our  experience  disable  us  from  con- 
ceiving the  negations  of  them ; then  answering  to  each  absolute  uniformi- 
ty in  nature  which  we  can  cognize,  there  must  exist  in  us  a belief  of  which 
the  negation  is  inconceivable,  and  which  is  absolutely  true.  In  this  wide 
range  of  cases  subjective  inconceivableness  must  correspond  to  objective 
impossibility.  Further  experience  will  produce  correspondence  where  it 
may  not  yet  exist;  and  we  may  expect  the  correspondence  to  become  ulti- 
mately complete.  In  nearly  all  cases  this  test  of  inconceivableness  must  be 
valid  now  ” (I  wish  I could  think  we  were  so  nearly  arrived  at  omnis- 
cience) ; “ and  where  it  is  not,  it  still  expresses  the  net  result  of  our  experi- 
ence up  to  the  present  time ; which  is  the  most  that  any  test  can  do.” 

To  this  I answer,  first,  that  it  is  by  no  means  true  that  the  inconceivabili- 
ty, by  us,  of  the  negative  of  a proposition  proves  all,  or  even  any,  “ pre-exist- 
ing experience  ” to  be  in  favor  of  the  affirmative.  There  may  have  been 
no  such  pre-existing  experiences,  but  only  a mistaken  supposition  of  expe- 
rience. How  did  the  inconceivability  of  antipodes  prove  that  experience 
had  given  any  testimony  against  their  possibility  ? flow  did  the  incapaci- 


19G 


REASONING. 


ty  men  felt  of  conceiving  sunset  otherwise  than  as  a motion  of  the  sun, 
represent  any  “net  result”  of  experience  in  support  of  its  being  the  sun 
and  not  the  earth  that  moves  ? It  is  not  experience  that  is  represented,  it 
is  only  a superficial  semblance  of  experience.  The  only  thing  proved  with 
regard  to  real  experience,  is  the  negative  fact,  that  men  have  not  had  it 
of  the  kind  which  would  have  made  the  inconceivable  proposition  conceiv- 
able. 

Next:  Even  if  it  were  true  that  inconceivableness  represents  the  net  re- 
sult of  all  past  experience,  why  should  we  stop  at  the  representative  when 
we  can  get  at  the  thing  represented  ? If  our  incapacity  to  conceive  the 
negation  of  a given  supposition  is  proof  of  its  truth,  because  proving  that 
our  experience  has  hitherto  been  uniform  in  its  favor,  the  real  evidence  for 
the  supposition  is  not  the  inconceivableness,  but  the  uniformity  of  experi- 
ence. Now  this,  which  is  the  substantial  and  only  proof,  is  directly  access- 
ible. We  are  not  obliged  to  presume  it  from  an  incidental  consequence. 
If  all  past  experience  is  in  favor  of  a belief,  let  this  be  stated,  and  the  be- 
lief openly  rested  on  that  ground : after  which  the  question  arises,  what 
that  fact  may  be  worth  as  evidence  of  its  truth?  For  uniformity  of  expe- 
rience is  evidence  in  very  different  degrees : in  some  cases  it  is  strong  evi- 
dence, in  others  weak,  in  others  it  scarcely  amounts  to  evidence  at  all. 
Tl;at  all  metals  sink  in  water,  was  a uniform  experience,  from  the  origin 
of  the  human  race  to  the  discovery  of  potassium  in  the  present  century 
by  Sir  Humphry  Davy.  That  all  swans  are  white,  was  a uniform  experi- 
ence down  to  the  discovery  of  Australia.  In  the  few  cases  in  which  uni- 
formity of  experience  does  amount  to  the  strongest  possible  proof,  as  with 
such  propositions  as  these,  Two  straight  lines  can  not  inclose  a space,  Ev- 
ery event  has  a cause,  it  is  not  because  their  negations  are  inconceivable, 
which  is  not  always  the  fact ; but  because  the  experience,  which  has  been 
thus  uniform,  pervades  all  nature.  It  will  be  shown  in  the  following  Book 
that  none  of  the  conclusions  either  of  induction  or  of  deduction  can  be 
considered  certain,  except  as  far  as  their  truth  is  shown  to  be  inseparably 
bound  up  with  truths  of  this  class. 

I maintain  then,  first,  that  uniformity  of  past  experience  is  very  far  from 
being  universally  a criterion  of  truth.  But  secondly,  inconceivableness  is 
still  further  from  being  a test  even  of  that  test.  Uniformity  of  contrary 
experience  is  only  one  of  many  causes  of  inconceivability.  Tradition 
handed  down  from  a period  of  more  limited  knowledge,  is  one  of  the  com- 
monest. The  mere  familiarity  of  one  mode  of  production  of  a phenome- 
non often  suffices  to  make  every  other  mode  appear  inconceivable.  What- 
ever connects  two  ideas  by  a strong  association  may,  and  continually  does, 
render  their  separation  in  thought  impossible ; as  Mr.  Spencer,  in  other 
parts  of  his  speculations,  frequently  recognizes.  It  was  not  for  want  of  ex- 
perience that  the  Cartesians  were  unable  to  conceive  that  one  body  could 
produce  motion  in  another  without  contact.  They  had  as  much  experience 
of  other  modes  of  producing  motion  as  they  had  of  that  mode.  The  plan- 
ets had  revolved,  and  heavy  bodies  had  fallen,  every  hour  of  their  lives. 
But  they  fancied  these  phenomena  to  be  produced  by  a hidden  machinery 
which  they  did  not  see,  because  without  it  they  were  unable  to  conceive 
what  they  did  see.  The  inconceivableness,  instead  of  representing  their 
experience,  dominated  and  overrode  their  experience.  Without  dwelling 
further  on  what  I have  termed  the  positive  argument  of  Mr.  Spencer  in 
support  of  his  criterion  of  truth,  I pass  to  his  negative  argument,  on  which 
he  lays  more  stress. 


THEORIES  CONCERNING  AXIOMS. 


197 


§ 3.  The  negative  argument  is,  that,  whether  inconceivability  be  good 
evidence  or  bad,  no  stronger  evidence  is  to  be  obtained.  That  what  is  in- 
conceivable can  not  be  true,  is  postulated  in  every  act  of  thought.  It  is 
the  foundation  of  all  our  original  premises.  Still  more  it  is  assumed  in  all 
conclusions  from  those  premises.  The  invariability  of  belief,  tested  by  the 
inconceivableness  of  its  negation,  “ is  our  sole  warrant  for  every  demon- 
stration. Logic  is  simply  a systematization  of  the  process  by  which  we  in- 
directly obtain  this  warrant  for  beliefs  that  do  not  directly  possess  it.  To 
gain  the  strongest  conviction  possible  respecting  any  complex  fact,  we  ei- 
ther analytically  descend  from  it  by  successive  steps,  each  of  which  we  un- 
consciously test  by  the  inconceivableness  of  its  negation,  until  we  reach 
some  axiom  or  truth  which  we  have  similarly  tested;  or  we  synthetically 
ascend  from  such  axiom  or  truth  by  such  steps.  In  either  case  we  connect 
some  isolated  belief,  with  a belief  which  invariably  exists,  by  a series  of 
intermediate  beliefs  which  invariably  exist.”  The  following  passage  sums 
up  the  theory : “ When  we  perceive  that  the  negation  of  the  belief  is  in- 
conceivable, we  have  all  possible  warrant  for  asserting  the  invariability  of 
its  existence:  and  in  asserting  this,  we  express  alike  our  logical  justifica- 
tion of  it,  and  the  inexorable  necessity  we  are  under  of  holding  it 

We  have  seen  that  this  is  the  assumption  on  which  every  conclusion  what- 
ever ultimately  rests.  We  have  no  other  guarantee  for  the  reality  of  con- 
sciousness, of  sensations,  of  personal  existence ; we  have  no  other  guaran- 
tee for  any  axiom ; we  have  no  other  guarantee  for  any  step  in  a demon- 
stration. Hence,  as  being  taken  for  granted  in  every  act  of  the  under- 
standing, it  must  be  regarded  as  the  Universal  Postulate.”  But  as  this 
postulate,  which  we  are  under  an  “ inexorable  necessity  ” of  holding  true,  is 
sometimes  false ; as  “ beliefs  that  once  were  shown  by  the  inconceivable- 
ness of  their  negations  to  invariably  exist,  have  since  been  found  untrue,” 
and  as  “ beliefs  that  now  possess  this  character  may  some  day  share  the 
same  fate;”  the  canon  of  belief  laid  down  by  Mr.  Spencer  is,  that  “the 
most  certain  conclusion  ” is  that  “ which  involves  the  postulate  the  fewest 
times.”  Reasoning,  therefore,  never  ought  to  prevail  against  one  of  the 
immediate  beliefs  (the  belief  in  Matter,  in  the  outward  reality  of  Extension, 
Space,  and  the  like),  because  each  of  these  involves  the  postulate  oilly  once; 
while  an  argument,  besides  involving  it  in  the  premises,  involves  it  again  in 
every  step  of  the  ratiocination,  no  one  of  the  successive  acts  of  inference 
being  recognized  as  valid  except  because  we  can  not  conceive  the  conclu- 
sion not  to  follow  from  the  premises. 

It  will  be  convenient  to  take  the  last  part  of  this  argument  first.  In  ev- 
ery reasoning,  according  to  Mr.  Spencer,  the  assumption  of  the  postulate  is 
renewed  at  every  step.  At  each  inference  we  judge  that  the  conclusion 
follows  from  the  premises,  our  sole  warrant  for  that  judgment  being  that 
we  can  not  conceive  it  not  to  follow.  Consequently  if  the  postulate  is  fal- 
lible, the  conclusions  of  reasoning  are  move  vitiated  by  that  uncertainty 
than  direct  intuitions  ; and  the  disproportion  is  greater,  the  more  numerous 
the  steps  of  the  argument. 

To  test  this  doctrine,  let  us  first  suppose  an  argument  consisting  only  of 
a single  step,  which  would  be  represented  by  one  syllogism.  This  argu- 
ment does  rest  on  an  assumption,  and  we  have  seen  in  the  preceding  chap- 
ters what  the  assumption  is.  It  is,  that  whatever  has  a mark,  has  what  it 
is  a mark  of.  The  evidence  of  this  axiom  I shall  not  consider  at  present  ;* 

* Mr.  Spencer  is  mistaken  in  supposing  me  to  claim  any  peculiar  necessity”  for  this  ax- 
iom as  compared  with  others.  I have  corrected  the  expressions  which  led  him  into  that  mis- 
apprehension of  my  meaning. 


198 


REASONING. 


let  us  suppose  it  (with  Mr.  Spencer)  to  be  the  inconceivableness  of  its  re- 
verse. 

Let  us  now  add  a second  step  to  the  argument : we  require,  what?  An- 
other assumption?  No:  the  same  assumption  a second  time;  and  so  on 
to  a third,  and  a fourth.  I confess  I do  not  see  how,  on  Mr.  Spencer’s  own 
principles,  the  repetition  of  the  assumption  at  all  weakens  the  force  of  the 
argument.  If  it  were  necessary  the  second  time  to  assume  some  other  ax- 
iom, the  argument  would  no  doubt  be  weakened,  since  it  would  be  necessary 
to  its  validity  that  both  axioms  should  be  true,  and  it  might  happen  that 
one  was  true  and  not  the  other : making  two  chances  of  error  instead  of 
one.  But  since  it  is  the  same  axiom,  if  it  is  true  once  it  is  true  every 
time;  and  if  the  argument,  being  of  a hundred  links,  assumed  the  axiom  a 
hundred  times,  these  hundred  assumptions  would  make  but  one  chance  of 
error  among  them  all.  It  is  satisfactory  that  we  are  not  obliged  to  sup- 
pose the  deductions  of  pure  mathematics  to  be  among  the  most  uncertain 
of  argumentative  processes,  which  on  Mr.  Spencer’s  theory  they  could 
hardly  fail  to  bo,  since  they  are  the  longest.  But  the  number  of  steps  in 
an  argument  does  not  subtract  from  its  reliableness,  if  no  new£>ram'ses,  of 
an  uncertain  character,  are  taken  up  by  the  way.* 

To  speak  next  of  the  premises.  Our  assurance  of  their  truth,  whether 
they  be  generalities  or  individual  facts,  is  grounded,  in  Mr.  Spencer’s  opin- 
ion, on  the  inconceivableness  of  their  being  false.  It  is  necessary  to  advert 
to  a double  meaning  of  the  word  inconceivable,  which  Mr.  Spencer  is  aware 

* Mr.  Spencer,  in  recently  returning  to  the  subject  (Principles  of  Psychology,  new  edition, 
chap.  xii.  : “ The  Test  of  Relative  Validity”),  makes  two  answers  to  the  preceding  remarks. 
One  is : 

“Were  an  argument  formed  by  repeating  the  same  proposition  over  and  over  again,  it 
would  be  true  that  any  intrinsic  fallibility  of  the  postulate  would  not  make  the  conclusion 
more  untrustworthy  than  the  first  step.  But  an  argument  consists  of  unlike  propositions. 
Now,  since  Mr.  Mill's  criticism  on  the  Universal  Postulate  is  that  in  some  cases,  which  he 
names,  it  has  proved  to  be  an  untrustworthy  test ; it  follows  that  in  any  argument  consisting 
of  heterogeneous  propositions,  there  is  a risk,  increasing  as  the  number  of  propositions  in- 
creases, that  some  one  of  them  belongs  to  this  class  of  cases,  and  is  wrongly  accepted  because 
of  the  inconceivableness  of  its  negation.” 

No  doubt:  but  this  supposes  new  premises  to  be  taken  in.  The  point  we  are  discussing  is 
the  fallibility  not  of  the  premises,  but  of  the  reasoning,  as  distinguished  from  the  premises. 
Now  the  validity  of  the  reasoning  depends  always  upon  the  same  axiom,  repeated  (in  thought) 
“over  and  over  again,”  viz.,  that  whatever  has  a mark,  has  what  it  is  a mark  of.  Even, 
therefore,  on  the  assumption  that  this  axiom  rests  ultimately  on  the  Universal  Postulate,  and 
that,  the  Postulate  not  being  wholly  trustworthy,  the  axiom  may  be  one  of  the  cases  of  its 
failure;  all  the  risk  there  is  of  this  is  incurred  at  the  very  first  step  of  the  reasoning,  and  is 
not  added  to,  however  long  may  be  the  series  of  subsequent  steps. 

I am  here  arguing,  of  course,  from  Mr.  Spencer’s  point  of  view.  From  my  own  the  case  is 
still  clearer;  for,  in  my  view,  the  truth  that  whatever  has  a mark  has  what  it  is  a mark  of,  is 
wholly  trustworthy,  and  derives  none  of  its  evidence  from  so  very  untrustworthy  a test  as  the 
inconceivability  of  the  negative. 

Mr.  Spencer's  second  answer  i$  valid  up  to  a certain  point ; it  is,  that  every  prolongation  of 
the  process  involves  additional  chances  of  casual  error,  from  carelessness  in  the  reasoning 
operation.  This  is  an  important  consideration  in  the  private  speculations  of  an  individual 
reasoner;  and  even  with  respect  to  mankind  at  large,  it  must  he  admitted  that,  though  mere 
oversights  in  the  syllogistic  process,  like  errors  of  addition  in  an  account,  are  special  to  the 
individual,  and  seldom  escape  detection,  confusion  of  thought  produced  (for  example)  by  am- 
biguous terms  has  led  whole  nations  or  ages  to  accept  fallacious  reasoning  as  valid.  But  this 
very  fact  points  to  causes  of  error  so  much  more  dangerous  than  the  mere  length  of  the  proc- 
ess, as  quite  to  vitiate  the  doctrine  that  the  “test  of  the  relative  validities  of  conflicting  con- 
clusions” is  the  number  of  times  the  fundamental  postulate  is  involved.  On  the  contrary,  the 
subjects  on  which  the  trains  of  reasoning  are  longest,  and  the  assumption,  therefore,  oftenest 
repeated,  are  in  general  those  which  are  best  fortified  against  the  really  formidable  causes  of 
fallacy  ; its  in  the  example  already  given  of  mathematics. 


THEORIES  CONCERNING  AXIOMS. 


199 


of,  and  would  sincerely  disclaim  founding  an  argument  upon,  but  from 
which  his  case  derives  no  little  advantage  notwithstanding.  By  inconceiv- 
ableness is  sometimes  meant,  inability  to  form  or  get  rid  of  an  idea / some- 
times, inability  to  form  or  get  rid  of  a belief.  The  former  meaning  is  the 
most  conformable  to  the  analogy  of  language;  for  a conception  always 
means  an  idea,  and  never  a belief.  The  wrong  meaning  of  “ inconceivable” 
is,  however,  fully  as  frequent  in  philosophical  discussion  as  the  right  mean- 
ing, and  the  intuitive  school  of  metaphysicians  could  not  well  do  without 
either.  To  illustrate  the  difference,  we  will  take  two  contrasted  examples. 
The  early  physical  speculators  considered  antipodes  incredible,  because  in- 
conceivable. But  antipodes  were  not  inconceivable  in  the  primitive  sense 
of  the  word.  An  idea  of  them  could  be  formed  without  difficulty:  they 
could  be  completely  pictured  to  the  mental  eye.  What  was  difficult,  and, 
as  it  then  seemed,  impossible,  was  to  apprehend  them  as  believable.  The 
idea  could  be  put  together,  of  men  sticking  on  by  their  feet  to  the  under 
side  of  the  earth  ; but  the  belief  would  follow,  that  they  must  fall  off.  An- 
tipodes were  not  unimaginable,  but  they  were  unbelievable. 

On  the  other  hand,  when  I endeavor  to  conceive  an  end  to  extension,  the 
two  ideas  refuse  to  come  together.  When  I attempt  to  form  a conception 
of  the  last  point  of  space,  I can  not  help  figuring  to  myself  a vast  space 
beyond  that  last  point.  The  combination  is,  under  the  conditions  of  our 
experience,  unimaginable.  This  double  meaning  of  inconceivable  it  is  very 
important  to  bear  in  mind,  for  the  argument  from  inconceivableness  almost 
always  turns  on  the  alternate  substitution  of  each  of  those  meanings  for 
the  other. 

In  which  of  these  two  senses  does  Mr.  Spencer  employ  the  term,  when 
he  makes  it  a test  of  the  truth  of  a proposition  that  its  negation  is  incon- 
ceivable ? Until  Mr.  Spencer  expressly  stated  tire  contrary,  I inferred  from 
the  course  of  his  argument,  that  he  meant  unbelievable.  lie  has,  however, 
in  a paper  published  in  the  fifth  number  of  the  Fortnightly  Fevieio,  dis- 
claimed this  meaning,  and  declared  that  by  an  inconceivable  proposition 
he  means,  now  and  always, “one  of  which  the  terms  can  not,  by  any  effort, 
be  brought  before  consciousness  in  that  relation  which  the  proposition  as- 
serts between  them — a proposition  of  which  the  subject  and  predicate  offer 
an  insurmountable  resistance  to  union  in  thought.”  We  now,  therefore, 
know  positively  that  Mr.  Spencer  always  endeavors  to  use  the  word  incon- 
ceivable in  this,  its  proper,  sense : but  it  may  yet  be  questioned  whether 
his  endeavor  is  always  successful ; whether  the  other,  and  popular  use  of 
the  word,  does  not  sometimes  creep  in  with  its  associations,  and  prevent 
him  from  maintaining  a clear  separation  between  the  two.  When,  for 
example,  he  says,  that  when  I feel  cold,  I can  not  conceive  that  I am  not 
feeling  cold,  this  expression  can  not  be  translated  into  “I  can  not  con- 
ceive myself  not  feeling  cold,”  for  it  is  evident  that  I can : the  word 
conceive,  therefore,  is  here  used  to  express  the  recognition  of  a matter  of 
fact— the  perception  of  truth  or  falsehood ; which  I apprehend  to  be  ex- 
actly the  meaning  of  an  act  of  belief,  as  distinguished  from  simple  con- 
ception. Again,  Mr.  Spencer  calls  the  attempt  to  conceive  something 
which  is  inconceivable  “ an  abortive  effort  to  cause  the  non-existence,” 
not  of  a conception  or  mental  representation,  but  of  a belief.  There  is 
need,  therefore,  to  revise  a considerable  part  of  Mr.  Spencer’s  language,  if 
it  is  to  be  kept  always  consistent  with  his  definition  of  inconceivability. 
But  in  truth  the  point  is  of  little  importance;  since  inconceivability,  in 
Mr.  Spencer’s  theory,  is  only  a test  of  truth,  inasmuch  as  it  is  a test  of 


200 


REASONING. 


bclievability.  The  inconceivableness  of  a supposition  is  the  extreme  case 
of  its  unbelievability.  This  is  the  very  foundation  of  Mr.  Spencer’s  doc- 
trine. The  invariability  of  the  belief  is  with  him  the  real  guarantee. 
The  attempt  to  conceive  the  negative  is  made  in  order  to  test  the  inevita- 
bleness of  the  belief.  It  should  be  called,  an  attempt  to  believe  the  nega- 
tive. When  Mr.  Spencer  says  that  while  looking  at  the  sun  a man  can  not 
conceive  that  he  is  looking  into  darkness,  he  should  have  said  that  a man 
can  not  believe  that  he  is  doing  so.  For  it  is  surely  possible,  in  broad  day- 
light, to  imagine  one’s  self  looking  into  darkness.*  As  Mr.  Spencer  him- 
self says,  speaking  of  the  belief  of  our  own  existence,  “That  he  might  not 
exist,  he  can  conceive  well  enough  ; *but  that  he  does  not  exist,  he  finds  it 
impossible  to  conceive,”  i.  e.,  to  believe.  So  that  the  statement  resolves  it- 
self into  this:  That  I exist,  and  that  I have  sensations, I believe,  because  I 
can  not  believe  otherwise.  And  in  this  case  every  one  will  admit  that  the 
impossibility  is  real.  Any  one’s  present  sensations,  or  other  states  of  sub- 
jective consciousness,  that  one  person  inevitably  believes.  They  are  facts 
known  per  se  : it  is  impossible  to  ascend  beyond  them.  Their  negative  is 
really  unbelievable,  and  therefore  there  is  never  any  question  about  believ- 
ing it.  Mr.  Spencer’s  theory  is  not  needed  for  these  truths. 

But  according  to  Mr.  Spencer  there  are  other  beliefs,  relating  to  other 
things  than  our  own  subjective  feelings,  for  which  we  have  the  same  guar- 
antee— which  are,  in  a similar  manner,  invariable  and  necessary.  With  re- 
gard to  these  other  beliefs,  they  can  not  be  necessary,  since  they  do  not  al- 
ways exist.  There  have  been,  and  are,  many  persons  who  do  not  believe 
the  reality  of  an  external  world,  still  less  the  reality  of  extension  and  figure 
as  the  forms  of  that  external  world  ; who  do  not  believe  that  space  and  time 
have  an  existence  independent  of  the  mind — nor  anyr  other  of  Mr.  Spencer’s 
objective  intuitions.  The  negations  of  these  alleged  invariable  beliefs  are 
not  unbelievable,  for  they  are  believed.  It  may  be  maintained,  without  ob- 
vious error,  that  we  can  not  imagine  tangible  objects  as  mere  states  of  our 
own  and  other  people’s  consciousness;  that  the  perception  of  them  irresist- 
ibly suggests  to  us  the  idea  of  something  external  to  ourselves  : and  I am 
not  in  a condition  to  say  that  this  is  not  the  fact  (though  I do  not  think 
any  one  is  entitled  to  affirm  it  of  any  person  besides  himself).  But  many 
thinkers  have  believed,  whether  they  could  conceive  it  or  not,  that  what  we 
represent  to  ourselves  as  material  objects,  are  mere  modifications  of  con- 
sciousness ; complex  feelings  of  touch  and  of  muscular  action.  Mr.  Spencer 
may  think  the  inference  correct  from  the  unimaginable  to  the  unbelievable, 
because  he  holds  that  belief  itself  is  but  the  persistence  of  an  idea,  and  that 
what  we  can  succeed  in  imagining  we  can  not  at  the  moment  help  appre- 
hending as  believable.  But  of  what  consequence  is  it  what  we  apprehend 
at  the  moment,  if  the  moment  is  in  contradiction  to  the  permanent  state  of 
our  mind  ? A person  who  has  been  frightened  when  an  infant  by  stories 
of  ghosts,  though  he  disbelieves  them  in  after  years  (and  perhaps  never  be- 
lieved them),  may  be  unable  all  his  life  to  be  in  a dark  place,  in  circum- 
stances stimulating  to  the  imagination,  without  mental  discomposure.  The 
idea  of  ghosts,  with  all  its  attendant  terrors,  is  irresistibly  called  up  in  his 
mind  by  the  outward  circumstances.  Mr.  Spencer  may  say,  that  while  he 

* Mr.  Spencer  makes  a distinction  between  conceiving  myself  looking  into  darkness,  and 
conceiving  that  1 am  then  and  there  looking  into  darkness.  To  me  it  seems  that  this  change 
of  the  expression  to  the  form  I am , just  marks  the  transition  from  conception  to  belief,  and 
that  the  phrase  “to  conceive  that  I am,"  or  “that  any  thing  is,"  is  not  consistent  with  using 
the  word  conceive  in  its  rigorous  sense. 


THEORIES  CONCERNING  AXIOMS. 


201 


is  under  the  influence  of  this  terror  he  does  not  disbelieve  in  ghosts,  but 
has  a temporary  and  uncontrollable  belief  in  them.  Be  it  so ; but  allowing 
it  to  be  so,  which  would  it  be  truest  to  say  of  this  man  on  the  whole — that 
he  believes  in  ghosts,  or  that  he  does  not  believe  in  them  ? Assuredly  that 
he  does  not  believe  in  them.  The  case  is  similar  with  those  who  disbelieve 
a material  world.  Though  they  can  not  get  rid  of  the  idea ; though  while 
looking  at  a solid  object  they  can  not  help  having  the  conception,  and  there- 
fore, according  to  Mr.  Spencer’s  metaphysics,  the  momentary  belief,  of  its 
externality ; even  at  that  moment  they  would  sincerely  deny  holding  that 
belief : and  it  would  be  incorrect  to  call  them  other  than  disbelievers  of  the 
doctrine.  The  belief  therefore  is  not  invariable ; and  the  test  of  inconceiv- 
ableness fails  in  the  only  cases  to  which  there  could  ever  be  any  occasion  to 
apply  it. 

That  a thing  may  be  perfectly  believable,  and  yet  may  not  have  become 
conceivable,  and  that  we  may  habitually  believe  one  side  of  an  alternative, 
and  conceive  only  in  the  other,  is  familiarly  exemplified  in  the  state  of  mind 
of  educated  persons  respecting  sunrise  and  sunset.  All  educated  persons 
either  know  by  investigation,  or  believe  on  the  authority  of  science,  that 
it  is  the  earth  and  not  the  sun  which  moves : but  there  are  probably  few 
who  habitually  conceive  the  phenomenon  otherwise  than  as  the  ascent  or 
descent  of  the  sun.  Assuredly  no  one  can  do  so  without  a prolonged  trial; 
and  it  is  probably  not  easier  now  than  in  the  first  generatiQn  after  Coper- 
nicus. Mr.  Spencer  does  not  say,  “ In  looking  at  sunrise  it  is  impossible 
not  to  conceive  that  it  is  the  sun  which  moves,  therefore  this  is  what  every 
body  believes,  and  we  have  all  the  evidence  for  it  that  we  can  have  for  any 
truth.”  Yet  this  would  be  an  exact  parallel  to  his  doctrine  about  the  belief 
in  matter. 

The  existence  of  matter,  and  other  Yount  ena,  as  distinguished  from  the 
phenomenal  world,  remains  a question  of  argument,  as  it  was  before  ; and 
the  very  general,  but  neither  necessary  nor  universal,  belief  in  them,  stands 
as  a psychological  phenomenon  to  be  explained,  either  on  the  hypothesis  of 
its  truth,  or  on  some  other.  The  belief  is  not  a conclusive  proof  of  its  own 
truth,  unless  there  are  no  such  things  as  iclola  tribus  • but  being  a fact,  it 
calls  on  antagonists  to  show,  from  what  except  the  real  existence  of  the 
thing  believed,  so  general  and  apparently  spontaneous  a belief  can  have 
originated.  And  its  opponents  have  never  hesitated  to  accept  this  chal- 
lenge.* The  amount  of  their  success  in  meeting  it  will  probably  deter- 
mine the  ultimate  verdict  of  philosophers  on  the  question. 

§ 4.  In  the  revision,  or  rather  reconstruction,  of  his  “Principles  of  Psy- 
chology,” as  one  of  the  stages  or  platforms  in  the  imposing  structure  of 
his  System  of  Philosophy,  Mr.  Spencer  has  resumed  what  he  justly  termsf 
the  “ amicable  controversy  that  has  been  long  pending  between  us ;”  ex- 
pressing at  the  same  time  a regret,  which  I cordially  share,  that  “this 
lengthened  exposition  of  a single  point  of  difference,  unaccompanied  by 
an  exposition  of  the  numerous  points  of  concurrence,  unavoidably  produces 
an  appearance  of  dissent  very  far  greater  than  that  which  exists.”  I be- 
lieve, with  Mr.  Spencer,  that  the  difference  between  us,  if  measured  by  our 
conclusions,  is  “ superficial  rather  than  substantial ;”  and  the  value  I attach 
to  so  great  an  amount  of  agreement,  in  the  field  of  analytic  psychology, 

* I have  myself  accepted  the  contest,  and  fought  it  out  on  this  battle-ground,  in  the  eleventh 
chapter  of  An  Examination  of  Sir  William  Hamilton's  Philosophy. 

f Chap.  xi. 


202 


REASONING. 


with  a thinker  of  his  force  and  depth,  is  such  as  I can  hardly  overstate. 
But  I also  agree  with  him  that  the  difference  which  exists  in  our  premises 
is  one  of  “ profound  importance,  philosophically  considered;”  and  not  to 
be  dismissed  while  any  part  of  the  case  of  either  of  us  has  not  been  fully 
examined  and  discussed. 

In  h is  present  statement  of  the  Universal  Postulate,  Mr.  Spencer  has  ex- 
changed his  former  expression,  “ beliefs  which  invariably  exist,”  for  the 
following:  “cognitions  of  which  the  predicates  invariably  exist  along  with 
their  subjects.”  And  he  says  that  “an  abortive  effort  to  conceive  the  ne- 
gation of  a proposition,  shows  that  the  cognition  expressed  is  one  of  which 
the  predicate  invariably  exists  along  with  its  subject ; and  the  discovery 
that  the  predicate  invariably  exists  along  with  its  subject,  is  the  discovery 
that  this  cognition  is  one  we  are  compelled  to  accept.”  Both  these  prem- 
ises of  Mr.  Spencer’s  syllogism  I am  able  to  assent  to,  but  in  different  senses 
of  the  middle  term.  If  the  invariable  existence  of  the  predicate  along 
with  its  subject,  is  to  be  understood  in  the  most  obvious  meaning,  as  an 
existence  in  actual  Nature,  or  in  other  words,  in  our  objective,  or  sensa- 
tional, experience,  I of  course  admit  that  this,  once  ascertained,  compels  us 
to  accept  the  proposition  : but  then  I do  not  admit  that  the  failure  of  an  at- 
tempt to  conceive  the  negative,  proves  the  predicate  to  be  always  co-exist- 
ent with  the  subject  in  actual  Nature.  If,  on  the  other  hand  (which  I believe 
to  be  Mr.  Spencer’s  meaning)  the  invariable  existence  of  the  predicate  along 
with  the  subject  is  to  be  understood  only  of  our  conceptive  faculty,  i.  e., 
that  the  one  is  inseparable  from  the  other  in  our  thoughts ; then,  indeed, 
the  inability  to  separate  the  two  ideas  proves  their  inseparable  conjunc- 
tion, here  and  now,  in  the  mind  which  has  failed  in  the  attempt ; but  this 
inseparability  in  thought  does  not  prove  a corresponding  inseparability  in 
fact ; nor  even  in  the  thoughts  of  other  people,  or  of  the  same  person  in  a 
possible  future. 

“That  some  propositions  have  been  wrongly  accepted  as  true,  because 
their  negations  were  supposed  inconceivable  when  they  were  not,”  does 
not,  in  Mr.  Spencer’s  opinion,  “disprove  the  validity  of  the  test not  only 
because  any  test  whatever  “ is  liable  to  yield  untrue  results,  either  from  in- 
capacity or  from  carelessness  in  those  who  use  it,”  but  because  the  propo- 
sitions in  question  “ were  complex  propositions,  not  to  be  established  by  a 
test  applicable  to  propositions  no  further  decomposable.”  “ A test  legiti- 
mately applicable  to  a simple  proposition,  the  subject  and  predicate  of  which 
are  in  direct  relation,  can  not  be  legitimately  applied  to  a complex  proposi- 
tion, the  subject  and  predicate  of  which  are  indirectly  related  through  the 
many  simple  propositions  implied.”  “ That  things  which  are  equal  to  the 
same  thing  are  equal  to  one  another,  is  a fact  which  can  be  known  by  di- 
rect comparison  of  actual  or  ideal  relations But  that  the  square  of 

the  hypothenuse  of  a right-angled  triangle  equals  the  sum  of  the  squares 
of  the  other  two  sides,  can  not  be  known  immediately  by  comparison  of 
two  states  of  consciousness  : here  the  truth  can  be  reached  oidy  mediately, 
through  a series  of  simple  judgments  respecting  the  likenesses  or  unlike- 
nesses of  certain  relations.”  Moreover,  even  when  the  proposition  admits 
of  being  tested  by  immediate  consciousness,  people  often  neglect  to  do  it. 
A school-boy,  in  adding  up  a column  of  figures,  will  say  “ 35  and  9 are  46,” 
though  this  is  contrary  to  the  verdict  which  consciousness  gives  when  35 
and  9 are  really  called  up  before  it ; but  this  is  not  done.  And  not  only 
school-boys,  but  men  and  thinkers,  do  not  always  “ distinctly  translate  into 
their  equivalent  states  of  consciousness  the  words  they  use.” 


THEORIES  CONCERNING  AXIOMS. 


203 


It  is  but  just  to  give  Mr.  Spencer’s  doctrine  the  benefit  of  tbe  limitation 
lie  claims — viz.,  that  it  is  only  applicable  to  propositions  which  are  assented 
to  on  simple  inspection,  without  any  intervening  media  of  proof.  But  this 
limitation  does  not  exclude  some  of  the  most  marked  instances  of  proposi- 
tions now  known  to  be  false  or  groundless,  but  whose  negative  was  once 
found  inconceivable : such  as,  that  in  sunrise  and  sunset  it  is  the  sun  which 
moves;  that  gravitation  may  exist  without  an  intervening  medium;  and 
even  the  case  of  antipodes.  The  distinction  drawn  by  Mr.  Spencer  is  real ; 
but,  in  the  case  of  the  propositions  classed  by  him  as  complex,  conscious- 
ness, until  the  media  of  proof  are  supplied,  gives  no  verdict  at  all:  it  nei- 
ther declares  the  equality  of  the  square  of  the  hypothenuse  with  the  sum 
of  the  squares  of  the  sides  to  be  inconceivable,  nor  their  inequality  to  be 
inconceivable.  But  in  all  the  three  cases  which  I have  just  cited,  the  in- 
conceivability seems  to  be  apprehended  directly ; no  train  of  argument  was 
needed,  as  in  the  case  of  the  square  of  the  hypothenuse,  to  obtain  the  ver- 
dict of  consciousness  on  the  point.  Neither  is  any  of  the  three  a case  like 
that  of  the  school-boy’s  mistake,  in  which  the  mind  was  never  really  brought 
into  contact  with  the  proposition.  They  are  cases  in  which  one  of  two  op- 
posite predicates,  mero  adspectu,  seemed  to  be  incompatible  with  the  sub- 
ject, and  the  other,  therefore,  to  be  proved  always  to  exist  with  it.* 

As  now  limited  by  Mr.  Spencer,  the  ultimate  cognitions  fit  to  be  suomit- 
ted  to  his  test  are  only  those  of  so  universal  and  elementary  a character  as 
to  be  represented  in  the  earliest  and  most  unvarying  experience,  or  appar- 
ent experience,  of  all  mankind.  In  such  cases  the  inconceivability  of  the 
negative,  if  real,  is  accounted  for  by  the  experience : and  why  (I  have  ask- 
ed) should  the  truth  be  tested  by  the  inconceivability,  when  we  can  go  fur- 
ther back  for  proof — namely,  to  the  experience  itself?  To  this  Mr.  Spen- 
cer answers,  that  the  experiences  can  not  be  all  recalled  to  mind,  and  if  re- 
called, would  be  of  unmanageable  multitude.  To  test  a proposition  by  ex- 
perience seems  to  him  to  mean  that  “ before  accepting  as  certain  the  prop- 
osition that  any  rectilineal  figure  must  have  as  many  angles  as  it  has  sides,” 
I have  “ to  think  of  every  triangle,  square,  pentagon,  hexagon,  etc.,  which  I 
have  ever  seen,  and  to  verify  the  asserted  relation  in  each  case.”  I can 
only  say,  with  surprise,  that  I do  not  understand  this  to  be  the  meaning  of 
an  appeal  to  experience.  It  is  enough  to  know  that  one  has  been  seeing 
the  fact  all  one’s  life,  and  has  never  remarked  any  instance  to  the  contrary, 
and  that  other  people,  with  every  opportunity  of  observation,  unanimously 
declare  the  same  thing.  It  is  true,  even  this  experience  may  be  insufficient, 
and  so  it  might  be  even  if  I could  recall  to  mind  every  instance  of  it;  but 

* In  one  of  the  three  cases,  Mr.  Spencer,  to  my  no  small  surprise,  thinks  that  the  belief  of 
mankind  “can  not  be  rightly  said  to  have  undergone”  the  change  I allege.  Mr.  Spencer 
himself  still  thinks  we  are  unable  to  conceive  gravitation  acting  through  empty  space.  “If 
an  astronomer  avowed  that  he  could  conceive  gravitative  force  as  exercised  through  space  ab- 
solutely void,  my  private  opinion  would  be  that  he  mistook  the  nature  of  conception.  Con- 
ception implies  representation.  Here  the  elements  of  the  representation  are  the  two  bodies 
and  an  agency  by  which  either  affects  the  other.  To  conceive  this  agency  is  to  represent  it 
in  some  terms  derived  from  our  experiences — that  is,  from  our  sensations.  As  this  agency 
gives  us  no  sensations,  we  are  obliged  (if  we  try  to  conceive  it)  to  use  symbols  idealized  from 
our  sensations — imponderable  units  forming  a medium.” 

If  Mr.  Spencer  means  that  the  action  of  gravitation  gives  us  no  sensations,  the  assertion  is 
one  than  which  I have  not  seen,  in  the  writings  of  philosophers,  many  more  startling.  What 
other  sensation  do  we  need  than  the  sensation  of  one  body  moving  toward  another?  “The 
elements  of  the  representation”  are  not  two  bodies  and  an  “agency,”  but  two  bodies  and  an 
effect ; viz.,  the  fact  of  their  approaching  one  auother.  If  we  are  able  to  conceive  a vacuum, 
is  there  any  difficulty  in  conceiving  a body  falling  to  the  earth  through  it? 


204 


REASONING. 


its  insufficiency,  instead  of  being'  brought  to  light,  is  disguised,  if  instead  of 
sifting  the  experience  itself,  I appeal  to  a test  which  bears  no  relation  to 
the  sufficiency  of  the  experience,  but,  at  the  most,  only  to  its  familiarity. 
These  remarks  do  not  lose  their  force  even  if  we  believe,  with  Mr.  Spencer, 
that  mental  tendencies  originally  derived  from  experience  impress  them- 
selves permanently  on  the  cerebral  structure  and  are  transmitted  by  inher- 
itance, so  that  modes  of  thinking  which  are  acquired  by  the  race  become 
innate  and  a priori  in  the  individual,  thus  representing,  in  Mr.  Spencer’s 
opinion,  the  experience  of  his  progenitors,  in  addition  to  his  own.  All  that 
would  follow  from  this  is,  that  a conviction  might  be  really  innate,  i.  e.,  prior 
to  individual  experience,  and  yet  not  be  true,  since  the  inherited  tendency 
to  accept  it  may  have  been  originally  the  result  of  other  causes  than  its 
truth. 

Mr.  Spencer  would  have  a much  stronger  case,  if  he  could  really  show 
that  the  evidence  of  Reasoning  rests  on  the  Postulate,  or,  in  other  words, 
that  we  believe  that  a conclusion  follows  from  premises  only  because  we 
can  not  conceive  it  not  to  follow.  But  this  statement  seems  to  me  to  be 
of  the  same  kind  as  one  I have  previously  commented  on,  viz.,  that  I believe 
I see  light,  because  I can  not,  while  the  sensation  remains,  conceive  that  I 
am  looking  into  darkness.  Both  these  statements  seem  to  me  incompatible 
with  the  meaning  (as  very  rightly  limited  by  Mr.  Spencer)  of  the  verb  to 
conceive.  To  say  that  when  I apprehend  that  A is  B and  that  B is  C,  I 
can  not  conceive  that  A is  not  C,  is  to  my  mind  merely  to  say  that  I am 
compelled  to  believe  that  A is  C.  If  to  conceive  be  taken  in  its  proper 
meaning,  viz.,  to  form  a mental  representation,  I may  be  able  to  conceive  A 
as  not  being  C.  After  assenting,  with  full  understanding,  to  the  Coperni- 
can  proof  that  it  is  the  earth  and  not  the  sun  that  moves,  I not  only  can 
conceive,  or  represent  to  myself,  sunset  as  a motion  of  the  sun,  but  almost 
every  one  finds  this  conception  of  sunset  easier  to  form,  than  that  which 
they  nevertheless  know  to  be  the  true  one. 

§ 5.  Sir  William  Hamilton  holds  as  I do,  that  inconceivability  is  no  criteri- 
on of  impossibility.  “ There  is  no  ground  for  inferring  a certain  fact  to  be 
impossible,  merely  from  our  inability  to  conceive  its  possibility.”  “ Things 
there  are  which  may,  nay  must , be  true,  of  which  the  understanding  is 
wholly  unable  to  construe  to  itself  the  possibility.”*  Sir  William  Hamil- 
ton is,  however,  a firm  believer  in  the  a priori  character  of  many  axioms, 
and  of  the  sciences  deduced  from  them ; and  is  so  far  from  considering 
those  axioms  to  rest  on  the  evidence  of  experience,  that  he  declares  certain 
of  them  to  be  true  even  of  Noumena — of  the  Unconditioned — of  which  it 
is  one  of  the  principal  aims  of  his  philosophy  to  prove  that  the  nature  of 
our  faculties  debars  us  from  having  any  knowledge.  The  axioms  to  which 
he  attributes  this  exceptional  emancipation  from  the  limits  which  confine 
all  our  other  possibilities  of  knowledge;  the  chinks  through  which,  as  he 
represents,  one  ray  of  light  finds  its  way  to  us  from  behind  the  curtain 
which  veils  from  us  the  mysterious  world  of  Things  in  themselves — are 
the  two  principles,  which  he  terms,  after  the  school-men,  the  Principle  of 
Contradiction,  and  the  Principle  of  Excluded  Middle : the  first,  that  two 
contradictory  propositions  can  not  both  be  true;  the  second,  that  they  can 
not  both  be  false.  Armed  with  these  logical  weapons,  we  may  boldly  face 
Things  in  themselves,  and  tender  to  them  the  double  alternative,  sure  that 


* Discussions,  etc.,  2d  ed.,  p.  624. 


THEORIES  CONCERNING  AXIOMS. 


205 


they  must  absolutely  elect  one  or  the  other  side,  though  we  may  be  forever 
precluded  from  discovering  which.  To  take  his  favorite  example,  we  can 
not  conceive  the  infinite  divisibility  of  matter,  and  we  can  not  conceive  a 
minimum,  or  end  to  divisibility : yet  one  or  the  other  must  be  true. 

As  I have  hitherto  said  nothing  of  the  two  axioms  in  question,  those  of 
Contradiction  and  of  Excluded  Middle,  it  is  not  unseasonable  to  consider 
them  here.  The  former  asserts  that  an  affirmative  proposition  and  the  cor- 
responding negative  proposition  can  not  both  be  true ; which  has  generally 
been  held  to  be  intuitively  evident.  Sir  William  Hamilton  and  the  Ger- 
mans consider  it  to  be  the  statement  in  words  of  a form  or  law  of  our 
thinking  faculty.  Other  philosophers,  not  less  deserving  of  consideration, 
deem  it  to  be  an  identical  proposition ; an  assertion  involved  in  the  mean- 
ing of  terms;  a mode  of  defining  Negation,  and  the  word  Not. 

I am  able  to  go  one  step  with  these  last.  An  affirmative  assertion  and 
its  negative  are  not  two  independent  assertions,  connected  with  each  other 
only  as  mutually  incompatible.  That  if  the  negative  be  true,  the  affirmative 
must  be  false,  really  is  a mere  identical  proposition ; for  the  negative  prop- 
osition asserts  nothing  but  the  falsity  of  the  affirmative,  and  has  no  other 
sense  or  meaning  whatever.  The  Principium  Contradictionis  should  there- 
fore put  off  the  ambitious  phraseology  which  gives  it  the  air  of  a funda- 
mental antithesis  pervading  nature,  and  should  be  enunciated  in  the  simpler 
form,  that  the  same  proposition  can  not  at  the  same  time  be  false  and  true. 
But  I can  go  no  further  with  the  Nominalists ; for  I can  not  look  upon  this 
last  as  a merely  verbal  proposition.  I consider  it  to  be,  like  other  axioms, 
one  of  our  first  and  most  familiar  generalizations  from  experience.  The 
original  foundation  of  it  I take  to  be,  that  Belief  and  Disbelief  are  two  dif- 
ferent mental  states,  excluding  one  another.  This  we  know  by  the  simplest 
observation  of  our  own  minds.  And  if  we  carry  our  observation  outward, 
we  also  find  that  light  and  darkness,  sound  and  silence,  motion  and  quies- 
cence, equality  and  inequality,  preceding  and  following,  succession  and  si- 
multaneousness, any  positive  phenomenon  whatever  and  its  negative,  are 
distinct  phenomena,  pointedly  contrasted,  and  the  one  always  absent  where 
the  other  is  present.  I consider  the  maxim  in  question  to  be  a generaliza- 
tion from  all  these  facts. 

In  like  manner  as  the  Principle  of  Contradiction  (that  one  of  two  contra- 
dictories must  be  false)  means  that  an  assertion  can  not  be  both  true  and 
false,  so  the  Principle  of  Excluded  Middle,  or  that  one  of  two  contradic- 
tories must  be  true,  means  that  an  assertion  must  be  either  true  or  false : 
either  the  affirmative  is  true,  or  otherwise  the  negative  is  true,  which  means 
that  the  affirmative  is  false,  I can  not  help  thinking  this  principle  a sur- 
prising specimen  of  a so-called  necessity  of  Thought,  since  it  is  not  even 
true,  unless  with  a large  qualification.  A jiroposition  must  be  either  true 
or  false,  provided  that  the  predicate  be  one  which  can  in  any  intelligible 
sense  be  attributed  to  the  subject;  (and  as  this  is  always  assumed  to  be  the 
case  in  treatises  on  logic,  the  axiom  is  always  laid  down  there  as  of  absolute 
truth).  “Abracadabra  is  a second  intention”  is  neither  true  nor  false.  Be- 
tween the  true  and  the  false  there  is  a third  possibility,  the  Unmeaning: 
and  this  alternative  is  fatal  to  Sir  William  Hamilton’s  extension  of  the  max- 
im to  Noumena.  That  Matter  must  either  have  a minimum  of  divisibility 
or  be  infinitely  divisible,  is  more  than  we  can  ever  know.  For  in  the  first 
place,  Matter,  in  any  other  than  the  phenomenal  sense  of  the  term,  may  not 
exist : and  it  will  scarcely  be  said  that  a nonentity  must  be  either  infinite- 
ly or  finitely  divisible.  In  the  second  place,  though  matter,  considered  as 


206 


REASONING. 


the  occult  cause  of  our  sensations,  do  really  exist,  yet  what  we  call  divisi- 
bility may  be  an  attribute  only  of  our  sensations  of  sight  and  touch,  and 
not  of  their  uncognizable  cause.  Divisibility  may  not  be  predicable  at  all, 
in  any  intelligible  sense,  of  Things  in  themselves,  nor  therefore  of  Matter 
in  itself ; and  the  assumed  necessity  of  being  either  infinitely  or  finitely  di- 
visible, may  be  an  inapplicable  alternative. 

On  this  question  I am  happy  to  have  the  full  concurrence  of  Mr.  Herbert 
Spencer,  from  whose  paper  in  the  Fortnightly  Review  I extract  the  follow- 
ing passage.  The  germ  of  an  idea  identical  with  that  of  Mr.  Spencer  may 
be  found  in  the  present  chapter,  on  a preceding  page ; but  in  Mr.  Spencer 
it  is  not  an  undeveloped  thought,  but  a philosophical  theory. 

“When  remembering  a certain  thing  as  in  a certain  place,  the  place  and 
the  thing  are  mentally  represented  together ; while  to  think  of  the  non-ex- 
istence of  the  thing  in  that  place  implies  a consciousness  in  which  the  place 
is  represented,  but  not  the  thing.  Similarly,  if  instead  of  thinking  of  an 
object  as  colorless,  we  think  of  its  having  color,  the  change  consists  in  the 
addition  to  the  concept  of  an  element  that  was  before  absent  from  it — the 
object  can  not  be  thought  of  first  as  red  and  then  as  not  red,  without  one 
component  of  the  thought  being  totally  expelled  from  the  mind  by  another. 
The  law  of  the  Excluded  Middle,  then,  is  simply  a generalization  of  the  uni- 
versal experience  that  some  mental  states  are  directly  destructive  of  other 
states.  It  formulates  a certain  absolutely  constant  law,  that  the  appearance 
of  any  positive  mode  of  consciousness  can  not  occur  without  excluding  a 
correlative  negative  mode ; and  that  the  negative  mode  can  not  occur  with- 
out excluding  the  correlative  positive  mode : the  antithesis  of  positive  and 
negative  being,  indeed,  merely  an  expression  of  this  experience.  Hence  it 
follows  that  if  consciousness  is  not  in  one  of  the  two  modes  it  must  be  in 
the  other.”* 

I must  here  close  this  supplementary  chapter,  and  with  it  the  Second 
Book.  The  theory  of  Induction,  in  the  most  comprehensive  sense  of  the 
term,  will  form  the  subject  of  the  Third. 

* Professor  Bain  {Logic,  i.,  10)  identifies  the  Principle  of  Contradiction  with  his  Law  of 
Relativity,  viz.,  that  “ every  thing  that  can  be  thought  of,  every  affirmation  that  can  be  made, 
has  an  opposite  or  counter  notion  or  affirmation a proposition  which  is  one  of  the  general 
results  of  the  whole  body  of  human  experience.  For  further  considerations  respecting  the 
axioms  of  Contradiction  and  Excluded  Middle,  see  the  twenty-first  chapter  of  An  Examina- 
tion of  Sir  William  Hamilton's  Philosophy. 


BOOK  III. 

OF  INDUCTION. 


“According  to  the  doctrine  now  stated,  the  highest,  or  rather  the  only  proper  object  of 
physics,  is  to  ascertain  those  established  conjunctions  of  successive  events,  which  constitute 
the  order  of  the  universe ; to  record  the  phenomena  which  it  exhibits  to  our  observations,  or 
which  it  discloses  to  our  experiments  ; and  to  refer  these  phenomena  to  their  general  laws.” 
— It.  Stewart,  Elements  of  the  Philosoj>hy  of  the  Human  Mind,  vol.  ii. , chap,  iv.,  sect.  1. 

“In  such  cases  the  inductive  and  deductive  methods  of  inquiry  may  be  said  to  go  hand  in 
hand,  the  one  verifying  the  conclusions  deduced  by  the  other ; and  the  combination  of  experi- 
ment and  theory,  which  may  thus  be  brought  to  bear  in  such  cases,  forms  an  engine  of  dis- 
covery infinitely  more  powerful  than  either  taken  separately.  This  state  of  any  department 
of  science  is  perhaps  of  all  others  the  most  interesting,  and  that  which  promises  the  most  to 
research.” — Sir  J.  Herschel,  Discourse  on  the  Study  of  Natural  Philosophy . 


CHAPTER  I. 

PRELIMINARY  OBSERVATIONS  ON  INDUCTION  IN  GENERAL. 

§ 1.  The  portion  of  the  present  inquiry  upon  which  we  are  now  about 
to  enter,  may  be  considered  as  the  principal,  both  from  its  surpassing  in 
intricacy  all  the  other  branches,  and  because  it  relates  to  a process  which 
has  been  shown  in  the  preceding  Book  to  be  that  in  which  the  investiga- 
tion of  nature  essentially  consists.  We  have  found  that  all  Inference,  con- 
sequently all  Proof,  and  all  discovery  of  truths  not  self-evident,  consists  of 
inductions,  and  the  interpretation  of  inductions  ; • that  all  our  knowledge, 
not  intuitive,  comes  to  us  exclusively  from  that  source.  What  Induction 
is,  therefore,  and  what  conditions  render  it  legitimate,  can  not  but  be  deem- 
ed the  main  question  of  the  science  of  logic — the  question  which  includes 
all  others.  It  is,  however,  one  which  professed  writers  on  logic  have  al- 
most entirely  passed  over.  The  generalities  of  the  subject  have  not  been 
altogether  neglected  by  metaphysicians ; but,  for  want  of  sufficient  ac- 
quaintance with  the  processes  by  which  science  has  actually  succeeded  in 
establishing  general  truths,  their  analysis  of  the  inductive  operation,  even 
when  unexceptionable  as  to  correctness,  has  not  been  specific  enough  to  be 
made  the  foundation  of  practical  rules,  which  might  be  for  induction  itself 
what  the  rules  of  the  syllogism  are  for  the  interpretation  of  induction : 
while  those  by  whom  physical  science  has  been  carried  to  its  present  state 
of  improvement — and  who,  to  arrive  at  a complete  theory  of  the  process, 
needed  only  to  generalize,  and  adapt  to  all  varieties  of  problems,  the  meth- 
ods which  they  themselves  employed  in  their  habitual  pursuits — never  un- 
til very  lately  made  any  serious  attempt  to  philosophize  on  the  subject,  nor 
regarded  the  mode  in  which  they  arrived  at  their  conclusions  as  deserving 
of  study,  independently  of  the  conclusions  themselves. 


INDUCTION. 


208 

§ 2.  For  the  purposes  of  the  present  inquiry,  Induction  may  be  defined, 
the  operation  of  discovering  and  proving  general  propositions.  It  is  true 
that  (as  already  shown)  the  process  of  indirectly  ascertaining  individual 
facts,  is  as  truly  inductive  as  that  by  which  we  establish  general  truths. 
But  it  is  not  a different  kind  of  induction  ; it  is  a form  of  the  very  same 
process : since,  on  the  one  hand,  generals  are  but  collections  of  particulars, 
definite  in  kind  but  indefinite  in  number ; and  on  the  other  hand,  whenever 
the  evidence  which  we  derive  from  observation  of  known  cases  justifies  us 
in  drawing  an  inference  respecting  even  one  unknown  case,  we  should  on 
the  same  evidence  be  justified  in  drawing  a similar  inference  with  respect 
to  a whole  class  of  cases.  The  inference  either  does  not  hold  at  all,  or  it 
holds  in  all  cases  of  a certain  description ; in  all  cases  which,  in  certain  de- 
finable respects,  resemble  those  we  have  observed. 

If  these  remarks  are  just;  if  the  principles  and  rules  of  inference  are  the 
same  whether  we  infer  general  propositions  or  individual  facts;  it  follows 
that  a complete  logic  of  the  sciences  would  be  also  a complete  logic  of  prac- 
tical business  and  common  life.  Since  there  is  no  case  of  legitimate  infer- 
ence from  experience,  in  which  the  conclusion  may  not  legitimately  be  a 
general  proposition ; an  analysis  of  the  process  by  which  general  truths  are 
arrived  at,  is  virtually  an  analysis  of  all  induction  whatever.  Whether  we 
are  inquiring  into  a scientific  principle  or  into  an  individual  fact,  and  wheth- 
er we  proceed  by  experiment  or  by  ratiocination,  every  step  in  the  train  of 
inferences  is  essentially  inductive,  and  the  legitimacy  of  the  induction  de- 
pends in  both  cases  on  the  same  conditions. 

True  it  is  that  in  the  case  of  the  practical  inquirer,  who  is  endeavoring 
to  ascertain  facts  not  for  the  purposes  of  science  but  for  those  of  business, 
such, for  instance,  as  the  advocate  or  the  judge,  the  chief  difficulty  is  one  in 
which  the  principles  of  induction  will  afford  him  no  assistance.  It  lies  not 
in  making  his  inductions,  but  in  the  selection  of  them;  in  choosing  from 
among  all  general  propositions  ascertained  to  be  true,  those  which  furnish 
marks  by  which  he  may  trace  whether  the  given  subject  possesses  or  not 
the  predicate  in  question.  In  arguing  a doubtful  question  of  fact  before 
a jury,  the  general  propositions  or  principles  to  which  the  advocate  ap- 
peals are  mostly,  in  themselves,  sufficiently  trite,  and  assented  to  as  soon  as 
stated  : his  skill  lies  in  bringing  his  case  under  those  propositions  or  princi- 
ples; in  calling  to  mind  such  of  the  known  or  received  maxims  of  probabil- 
ity as  admit  of  application  to  the  case  in  hand,  and  selecting  from  among 
them  those  best  adapted  to  his  object.  Success  is  here  dependent  on  nat- 
ural or  acquired  sagacity,  aided  by  knowledge  of  the  particular  subject,  and 
of  subjects  allied  with  it.  Invention,  though  it  can  be  cultivated,  can  not 
be  reduced  to  rule ; there  is  no  science  which  will  enable  a man  to  bethink 
himself  of  that  which  will  suit  his  purpose. 

But  when  he  has  thought  of  something,  science  can  tell  him  whether 
that  which  he  has  thought  of  will  suit  his  purpose  or  not.  The  inquirer 
or  arguer  must  be  guided  by  his  own  knowledge  and  sagacity  in  the  choice 
of  the  inductions  out  of  which  he  will  construct  his  argument.  But  the 
validity  of  the  argument  when  constructed,  depends  on  principles,  and  must 
be  tried  by  tests  which  are  the  same  for  all  descriptions  of  inquiries, 
whether  the  result  be  to  give  A an  estate,  or  to  enrich  science  with  a new 
general  truth.  In  the  one  case  and  in  the  other,  the  senses,  or  testimony, 
must  decide  on  the  individual  facts;  the  rules  of  the  syllogism  will  deter- 
mine whether,  those  facts  being  supposed  correct,  the  case  really  falls  with- 
in the  formulae  of  the  different  inductions  under  which  it  has  been  succes- 


INDUCTION  IN  GENEEAL. 


209 


sively  brought;  and  finally,  the  legitimacy  of  the  inductions  themselves 
must  be  decided  by  other  rules,  and  these  it  is  now  our  purpose  to  investi- 
gate. If  this  third  part  of  the  operation  be,  in  many  of  the  questions  of 
practical  life,  not  the  most,  but  the  least  arduous  portion  of  it,  we  have 
seen  that  this  is  also  the  case  in  some  great  departments  of  the  field  of  sci- 
ence ; in  all  those  which  are  principally  deductive,  and  most  of  all  in  math- 
ematics; where  the  inductions  themselves  are  few  in  number,  and  so  obvi- 
ous and  elementary  that  they  seem  to  stand  in  no  need  of  the  evidence  of 
experience,  while  to  combine  them  so  as  to  prove  a given  theorem  or  solve 
a problem,  may  call  for  the  utmost  powers  of  invention  and  contrivance 
with  which  our  species  is  gifted. 

If  the  identity  of  the  logical  processes  which  prove  particular  facts  and 
those  which  establish  general  scientific  truths,  required  any  additional  con- 
firmation, it  would  be  sufficient  to  consider  that  in  many  branches  of  sci- 
ence, single  facts  have  to  be  proved,  as  well  as  principles ; facts  as  com- 
pletely individual  as  any  that  are  debated  in  a court  of  justice;  but  which 
are  proved  in  the  same  manner  as  the  other  truths  of  the  science,  and  with- 
out disturbing  in  any  degree  the  homogeneity  of  its  method.-  A remark- 
able example  of  this  is  afforded  by  astronomy.  The  individual  facts  on 
which  that  science  grounds  its  most  important  deductions,  such  facts  as 
the  magnitudes  of  the  bodies  of  the  solar  system,  their  distances  from  one 
another,  the  figure  of  the  earth,  and  its  rotation,  are  scarcely  any  of  them 
accessible  to  our  means  of  direct  observation  : they  are  proved  indirectly, 
by  the  aid  of  inductions  founded  on  other  facts  which  we  can  more  easily 
reach.  For  example,  the  distance  of  the  moon  from  the  earth  was  deter- 
mined by  a very  circuitous  process.  The  share  which  direct  observation 
had  in  the  work  consisted  in  ascertaining,  at  one  and  the  same  instant,  the 
zenith  distances  of  the  moon,  as  seen  from  two  points  very  remote  from 
one  another  on  the  earth’s  surface.  The  ascertainment  of  these  angular 
distances  ascertained  their  supplements;  and  since  the  angle  at  the  earth’s 
centre  subtended  by  the  distance  between  the  two  places  of  observation 
was  deducible  by  spherical  trigonometry  from  the  latitude  and  longi- 
tude of  those  places,  the  angle  at  the  moon  subtended  by  the  same  line 
became  the  fourth  angle  of  a quadrilateral  of  which  the  other  three 
angles  were  known.  The  four  angles  being  thus  ascertained,  and  two 
sides  of  the  quadrilateral  being  radii  of  the  earth ; the  two  remaining 
sides  and  the  diagonal,  or,  in  other  words,  the  moon’s  distance  from  the 
two  places  of  observation  and  from  the  centre  of  the  earth,  could  be  as- 
certained, at  least  in  terms  of  the  earth’s  radius,  from  elementary  theo- 
rems of  geometry.  At  each  step  in  this  demonstration  a new  induction 
is  taken  in,  represented  in  the  aggregate  of  its  results  by  a general  propo- 
sition. 

Not  only  is  the  process  by  which  an  individual  astronomical,  fact  was 
thus  ascertained,  exactly  similar  to  those  by  which  the  same  science  estab- 
lishes its  general  truths,  but  also  (as  we  have  shown  to  be  the  case  in  all 
legitimate  reasoning)  a general  proposition  might  have  been  concluded  in- 
stead of  a single  fact.  In  strictness,  indeed,  the  result  of  the  reasoning  is 
a general  proposition ; a theorem  respecting  the  distance,  not  of  the  moon 
in  particular,  but  of  any  inaccessible  object;  showing  in  what  relation  that 
distance  stands  to  certain  other  quantities.  And  although  the  moon  is  al- 
most the  only  heavenly  body  the  distance  of  which  from  the  earth  can  real- 
ly be  thus  ascertained,  this  is  merely  owing  to  the  accidental  circumstances 
of  the  other  heavenly  bodies,  which  render  them  incapable  of  affording  such 

14 


210 


INDUCTION. 


data  as  the  application  of  the  theorem  requires ; for  the  theorem  itself  is 
as  true  of  them  as  it  is  of  the  moon.* 

We  shall  fall  into  no  error,  then,  if  in  treating  of  Induction,  we  limit  our 
attention  to  the  establishment  of  general  propositions.  The  principles  and 
rules  of  Induction  as  directed  to  this  end,  are  the  principles  and  rules  of 
all  Induction;  and  the  logic  of  Science  is  the  universal  Logic,  applicable  to 
all  inquiries  in  which  man  can  engage. 


CHAPTER  II. 

OP  INDUCTIONS  IMPROPERLY  SO  CALLED. 

§ 1.  Induction,  then,  is  that  operation  of  the  mind,  by  which  we  infer 
that  what  we  know  to  be  true  in  a particular  case  or  cases,  will  be  true  in 
all  cases  which  resemble  the  former  in  certain  assignable  respects.  In  other 
words,  Induction  is  the  process  by  which  we  conclude  that  what  is  true  of 
certain  individuals  of  a class  is  true  of  the  whole  class,  or  that  what  is  true 
at  certain  times  will  be  true  in  similar  circumstances  at  all  times. 

This  definition  excludes  from  the  meaning  of  the  term  Induction,  various 
logical  operations,  to  which  it  is  not  unusual  to  apply  that  name. 

Induction,  as  above  defined,  is  a process  of  inference;  it  proceeds  from 
the  known  to  the  unknown ; and  any  operation  involving  no  inference,  any 
process  in  which  what  seems  the  conclusion  is  no  wider  than  the  premises 
from  which  it  is  drawn,  does  not  fall  within  the  meaning  of  the  term.  Yet 

* Dr.  Whewell  thinks  it  improper  to  apply  the  term  Induction  to  any  operation  not  termi- 
nating in  the  establishment  of  a general  truth.  Induction,  he  says  ( Philosophy  of  Discovery, 
p.  215),  “is  not  the  sam:  thing  as  experience  and  observation.  Induction  is  experience  or 
observation  consciously  looked  at  in  a general  form.  This  consciousness  and  generality  are 
necessary  parts  of  that  knowledge  which  is  science.”  And  he  objects  (p.  241)  to  the  mode  in 
which  the  word  Induction  is  employed  in  this  work,  as  an  undue  extension  of  that  term  “not 
only  to  the  cases  in  which  the  general  induction  is  consciously  applied  to  a particular  in- 
stance, but  to  the  cases  in  which  the  particular  instance  is  dealt  with  by  means  of  experience 
in  that  rude  sense  in  which  experience  can  be  asserted  of  brutes,  and  in  which  of  course  we 
can  in  no  way  imagine  that  the  law  is  possessed  or  understood  as  a general  proposition.” 
This  use  of  the  term  he  deems  a “confusion  of  knowledge  with  practical  tendencies.” 

I disclaim*  as  strongly  as  Dr.  Whewell  can  do,  the  application  of  such  terms  as  induction, 
inference,  or  reasoning,  to  operations  performed  bv  mere  instinct,  that  is,  from  an  animal  im- 
pulse, without  the  exertion  of  any  intelligence.  But  I perceive  no  ground  for  confining  the 
use  of  those  terms  to  cases  in  which  the  inference  is  drawn  in  the  forms  and  with  the  precau- 
tions required  by  scientific  propriety.  To  the  idea  of  Science,  an  express  recognition  and 
distinct  apprehension  of  general  laws  as  such,  is  essential : but  nine-tenths  of  the  conclusions 
drawn  from  experience  in  the  course  of  practical  life,  are  drawn  without  any  such  recognition: 
they  are  direct  inferences  from  known  cases,  to  a case  supposed  to  be  similar.  I have  endeav- 
ored to  show  that  this  is  not  only  as  legitimate  an  operation,  but  substantially  tbe  same  oper- 
ation, as  that  of  ascending  from  known  cases  to  a general  proposition  ; except  that  the  latter 
process  has  one  great  security  for  correctness  which  the  former  does  not  possess.  In  science, 
the  inference  must  necessarily  pass  through  the  intermediate  stage  of  a general  proposition, 
because  Science  wants  its  conclusions  for  record,  and  not  for  instantaneous  use.  But  the  in- 
ferences drawn  for  the  guidance  of  practical  affairs,  by  persons  who  would  often  be  quite  in- 
capable of  expressing  in  unexceptionable  terms  the  corresponding  generalizations,  may  and 
frequently  do  exhibit  intellectual  powers  quite  equal  to  any  which  have  ever  been  displayed 
in  science;  and  if  these  inferences  are  not  inductive,  what  are  they?  The  limitation  imposed 
on  the  term  by  Dr.  Whewell  seems  perfectly  arbitrary;  neither  justified  by  any  fundamental 
distinction  between  what  he  includes  and  what  he  desires  to  exclude,  nor  sanctioned  by  usage, 
at  least  from  tbe  time  of  Ileid  and  Stewart,  the' principal  legislators  (as  far  as  the  English 
language  is  concerned)  of  modern  metaphysical  terminology. 


INDUCTIONS  IMPROPERLY  SO  CALLED. 


211 


in  the  common  books  of  Logic  we  find  this  laid  down  as  the  most  perfect, 
indeed  the  only  quite  perfect,  form  of  induction.  In  those  books,  every 
process  which  sets  out  from  a less  general  and  terminates  in  a more  gen- 
eral expression — which  admits  of  being  stated  in  the  form,  “ This  and  that 
A are  B,  therefore  every  A is  B is  called  an  induction,  whether  any- 
thing be  really  concluded  or  not : and  the  induction  is  asserted  not  to  be 
perfect,  unless  every  single  individual  of  the  class  A is  included  in  the 
antecedent,  or  premise : that  is,  unless  what  we  affirm  of  the  class  has 
already  been  ascertained  to  be  true  of  every  individual  in  it,  so  that  the 
nominal  conclusion  is  not  really  a conclusion,  but  a mere  re-assertion  of  the 
premises.  If  we  were  to  say,  All  the  planets  shine  by  the  sun’s  light,  from 
observation  of  each  separate  planet,  or  All  the  Apostles  were  Jews,  because 
this  is  true  of  Peter,  Paul,  John,  and  every  other  apostle — these,  and  such 
as  these,  would,  in  the  phraseology  in  question,  be  called  perfect,  and  the 
only  perfect,  Inductions.  This,  however,  is  a totally  different  kind  of  in- 
duction from  ours;  it  is  not  an  inference  from  facts  known  to  facts  un- 
known, but  a mere  short-hand  registration  of  facts  known.  The  two  sim- 
ulated arguments  which  we  have  quoted,  are  not  generalizations ; the  prop- 
ositions purporting  to  be  conclusions  from  them,  are  not  really  general 
propositions.  A general  proposition  is  one  in  which  the  predicate  is  af- 
firmed or  denied  of  an  unlimited  number  of  individuals ; namely,  all,  wheth- 
er few  or  many,  existing  or  capable  of  existing,  which  possess  the  proper- 
ties connoted  by  the  subject  of  the  proposition.  “ All  men  are  mortal  ” does 
not  mean  all  now  living,  but  all  men  past,  present,  and  to  come.  When  the 
signification  of  the  term  is  limited  so  as  to  render  it  a name  not  for  any 
and  every  individual  falling  under  a certain  general  description,  but  only 
for  each  of  a number  of  individuals,  designated  as  such,  and  as  it  were 
counted  off  individually,  the  proposition,  though  it  may  be  general  in  its 
language,  is  no  general  proposition,  but  merely  that  number  of  singular 
propositions,  written  in  an  abridged  character.  The  operation  may  be  very- 
useful,  as  most  forms  of  abridged  notation  are;  but  it  is  no  part  of  the  in- 
vestigation of  truth,  though  often  bearing  an  important  part  in  the  prepa- 
ration of  the  materials  for  that  investigation. 

As  we  may  sum  up  a definite  number  of  singular  propositions  in  one 
proposition,  which  will  be  apparently,  but  not  really,  general,  so  we  may 
sum  up  a definite  number  of  general  propositions  in  one  proposition,  which 
will  be  apparently,  but  not  really,  more  general.  If  by  a separate  induc- 
tion applied  to  every  distinct  species  of  animals,  it  has  been  established 
that  each  possesses  a nervous  system,  and  we  affirm  thereupon  that  all  an- 
imals have  a nervous  system ; this  looks  like  a generalization,  though  as 
the  conclusion  merely  affirms  of  all  what  has  already  been  affirmed  of  each, 
it  seems  to  tell  us  nothing  but  what  we  knew  before.  A distinction,  how- 
ever, must  be  made.  If  in  concluding  that  all  animals  have  a nervous  sys- 
tem, we  mean  the  same  thing  and  no  more  as  if  we  had  said  “ all  known 
animals,”  the  proposition  is  not  general,  and  the  process  by  which  it  is  ar- 
rived at  is  not  induction.  But  if  our  meaning  is  that  the  observations 
made  of  the  various  species  of  animals  have  discovered  to  us  a law  of  an- 
imal nature,  and  that  we  are  in  a condition  to  say  that  a nervous  system 
will  be  found  even  in  animals  yet  undiscovered,  this  indeed  is  an  induc- 
tion; but  in  this  case  the  general  proposition  contains  more  than  the  sum 
of  the  special  propositions  from  which  it  is  inferred.  The  distinction  is 
still  more  forcibly  brought  out  when  we  consider,  that  if  this  real  general- 
ization be  legitimate  at  all,  its  legitimacy  probably  does  not  require  that 


212 


INDUCTION. 


we  should  have  examined  without  exception  every  known  species.  It  is 
the  number  and  nature  of  the  instances,  and  not  their  being  the  whole  of 
those  which  happen  to  be  known,  that  makes  them  sufficient  evidence  to 
prove  a general  law : while  the  more  limited  assertion,  which  stops  at  all 
known  animals,  can  not  be  made  unless  we  have  rigorously  verified  it  in 
every  species.  In  like  manner  (to  return  to  a former  example)  we  might 
have  inferred,  not  that  all  the  planets,  but  that  all  planets,  shine  by  reflect- 
ed light : the  former  is  no  induction ; the  latter  is  an  induction,  and  a bad 
one,  being  disproved  by  the  case  of  double  stars  — self-luminous  bodies 
which  are  properly  planets,  since  they  revolve  round  a centre. 

§ 2.  There  are  several  processes  used  in  mathematics  which  require  to 
be  distinguished  from  Induction,  being  not  unfrequently  called  by  that 
name,  and  being  so  far  similar  to  Induction  properly  so  called,  that  the 
propositions  they  lead  to  are  really  general  propositions.  For  example, 
when  we  have  proved  with  respect  to  the  circle,  that  a straight  line  can 
not  meet  it  in  more  than  two  points,  and  when  the  same  thing  has  been 
successively  proved  of  the  ellipse,  the  parabola,  and  the  hyperbola,  it  may 
be  laid  down  as  a universal  property  of  the  sections  of  the  cone.  The 
distinction  drawn  in  the  two  previous  examples  can  have  no  place  here, 
there  being  no  difference  between  all  known  sections  of  the  cone  and  all 
sections,  since  a cone  demonstrably  can  not  be  intersected  by  a plane  ex- 
cept in  one  of  these  four  lines.  It  would  be  difficult,  therefore,  to  refuse 
to  the  proposition  arrived  at,  the  name  of  a generalization,  since  there  is 
no  room  for  any  generalization  beyond  it.  But  there  is  no  induction,  be- 
cause there  is  no  inference  : the  conclusion  is  a mere  summing  up  of  what 
was  asserted  in  the  various  propositions  from  which  it  is  drawn.  A case 
somewhat,  though  not  altogether,  similar,  is  the  proof  of  a geometrical  theo- 
rem by  means  of  a diagram.  Whether  the  diagram  be  on  paper  or  only 
in  the  imagination,  the  demonstration  (as  formerly  observed*)  does  not 
prove  directly  the  general  theorem ; it  proves  only  that  the  conclusion, 
which  the  theorem  asserts  generally,  is  true  of  the  particular  triangle  or 
circle  exhibited  in  the  diagram;  but  since  we  perceive  that  in  the  same 
way  in  which  we  have  proved  it  of  that  circle,  it  might  also  be  proved  of 
any  other  circle,  we  gather  up  into  one  general  expression  all  the  singular 
propositions  susceptible  of  being  thus  proved,  and  embody  them  in  a uni- 
versal proposition.  Having  shown  that  the  three  angles  of  the  triangle 
ABC  are  together  equal  to  two  right  angles,  we  conclude  that  this  is  true 
of  every  other  triangle,  not  because  it  is  true  of  ABC,  but  for  the  same 
reason  which  proved  it  to  be  true  of  ABC.  If  this  were  to  be  called  In- 
duction, an  appropriate  name  for  it  would  be,  induction  by  parity  of  rea- 
soning. But  the  term  can  not  properly  belong  to  it;  the  characteristic 
quality  of  Induction  is  wanting,  since  the  truth  obtained,  though  really 
general,  is  not  believed  on  the  evidence  of  particular  instances.  We  do  not 
conclude  that  all  triangles  have  the  property  because  some  triangles  have, 
but  from  the  ulterior  demonstrative  evidence  which  was  the  ground  of  our 
conviction  in  the  particular  instances. 

There  are  nevertheless,  in  mathematics,  some  examples  of  so-called  In 
d action,  in  which  the  conclusion  does  bear  the  appearance  of  a generaliza- 
tion grounded  on  some  of  the  particular  cases  included  in  it.  A mathe- 
matician, when  he  has  calculated  a sufficient  number  of  the  terms  of  an  al- 


Supra,  p.  145. 


INDUCTIONS  IMPROPERLY  SO  CALLED. 


213 


gebraical  or  arithmetical  series  to  have  ascertained  what  is  called  the  law 
of  the  series,  does  not  hesitate  to  fill  up  any  number  of  the  succeeding  terms 
without  repeating  the  calculations.  But  I apprehend  he  only  does  so  when 
it  is  apparent  from  a priori  considerations  (which  might  be  exhibited  in 
the  form  of  demonstration)  that  the  mode  of  formation  of  the  subsequent 
terms,  each  from  that  which  preceded  it,  must  be  similar  to  the  formation 
of  the  terms  which  have  been  already  calculated.  And  when  the  attempt 
has  been  hazarded  without  the  sanction  of  such  general  considerations,  there 
are  instances  on  record  in  which  it  has  led  to  false  results. 

It  is  said  that  Newton  discovered  the  binomial  theorem  by  induction; 
by  raising  a binomial  successively  to  a certain  number  of  powers,  and 
comparing  those  powers  with  one  another  until  he  detected  the  relation  in 
which  the  algebraic  formula  of  each  power  stands  to  the  exponent  of  that 
power,  and  to  the  two  terms  of  the  binomial.  The  fact  is  not  improbable : 
but  a mathematician  like  Newton,  who  seemed  to  arrive  per  saltum  at 
principles  and  conclusions  that  ordinary  mathematicians  only  reached  by  a 
succession  of  steps,  certainly  could  not  have  performed  the  comparison  in 
question  without  being  led  by  it  to  the  a priori  ground  of  the  law;  since 
any  one  who  understands  sufficiently  the  nature  of  multiplication  to  ven- 
ture upon  multiplying  several  lines  of  symbols  at  one  operation,  can  not 
but  perceive  that  in  raising  a binomial  to  a power,  the  co-efficients  must 
depend  on  the  laws  of  permutation  and  combination:  and  as  soon  as  this 
is  recognized,  the  theorem  is  demonstrated.  Indeed,  when  once  it  was  seen 
that  the  law  prevailed  in  a few  of  the  lower  powers,  its  identity  with  the 
law  of  permutation  would  at  once  suggest  the  considerations  which  prove 
it  to  obtain  universally.  Even,  therefore,  such  cases  as  these,  are  but  ex- 
amples of  what  I have  called  Induction  by  parity  of  reasoning,  that  is,  not 
really  Induction,  because  not  involving  inference  of  a general  proposition 
from  particular  instances. 

§ 3.  There  remains  a third  improper  use  of  the  term  Induction,  which  it 
is  of  real  importance  to  clear  up,  because  the  theory  of  Induction  has  been, 
in  no  ordinary  degree,  confused  by  it,  and  because  the  confusion  is  exem- 
plified in  the  most  recent  and  elaborate  treatise  on  the  inductive  philosophy 
which  exists  in  our  language.  The  error  in  question  is  that  of  confound- 
ing a mere  description,  by  general  terms,  of  a set  of  observed  phenomena, 
with  an  induction  from  them. 

Suppose  that  a phenomenon  consists  of  parts,  and  that  these  parts  are 
only  capable  of  being  observed  separately,  and  as  it  were  piecemeal. 
When  the  observations  have  been  made,  there  is  a convenience  (amounting 
for  many  purposes  to  a necessity)  in  obtaining  a representation  of  the  phe- 
nomenon as  a whole,  by  combining,  or  as  we  may  say,  piecing  these  de- 
tached fragments  together.  A navigator  sailing  in  the  midst  of  the  ocean 
discovers  land : he  can  not  at  first,  or  by  any  one  observation,  determine 
whether  it  is  a continent  or  an  island ; but  he  coasts  along  it,  and  after  a 
few  days  finds  himself  to  have  sailed  completely  round  it : he  then  pro- 
nounces it  an  island.  Now  there  was  no  particular  time  or  place  of  ob- 
servation at  which  he  could  perceive  that  this  land  was  entirely  surrounded 
by  water : he  ascertained  the  fact  by  a succession  of  partial  observations, 
and  then  selected  a general  expression  which  summed  up  in  two  or  three 
words  the  whole  of  what  he  so  observed.  But  is  there  any  thing  of  the 
nature  of  an  induction  in  this  process  ? Did  he  infer  any  thing  that  had 
not  been  observed,  from  something  else  which  had  ? Certainly  not.  He 


INDUCTION. 


214 


had  observed  the  whole  of  what  the  proposition  asserts.  That  the  land  in 
question  is  an  island,  is  not  an  inference  from  the  partial  facts  which  the 
navigator  saw  in  the  course  of  his  circumnavigation ; it  is  the  facts  them- 
selves; it  is  a summary  of  those  facts;  the  description  of  a complex  fact, 
to  which  those  simpler  ones  are  as  the  parts  of  a whole. 

Now  there  is,  I conceive,  no  difference  in  kind  between  this  simple  op- 
eration, and  that  by  which  Kepler  ascertained  the  nature  of  the  planetary 
orbits:  and  Kepler’s  operation,  all  at  least  that  was  characteristic  in  it,  was 
not  more  an  inductive  act  than  that  of  our  supposed  navigator. 

The  object  of  Kepler  was  to  determine  the  real  path  described  by  each 
of  the  planets,  or  let  us  say  by  the  planet  Mars  (since  it  was  of  that  body 
that  he  first  established  the  two  of  his  three  laws  which  did  not  require  a 
comparison  of  planets).  To  do  this  there  was  no  other  mode  than  that  of 
direct  observation  : and  all  which  observation  could  do  was  to  ascertain  a 
great  number  of  the  successive  places  of  the  planet;  or  rather,  of  its  ap- 
parent places.  That  the  planet  occupied  successively  all  these  positions,  or 
at  all  events,  positions  which  produced  the  same  impressions  on  the  eye, 
and  that  it  passed  from  one  of  these  to  another  insensibly,  and  without  any 
apparent  breach  of  continuity;  thus  much  the  senses,  with  the  aid  of  the 
proper  instruments,  could  ascertain.  What  Kepler  did  more  than  this,  was 
to  find  what  sort  of  a curve  these  different  points  would  make,  supposing 
them  to  be  all  joined  together.  He  expressed  the  whole  series  of  the  ob- 
served places  of  Mars  by  what  Dr.  Whewell  calls  the  general  conception  of 
an  ellipse.  This  operation  was  far  from  being  as  easy  as  that  of  the  navi- 
gator who  expressed  the  series  of  his  observations  on  successive  points  of 
the  coast  by  the  general  conception  of  an  island.  But  it  is  the  very  same 
sort  of  operation;  and  if  the  one  is  not  an  induction  but  a description,  this 
must  also  be  true  of  the  other. 

The  only  real  induction  concerned  in  the  case,  consisted  in  inferring  that 
because  the  observed  places  of  Mars  were  correctly  represented  by  points 
in  an  imaginary  ellipse,  therefore  Mars  would  continue  to  revolve  in  that 
same  ellipse ; and  in  concluding  (before  the  gap  had  been  filled  up  by  fur- 
ther observations)  that  the  positions  of  the  planet  during  the  time  which 
intervened  between  two  observations,  must  have  coincided  with  the  inter- 
mediate points  of  the  curve.  For  these  were  facts  which  had  not  been  di- 
rectly observed.  They  were  inferences  from  the  observations;  facts  in- 
ferred, as  distinguished  from  facts  seen.  But  these  inferences  were  so  far 
from  being  a part  of  Kepler’s  philosophical  operation,  that  they  had  been 
drawn  long  before  he  was  born.  Astronomers  had  long  known  that  the 
planets  periodically  returned  to  the  same  places.  When  this  had  been  as- 
certained, there  was  no  induction  left  for  Kepler  to  make,  nor  did  he  make 
any  further  induction.  He  merely  applied  his  new  conception  to  the  facts 
inferred,  as  he  did  to  the  facts  observed.  Knowing  already  that  the  plan- 
ets continued  to  move  in  the  same  paths;  when  he  found  that  an  ellipse 
correctly  represented  the  past  path,  he  knew  that  it  would  represent  the 
future  path.  In  finding  a compendious  expression  for  the  one  set  of  facts, 
he  found  one  for  the  other : but  he  found  the  expression  only,  not  the  in- 
ference; nor  did  he  (which  is  the  true  test  of  a general  truth)  add  any 
thing  to  the  power  of  prediction  already  possessed. 

§ 4.  The  descriptive  operation  which  enables  a number  of  details  to  be 
summed  up  in  a single  proposition,  Dr.  Whewell,  by  an  aptly  chosen  ex- 
pression, has  termed  the  Colligation  of  Facts.  In  most  of  his  observations 


INDUCTIONS  IMPROPERLY  SO  CALLED. 


215 


concerning  that  mental  process  I fully  agree,  and  would  gladly  transfer  all 
that  portion  of  his  book  into  my  own  pages.  I only  think  him  mistaken 
in  setting  up  this  kind  of  operation,  which  according  to  the  old  and  received 
meaning  of  the  term,  is  not  induction  at  all,  as  the  type  of  induction  gener 
ally ; and  laying  down,  throughout  his  work,  as  principles  of  induction,  the 
principles  of  mere  colligation. 

Dr.  Whewell  maintains  that  the  general  proposition  which  binds  togeth- 
er the  particular  facts,  and  makes  them,  as  it  were,  one  fact,  is  not  the  mere 
sum  of  those  facts,  but  something  more,  since  there  is  introduced  a concep- 
tion of  the  mind,  which  did  not  exist  in  the  facts  themselves.  “The  par- 
ticular facts,”  says  he,*  “ arc  not  merely  brought  together,  but  there  is  a 
new  element  added  to  the  combination  by  the  very  act  of  thought  by  which 
they  are  combined.  ....  When  the  Greeks,  after  long  observing  the  mo- 
tions of  the  planets,  saw  that  these  motions  might  be  rightly  considered  as 
produced  by  the  motion  of  one  wheel  revolving  in  the  inside  of  another 
wheel,  these  wheels  were  creations  of  their  minds,  added  to  the  facts  which 
they  perceived  by  sense.  And  even  if  the  wheels  were  no  longer  supposed 
to  be  material,  but  were  reduced  to  mere  geometrical  spheres  or  circles,  they 
were  not  the  less  products  of  the  mind  alone — something  additional  to  the 
facts  observed.  The  same  is  the  case  in  all  other  discoveries.  The  facts 
are  known,  but  they  are  insulated  and  unconnected,  till  the  discoverer  sup- 
plies from  his  own  store  a principle  of  connection.  The  pearls  are  there, 
but  they  will  not  hang  together  till  some  one  provides  the  string.” 

Let  me  first  remark  that  Dr.  Whewell,  in  this  passage,  blends  together, 
indiscriminately,  examples  of  both  the  processes  which  I am  endeavoring 
to  distinguish  from  one  another.  When  the  Greeks  abandoned  the  suppo- 
sition that  the  planetary  motions  were  produced  by  the  revolution  of  mate- 
rial wheels,  and  fell  back  upon  the  idea  of  “ mere  geometrical  spheres  or 
circles,”  there  was  more  in  this  change  of  opinion  than  the  mere  substitu- 
tion of  an  ideal  curve  for  a physical  one.  There  was  the  abandonment  of 
a theory,  and  the  replacement  of  it  by  a mere  description.  No  one  would 
think  of  calling  the  doctrine  of  material  wheels  a mere  description.  That 
doctrine  was  an  attempt  to  point  out  the  force  by  which  the  planets  were 
acted  upon,  and  compelled  to  move  in  their  orbits.  But  when,  by  a great 
step  in  philosophy,  the  materiality  of  the  wheels  was  discarded,  and  the  ge- 
ometrical forms  alone  retained,  the  attempt  to  account  for  the  motions  was 
given  up,  and  what  was  left  of  the  theory  was  a mere  description  of  the 
orbits.  The  assertion  that  the  planets  were  carried  round  by  wheels  re- 
volving in  the  inside  of  other  wheels,  gave  place  to  the  proposition,  that 
they  moved  in  the  same  lines  which  would  be  traced  by  bodies  so  carried : 
which  was  a mere  mode  of  representing  the  sum  of  the  observed  facts ; as 
Kepler’s  was  another  and  a better  mode  of  representing  the  same  observa- 
tions. 

It  is  true  that  for  these  simply  descriptive  operations,  as  well  as  for  the 
erroneous  inductive  one,  a conception  of  the  mind  was  required.  The  con- 
ception of  an  ellipse  must  have  presented  itself  to  Kepler’s  mind,  before  he 
could  identify  the  planetary  orbits  with  it.  According  to  Dr.  Whewell, 
the  conception  was  something  added  to  the  facts.  He  expresses  himself 
as  if  Kepler  had  put  something  into  the  facts  by  his  mode  of  conceiving 
them.  But  Kepler  did  no  such  thing.  The  ellipse  was  in  the  facts  before 
Kepler  recognized  it;  just  as  the  island  was  an  island  before  it  had  been 

* Novum  Organum  Renovatum,  pp.  72,  73. 


•JIG 


INDUCTION. 


sailed  round.  Kepler  did  not  put  what  he  had  conceived  into  the  facts, 
but  saw  it  in  them.  A conception  implies,  and  corresponds  to,  something 
conceived:  and  though  the  conception  itself  is  not  in  the  facts,  but  in  our 
mind,  yet  if  it  is  to  convey  any  knowledge  relating  to  them,  it  must  be  a con- 
ception of  something  which  really  is  in  the  facts,  some  property  which  they 
actually  possess,  and  which  they  would  manifest  to  our  senses,  if  our  senses 
were  able  to  take  cognizance  of  it.  If,  for  instance,  the  planet  left  behind 
it  in  space  a visible  track,  and  if  the  observer  were  in  a fixed  position  at 
such  a distance  from  the  plane  of  the  orbit  as  would  enable  him  to  see  the 
whole  of  it  at  once,  he  would  see  it  to  be  an  ellipse;  and  if  gifted  with  ap- 
propriate instruments  and  powers  of  locomotion,  he  could  prove  it  to  be 
such  by  measuring  its  different  dimensions.  Nay,  further:  if  the  track 
were  visible,  and  he  were  so  placed  that  he  could  see  all  parts  of  it  in  suc- 
cession, but  not  all  of  them  at  once,  he  might  be  able,  by  piecing  together 
his  successive  observations,  to  discover  both  that  it  was  an  ellipse  and  that 
the  planet  moved  in  it.  The  case  would  then  exactly  resemble  that  of  the 
navigator  who  discovers  the  land  to  be  an  island  by  sailing  round  it.  If 
the  path  was  visible,  no  one  I think  would  dispute  that  to  identify  it  with 
an  ellipse  is  to  describe  it:  and  I can  not  see  why  any  difference  should  be 
made  by  its  not  being  directly  an  object  of  sense,  when  every  point  in  it  is 
as  exactly  ascertained  as  if  it  were  so. 

Subject  to  the  indispensable  condition  which  has  just  been  stated,  I do 
not  conceive  that  the  part  which  conceptions  have  in  the  operation  of 
studying  facts,  has  ever  been  overlooked  or  undervalued.  No  one  ever  dis- 
puted that  in  order  to  reason  about  any  thing  we  must  have  a conception 
of  it;  or  that  when  we  include  a multitude  of  things  under  a general  ex- 
pression, there  is  implied  in  the  expression  a conception  of  something  com- 
mon to  those  things.  But  it  by  no  means  follows  that  the  conception  is 
necessarily  pre-existent,  or  constructed  by  the  mind  out  of  its  own  mate- 
rials. If  the  facts  are  rightly  classed  under  the  conception,  it  is  because 
there  is  in  the  facts  themselves  something  of  which  the  conception  is  itself 
a copy;  and  which  if  we  can  not  directly  perceive,  it  is  because  of  the  lim- 
ited power  of  our  organs,  and  not  because  the  thing  itself  is  not  there. 
The  conception  itself  is  often  obtained  by  abstraction  from  the  very  facts 
which,  in  Dr.  Whewell’s  language,  it  is  afterward  called  in  to  connect. 
This  he  himself  admits,  when  he  observes  (which  he  does  on  several  occa- 
sions), how  great  a service  would  be  rendered  to  the  science  of  physiology 
by  the  philosopher  “ who  should  establish  a precise,  tenable,  and  consistent 
conception  of  life.”*  Such  a conception  can  only  be  abstracted  from  the 
phenomena  of  life  itself;  from  the  very  facts  which  it  is  put  in  requisition 
to  connect.  In  other  cases,  no  doubt,  instead  of  collecting  the  conception 
from  the  very  phenomena  which  we  are  attempting  to  colligate,  we  select 
it  from  among  those  which  have  been  previously  collected  by  abstraction 
from  other  facts.  In  the  instance  of  Kepler’s  laws,  the  latter  was  the 
case.  The  facts  being  out  of  the  reach  of  being  observed,  in  any  such 
manner  as  would  have  enabled  the  senses  to  identify  directly  the  path  of 
the  planet,  the  conception  requisite  for  framing  a general  description  of 
that  path  could  not  be  collected  by  abstraction  from  the  observations 
themselves ; the  mind  had  to  supply  hypothetically,  from  among  the  con- 
ceptions it  had  obtained  from  other  portions  of  its  experience,  some  one 
which  would  correctly  represent  the  series  of  the  observed  facts.  It  had 


Novum  Orqanum  Renovatum , p.  32. 


INDUCTIONS  IMPROPERLY  SO  CALLED. 


217 


to  frame  a supposition  respecting  the  general  course  of  the  phenomenon, 
and  ask  itself,  If  this  be  the  general  description,  what  will  the  details  be  ? 
and  then  compare  these  with  the  details  actually  observed.  If  they  agreed, 
the  hypothesis  would  serve  for  a description  of  the  phenomenon:  if  not,  it 
was  necessarily  abandoned,  and  another  tried.  It  is  such  a case  as  this 
which  gives  rise  to  the  doctrine  that  the  mind,  in  framing  the  descriptions, 
adds  something  of  its  own  which  it  does  not  find  in  the  facts. 

Yet  it  is  a fact  surely,  that  the  planet  does  describe  an  ellipse ; and  a fact 
which  we  could  see,  if  we  had  adequate  visual  organs  and  a suitable  posi- 
tion. Not  having  these  advantages,  but  possessing  the  conception  of  an  el- 
lipse, or  (to  express  the  meaning  in  less  technical  language)  knowing  what 
an  ellipse  was,  Kepler  tried  whether  the  observed  places  of  the  planet  were 
consistent  with  such  a path.  He  found  they  were  so;  and  he,  consequent- 
ly, asserted  as  a fact  that  the  planet  moved  in  an  ellipse.  But  this  fact, 
which  Kepler  did  not  add  to,  but  found  in,  the  motions  of  the  planet,  name- 
ly, that  it  occupied  in  succession  the  various  points  in  the  circumference  of 
a given  ellipse,  was  the  very  fact,  the  separate  parts  of  which  had  been  sep- 
arately observed  ; it  was  the  sum  of  the  different  observations. 

Having  stated  this  fundamental  difference  between  my  opinion  and  that 
of  Dr.  Whewell,  I must  add,  that  his  account  of  the  manner  in  which  a 
conception  is  selected,  suitable  to  express  the  facts,  appears  to  me  perfectly 
just.  The  experience  of  all  thinkers  will,  I believe,  testify  that  the  process 
is  tentative;  that  it  consists  of  a succession  of  guesses;  many  being  reject- 
ed, until  one  at  last  occurs  fit  to  be  chosen.  We  know  from  Kepler  him- 
self that  before  hitting  upon  the  “conception”  of  an  ellipse,  he  tried  nine- 
teen other  imaginary  paths,  which,  finding  them  inconsistent  with  the  ob- 
servations, he  was  obliged  to  reject.  But  as  Dr.  Whewell  truly  says,  the 
successful  hypothesis,  though  a guess,  ought  generally  to  be  called,  not  a 
lucky,  but  a skillful  guess.  The  guesses  which  serve  to  give  mental  unity 
and  wholeness  to  a chaos  of  scattered  particulars,  are  accidents  which  rare- 
ly occur  to  any  minds  but  those  abounding  in  knowledge  and  disciplined  in 
intellectual' combinations. 

How  far  this  tentative  method,  so  indispensable  as  a means  to  the  colli- 
gation of  facts  for  purposes  of  description,  admits  of  application  to  Induc- 
tion itself,  and  what  functions  belong  to  it  in  that  department,  will  be  con- 
sidered in  the  chapter  of  the  present  Book  which  relates  to  Hypotheses. 
On  the  present  occasion  we  have  chiefly  to  distinguish  this  process  of  Col- 
ligation from  Induction  properly  so  called  ; and  that  the  distinction  may  be 
made  clearer,  it  is  well  to  advert  to  a curious  and  interesting  remark,  which 
is  as  strikingly  true  of  the  former  operation,  as  it  appears  to  me  unequivo- 
cally false  of  the  latter. 

In  different  stages  of  the  progress  of  knowledge,  philosophers  have  em- 
ployed, for  the  colligation  of  the  same  order  of  facts,  different  conceptions. 
The  early  rude  observations  of  the  heavenly  bodies,  in  which  minute  pre- 
cision was  neither  attained  nor  sought,  presented  nothing  inconsistent  with 
the  representation  of  the  path  of  a planet  as  an  exact  circle,  having  the  earth 
for  its  centre.  As  observations  increased  in  accuracy,  facts  were  disclosed 
which  were  not  reconcilable  with  this  simple  supposition  : for  the  colliga- 
tion of  those  additional  facts,  the  supposition  was  varied  ; and  varied  again 
and  again  as  facts  became  more  numerous  and  precise.  The  earth  was  re- 
moved from  the  centre  to  some  other  point  within  the  circle ; the  planet 
was  supposed  to  revolve  in  a smaller  circle  called  an  epicycle,  round  an  im- 
aginary point  which  revolved  in  a circle  round  the  earth : in  proportion  as 


21S 


INDUCTION. 


observation  elicited  fresh  facts  contradictory  to  these  representations,  other 
epicycles  and  other  eccentrics  were  added,  producing  additional  complica- 
tion ; until  at  last  Kepler  swept  all  these  circles  away,  and  substituted  the 
conception  of  an  exact  ellipse.  Even  this  is  found  not  to  represent  with 
complete  correctness  the  accurate  observations  of  the  present  day,  which 
disclose  many  slight  deviations  from  an  orbit  exactly  elliptical.  Now  Dr. 
Whewell  has  remarked  that  these  successive  general  expressions,  though 
apparently  so  conflicting,  were  all  correct:  they  all  answered  the  purpose 
of  colligation ; they  all  enabled  the  mind  to  represent  to  itself  with  facility, 
and  by  a simultaneous  glance,  the  whole  body  of  facts  at  the  time  ascer- 
tained : each  in  its  turn  served  as  a correct  description  of  the  phenomena, 
so  far  as  the  senses  had  up  to  that  time  taken  cognizance  of  them.  If  a 
necessity  afterward  arose  for  discarding  one  of  these  general  descriptions 
of  the  planet’s  orbit,  and  framing  a different  imaginary  line,  by  which  to 
express  the  series  of  observed  positions,  it  was  because  a number  of  new 
facts  had  now  been  added,  which  it  was  necessary  to  combine  with  the  old 
facts  into  one  general  description.  But  this  did  not  affect  the  correctness 
of  the  former  expression,  considered  as  a general  statement  of  the  only  facts 
which  it  was  intended  to  represent.  And  so  true  is  this,  that,  as  is  well  re- 
marked by  M.  Comte,  these  ancient  generalizations,  even  the  rudest  and 
most  imperfect  of  them,  that  of  uniform  movement  in  a circle,  are  so  far 
from  being  entirely  false,  that  they  are  even  now  habitually  employed  by 
astronomers  when  only  a rough  approximation  to  correctness  is  required. 
“ L’astronomie  moderne,  en  detruisant  sans  retour  les  hypotheses  primi- 
tives, envisagees  comme  lois  reelles  du  monde,  a soigneusement  maintenu 
leur  valeur  positive  et  permanente,  la  propriete  de  representer  commode- 
ment  les  phenomenes  quand  il  s’agit  d’une  premiere  ebauche.  Nos  res- 
sources  a cet  egard  sont  meme  bien  plus  etendues,  precisement  a cause 
que  nous  ne  nous  faisons  aucune  illusion  sur  la  realite  des  hypotheses;  ce 
qni  nous  permet  d’employer  sans  scrupule,  en  chaque  cas,  celle  que  nous 
jugeons  la  plus  avantageuse.”* 

Dr.  Whewell’s  remark,  therefore,  is  philosophically  correct.  Successive 
expressions  for  the  colligation  of  observed  facts,  or,  in  other  words,  succes- 
sive descriptions  of  a phenomenon  as  a whole,  which  has  been  observed 
only  in  parts,  may,  though  conflicting,  be  all  correct  as  far  as  they  go.  But 
it  would  surely  be  absurd  to  assert  this  of  conflicting  inductions. 

The  scientific  study  of  facts  may  be  undertaken  for  three  different  pur- 
poses: the  simple  description  of  the  facts;  their  explanation;  or  their  pre- 
diction : meaning  by  prediction,  the  determination  of  the  conditions  under 
which  similar  facts  may  be  expected  again  to  occur.  To  the  first  of  these 
three  operations  the  name  of  Induction  does  not  properly  belong : to  the 
other  two  it  does.  Now,  Dr.  Whewell’s  observation  is  true  of  the  first 
alone.  Considered  as  a mere  description,  the  circular  theory  of  the  heaven- 
ly motions  represents  perfectly  well  their  general  features:  and  by  adding 
epicycles  without  limit,  those  motions,  even  as  now  known  to  us,  might  be 
expressed  with  any  degree  of  accuracy  that  might  be  required.  The  ellip- 
tical theory,  as  a mere  description,  would  have  a great  advantage,  in  point 
of  simplicity,  and  in  the  consequent  facility  of  conceiving  it  and  reasoning 
about  it;  but  it  would  not  really  be  more  true  than  the  other.  Different 
descriptions,  therefore,  may  be  all  true:  but  not,  surely,  different  explana- 
tions. The  doctrine  that  the  heavenly  bodies  moved  by  a virtue  inherent 


Cours  de  Philosophie  Positive,  vol.  ii. , p.  202. 


INDUCTIONS  IMPROPERLY  SO  CALLED. 


219 


in  their  celestial  nature;  the  doctrine  that  they  were  moved  by  impact 
(which  led  to  the  hypothesis  of  vortices  as  the  only  impelling  force  capable 
of  whirling  bodies  in  circles),  and  the  Newtonian  doctrine,  that  they  are 
moved  by  the  composition  of  a centripetal  with  an  original  projectile 
force;  all  these  are  explanations,  collected  by  real  induction  from  supposed 
parallel  cases ; and  they  were  all  successively  received  by  philosophers,  as 
scientific  truths  on  the  subject  of  the  heavenly  bodies.  Can  it  be  said  of 
these,  as  was  said  of  the  different  descriptions,  that  they  are  all  true  as  far 
as  they  go  ? Is  it  not  clear  that  only  one  can  be  true  in  any  degree,  and 
the  other  two  must  be  altogether  false  ? So  much  for  explanations  : let  us 
now  compare  different  predictions  : the  first,  that  eclipses  will  occur  when 
one  planet  or  satellite  is  so  situated  as  to  cast  its  shadow  upon  another ; 
the  second,  that  they  will  occur  when  some  great  calamity  is  impending 
over  mankind.  Do  these  two  doctrines  only  differ  in  the  degree  of  their 
truth,  as  expressing  real  facts  with  unequal  degrees  of  accuracy?  Assur- 
edly the  one  is  true,  and  the  other  absolutely  false.* 

* Dr.  Whewell,  in  his  reply,  contests  the  distinction  here  drawn,  and  maintains,  that  not 
only  different  descriptions,  but  different  explanations  of  a phenomenon,  may  all  be  true.  Of 
the  three  theories  respecting  the  motions  of  the  heavenly  bodies,  he  says  ( Philosophy  of  Dis- 
covery',  p.  231):  “Undoubtedly  all  these  explanations  may  be  true  and  consistent  with  each 
other,  and  would  be  so  if  each  had  been  followed  out  so  as  to  show  in  what  manner  it  could 
be  made  consistent  with  the  facts.  And  this  was,  in  reality,  in  a great  measure  done.  The 
doctrine  that  the  heavenly  bodies  were  moved  by  vortices  was  successfully  modified,  so  that 
it  came  to  coincide  in  its  results  with  the  doctrine  of  an  inverse-quadratic  centripetal  force. 

When  this  point  was  reached,  the  vortex  was  merely  a machinery,  well  or  ill  devised, 

for  producing  such  a centripetal  force,  and  therefore  did  not  contradict  the  doctrine  of  a cen- 
tripetal force.  Newton  himself  does  not  appear  to  have  been  averse  to  explaining  gravity  by 
impulse.  So  little  is  it  true  that  if  one  theory  be  true  the  other  must  be  false.  The  attempt 
to  explain  gravity  by  the  impulse  of  streams  of  particles  flowing  through  the  universe  in  all 
directions,  which  I have  mentioned  in  the  Philosophy , is  so  far  from  being  inconsistent  with 
the  Newtonian  theory,  that  it  is  founded  entirely  upon  it.  And  even  with  regard  to  the  doc- 
trine, that  the  heavenly  bodies  move  by  an  inherent  virtue ; if  this  doctrine  had  been  main- 
tained in  any  such  way  that  it  was  brought  to  agree  with  the  facts,  the  inherent  virtue  must 
have  had  its  laws  determined  ; and  then  it  would  have  been  found  that  the  virtue  had  a refer- 
ence to  the  central  body  ; and  so,  the  ‘ inherent  virtue  ’ must  have  coincided  in  its  effect  with 
the  Newtonian  force ; and  then,  the  two  explanations  would  agree,  except  so  far  as  the  word 
‘inherent’  was  concerned.  And  if  such  a part  of  an  earlier  theory  as  this  word  inherent  in- 
dicates, is  found  to  be  untenable,  it  is  of  course  rejected  in  the  transition  to  later  and  more 
exact  theories,  in  Inductions  of  this  kind,  as  well  as  in  what  Mr.  Mill  calls  Descriptions. 
There  is,  therefore,  still  no  validity  discoverable  in  the  distinction  which  Mr.  Mill  attempts  to 
draw  between  descriptions  like  Kepler’s  law  of  elliptical  orbits,  and  other  examples  of  induc- 
tion.” 

If  the  doctrine  of  vortices  had  meant,  not  that  vortices  existed,  but  only  that  the  planets 
moved  in  the  same  manner  as  if  they  had  been  whirled  by  vortices  ; if  the  hypothesis  had  been 
merely  a mode  of  representing  the  facts,  not  an  attempt  to  account  for  them  ; if,  in  short,  it 
had  been  only  a Description  ; it  would,  no  doubt,  have  been  reconcilable  with  the  Newtonian 
theory.  The  vortices,  however,  were  not  a mere  aid  to  conceiving  the  motions  of  the  plan- 
ets, but  a supposed  physical  agent,  actively  impelling  them ; a material  fact,  which  might  be 
true  or  not  true,  but  could  not  be  both  true  and  not  true.  According  to  Descartes’s  theory  it 
was  true,  according  to  Newton's  it  was  not  true.  Dr.  Whewell  probably  means  that  since  the 
phrases,  centripetal  and  projectile  force,  do  not  declare  the  nature  but  only  the  direction  of 
the  forces,  the  Newtonian  theory  does  not  absolutely  contradict  any  hypothesis  which  may  be 
framed  respecting  the  mode  of  their  production.  The  Newtonian  theory,  regarded  as  a mere 
description  of  the  planetary  motions,  does  not ; but  the  Newtonian  theory  as  an  explanation 
of  them  does.  For  in  what  does  the  explanation  consist?  In  ascribing  those  motions  to  a 
general  law  which  obtains  between  all  particles  of  matter,  and  in  identifying  this  with  the  law 
by  which  bodies  fall  to  the  ground.  If  the  planets  are  kept  in  their  orbits  by  a force  which 
draws  the  particles  composing  them  toward  every  other  particle  of  matter  in  the  solar  system, 
they  are  not  kept  in  those  orbits  by  the  impulsive  force  of  certain  streams  of  matter  which 
whirl  them  round.  The  one  explanation  absolutely  excludes  the  other.  Either  the  planets 
are  not  moved  by  vortices,  or  they  do  not  move  by  a law  common  to  all  matter.  It  is  im- 


220 


INDUCTION. 


In  every  way,  therefore,  it  is  evident  that  to  explain  induction  as  the 
colligation  of  facts  by  means  of  appropriate  conceptions,  that  is,  concep- 
tions which  will  really  express  them,  is  to  confound  mere  description  of  the 
observed  facts  with  inference  from  those  facts,  and  ascribe  to  the  latter 
what  is  a characteristic  property  of  the  former. 

There  is,  however,  between  Colligation  and  Induction,  a real  correlation, 
which  it  is  important  to  conceive  correctly.  Colligation  is  not  always  in- 
duction; but  induction  is  always  colligation.  The  assertion  that  the  plan- 
ets move  in  ellipses,  was  but  a mode  of  representing  observed  facts ; it  was 
but  a colligation  ; while  the  assertion  that  they  are  drawn,  or  tend,  toward 
the  sun,  was  the  statement  of  a new  fact,  inferred  by  induction.  But  the 
induction,  once  made,  accomplishes  the  purposes  of  colligation  likewise.  It 
brings  the  same  facts,  which  Kepler  had  connected  by  his  conception  of  an 
ellipse,  under  the  additional  conception  of  bodies  acted  upon  by  a central 
force,  and  serves,  therefore,  as  a new  bond  of  connection  for  those  facts ; a 
new  principle  for  their  classification. 

Further,  the  descriptions  which  are  improperly  confounded  with  induc- 
tion, are  nevertheless  a necessary  preparation  for  induction  ; no  less  neces- 
sary than  correct  observation  of  the  facts  themselves.  Without  the  pre- 
vious colligation  of  detached  observations  by  means  of  one  general  concep- 
tion, we  could  never  have  obtained  any  basis  for  an  induction,  except  in 
the  case  of  phenomena  of  very  limited  compass.  We  should  not  be  able 

possible  that  both  opinions  can  be  true.  As  well  might  it  be  said  that  there  is  no  contradic- 
tion between  the  assertions,  that  a man  died  because  somebody  killed  him,  and  that  he  died  a 
natural  death. 

So,  again,  the  theory  that  the  planets  move  by  a virtue  inherent  in  their  celestial  nature,  is 
incompatible  with  either  of  the  two  others  : either  that  of  their  being  moved  by  vortices,  or 
that  which  regards  them  as  moving  by  a property  which  they  have  in  common  with  the  earth 
and  all  terrestrial  bodies.  Dr.  Whewell  says  that  the  theory  of  an  inherent  virtue  agrees  with 
Newton’s  when  the  word  inherent  is  left  out,  which  of  course  it  would  be  (he  says)  if  “ found 
to  be  untenable.”  But  leave  that  out,  and  w'here  is  the  theory?  The  word  inherent  is  the 
theory.  When  that  is  omitted,  there  remains  nothing  except  that  the  heavenly  bodies  move 
“by  a virtue,”  i.  e.,  bv  a power  of  some  sort;  or  by  virtue  of  their  celestial  nature,  which  di- 
rectly contradicts  the  doctrine  that  terrestrial  bodies  fall  by  the  same  law. 

If  Dr.  Whewell  is  not  yet  satisfied,  any  other  subject  will  serve  equally  well  to  test  his  doc- 
trine. lie  will  hardly  say  that  there  is  no  contradiction  between  the  emission  theory  and  the 
undulatory  theory  of  light ; or  that  there  can  be  both  one  and  two  electricities ; or  that  the 
hypothesis  of  the  production  of  the  higher  organic  forms  by  development  from  the  lower,  and 
the  supposition  of  separate  and  successive  acts  of  creation,  are  quite  reconcilable;  or  that 
the  theory  that  volcanoes  are  fed  from  a central  fire,  and  the  doctrines  which  ascribe  them  to 
chemical  action  at  a comparatively  small  depth  below  the  earth’s  surface,  are  consistent  with 
one  another,  and  all  true  as  far  as  they  go. 

If  different  explanations  of  the  same  fact  can  not  both  be  true,  still  less,  surely,  can  differ- 
ent predictions.  Dr.  Whewell  quarrels  (on  what  ground  it  is  not  necessary  here  to  consider) 
with  the  example  I had  chosen  on  this  point,  and  thinks  an  objection  to  an  illustration  a suf- 
ficient answer  to  a theory.  Examples  not  liable  to  his  objection  are  easily  found,  if  the  prop- 
osition that  conflicting  predictions  can  not  both  be  true,  can  be  made  clearer  by  an}'  examples. 
Suppose  the  phenomenon  to  be  a newly-discovered  comet,  and  that  one  astronomer  predicts 
its  return  once  in  every  300  years — another  once  in  every  400:  can  they  both  be  right? 
When  Columbus  predicted  that  by  sailing  constantly  westward  he  should  in  time  return  to 
the  point  from  which  he  set  out,  while  others  asserted  that  he  could  never  do  so  except  by 
turning  back,  were  both  he  and  his  opponents  true  prophets?  Were  the  predictions  which 
foretold  the  wonders  of  railways  and  steamships,  and  those  which  averred  that  the  Atlantic 
could  never  be  crossed  by  steam  navigation,  nor  a railway  train  propelled  ten  miles  an  hour, 
both  (in  Dr.  Whewell’s  words)  “ true,  and  consistent  with  one  another?” 

Dr.  Whewell  sees  no  distinction  between  holding  contradictory  opinions  on  a question  of 
fact,  and  merely  employing  different  analogies  to  facilitate  the  conception  of  the  same  fact. 
The  case  of  different  Inductions  belongs  to  the  former  class,  that  of  different  Descriptions  to 
the  latter. 


INDUCTIONS  IMPROPERLY  SO  CALLED. 


221 


to  affirm  any  predicates  at  all,  of  a subject  incapable  of  being  observed 
otherwise  than  piecemeal:  much  less  could  we  extend  those  predicates  by 
induction  to  other  similar  subjects.  Induction,  therefore,  always  presup- 
poses, not  only  that  the  necessary  observations  are  made  with  the  necessary 
accuracy,  but  also  that  the  results  of  these  observations  are,  so  far  as  prac- 
ticable, connected  together  by  general  descriptions,  enabling  the  mind  to 
represent  to  itself  as  wholes  whatever  phenomena  are  capable  of  being  so 
represented. 

§ 5.  Dr.  Whewell  has  replied  at  some  length  to  the  preceding  observa- 
tions, restating  his  opinions,  but  without  (as  far  as  I can  perceive)  adding 
any  thing  material  to  his  former  arguments.  Since,  however,  mine  have 
not  had  the  good  fortune  to  make  any  impression  upon  him,  I will  subjoin 
a few  remarks,  tending  to  show  more  clearly  in  what  our  difference  of 
opinion  consists,  as  well  as,  in  some  measure,  to  account  for  it. 

Nearly  all  the  definitions  of  induction,  by  writers  of  authority,  make  it 
consist  in  drawing  inferences  from  known  cases  to  unknown ; affirming  of 
a class,  a predicate  which  has  been  found  true  of  some  cases  belonging  to 
the  class;  concluding  because  some  things  have  a certain  property,  that 
other  things  which  resemble  them  have  the  same  property — or  because  a 
thing  has  manifested  a property  at  a certain  time,  that  it  has  and  will  have 
that  property  at  other  times. 

It  will  scarcely  be  contended  that  Kepler’s  operation  was  an  Induction 
in  this  sense  of  the  term.  The  statement,  that  Mars  moves  in  an  elliptical 
orbit,  was  no  generalization  from  individual  cases  to  a class  of  cases.  Nei- 
ther was  it  an  extension  to  all  time,  of  what  had  been  found  true  at  some 
particular  time.  The  whole  amount  of  generalization  which  the  case  ad- 
mitted of,  was  already  completed,  or  might  have  been  so.  Long  before 
the  elliptic  theory  was  thought  of,  it  had  been  ascertained  that  the  planets 
returned  periodically  to  the  same  apparent  places ; the  series  of  these 
places  was,  or  might  have  been,  completely  determined,  and  the  apparent 
course  of  each  planet  marked  out  on  the  celestial  globe  in  an  uninterrupted 
line.  Kepler  did  not  extend  an  observed  truth  to  other  cases  than  those  in 
which  it  had  been  observed : he  did  not  widen  the  subject  of  the  proposi- 
tion which  expressed  the  observed  facts.  The  alteration  he  made  was  in 
the  predicate.  Instead  of  saying,  the  successive  places  of  Mars  are  so  and 
so,  he  summed  them  up  in  the  statement,  that  the  successive  places  of  Mars 
are  points  in  an  ellipse.  It  is  true,  this  statement,  as  Dr.  Whewell  says, 
was  not  the  sum  of  the  observations  merely ; it  was  the  sum  of  the  obser- 
vations seen  under  a new  point  of  view*  But  it  was  not  the  sum  of  more 
than  the  observations,  as  a real  induction  is.  It  took  in  no  cases  but  those 
which  had  been  actually  observed,  or  which  could  have  been  inferred  from 
the  observations  before  the  new  point  of  view  presented  itself.  There  was 
not.  that  transition  from  known  cases  to  unknown,  which  constitutes  Induc- 
tion in  the  original  and  acknowledged  meaning  of  the  term. 

Old  definitions,  it  is  true,  can  not  prevail  against  new  knowledge : and  if 
the  Keplerian  operation,  as  a logical  process,  be  really  identical  with  what 
takes  place  in  acknowledged  induction,  the  definition  of  induction  ought  to 
be  so  widened  as  to  take  it  in ; since  scientific  language  ought  to  adapt  it- 
self to  the  true  relations  which  subsist  between  the  things  it  is  employed 
to  designate.  Here  then  it  is  that  I am  at  issue  with  Dr.  Whewell.  He 


* Phil,  of  Discov.,  p.  256. 


222 


INDUCTION. 


docs  think  the  operations  identical.  He  allows  of  no  logical  process  in  any 
case  of  induction,  other  than  what  there  was  in  Kepler’s  case,  namely, 
guessing  until  a guess  is  found  which  tallies  with  the  facts;  and  accord- 
ingly, as  we  shall  see  hereafter,  he  rejects  all  canons  of  induction,  because 
it  is  not  by  means  of  them  that  we  guess.  Dr.  Whewell’s  theory  of  the 
logic  of  science  would  be  very  perfect  if  it  did  not  pass  over  altogether  the 
question  of  Proof.  But  in  my  apprehension  there  is  such  a thing  as  proof, 
and  inductions  differ  altogether  from  descriptions  in  their  relation  to  that 
element.  Induction  is  proof ; it  is  inferring  something  unobserved  from 
something  observed:  it  requires,  therefore,  an  appropriate  test  of  proof ; 
and  to  provide  that  test,  is  the  special  purpose  of  inductive  logic.  When, 
on  the  contrary,  we  merely  collate  known  observations,  and,  in  Dr.  Whe- 
well’s phraseology,  connect  them  by  means  of  a new  conception ; if  the 
conception  does  serve  to  connect  the  observations,  we  have  all  we  want. 
As  the  proposition  in  which  it  is  embodied  pretends  to  no  other  truth  than 
what  it  may  share  with  many  other  modes  of  representing  the  same  facts, 
to  be  consistent  with  the  facts  is  all  it  requires : it  neither  needs  nor  ad- 
mits of  proof;  though  it  may  serve  to  prove  other  things, inasmuch  as,  by 
placing  the  facts  in  mental  connection  with  other  facts,  not  previously  seen 
to  resemble  them,  it  assimilates  the  case  to  another  class  of  phenomena, 
concerning  which  real  Inductions  have  already  been  made.  Thus  Kepler’s 
so-called  law  brought  the  orbit  of  Mars  into  the  class  ellipse,  and  by  doing 
so,  proved  all  the  properties  of  an  ellipse  to  be  true  of  the  orbit : but  in  this 
proof  Kepler’s  law  supplied  the  minor  premise,  and  not  (as  is  the  case  with 
real  Inductions)  the  major. 

Dr.  Whewell  calls  nothing  Induction  where  there  is  not  a new  mental 
conception  introduced,  and  every  thing  induction  where  there  is.  But  this 
is  to  confound  two  very  different  things,  Invention  and  Proof.  The  intro- 
duction of  a new  conception  belongs  to  Invention : and  invention  may  be 
required  in  any  operation,  but  is  the  essence  of  none.  A new  conception 
may  be  introduced  for  descriptive  purposes,  and  so  it  may  for  inductive 
purposes.  But  it  is  so  far  from  constituting  induction,  that  induction  does 
not  necessarily  stand  in  need  of  it.  Most  inductions  require  no  conception 
but  what  was  present  in  every  one  of  the  particular  instances  on  which  the 
induction  is  grounded.  That  all  men  are  mortal  is  surely  an  inductive 
conclusion ; yet  no  new  conception  is  introduced  by  it.  Whoever  knows 
that  any  man  has  died,  has  all  the  conceptions  involved  in  the  inductive 
generalization.  But  Dr.  Whewell  considers  the  process  of  invention  which 
consists  in  framing  a new  conception  consistent  with  the  facts,  to  be  not 
merely  a necessary  part  of  all  induction,  but  the  whole  of  it. 

The  mental  operation  which  extracts  from  a number  of  detached  obser- 
vations certain  general  characters  in  which  the  observed  phenomena  resem- 
ble one  another,  or  resemble  other  known  facts,  is  what  Bacon,  Locke,  and 
most  subsequent  metaphysicians,  have  understood  by  the  word  Abstrac- 
tion. A general  expression  obtained  by  abstraction,  connecting  known 
facts  by  means  of  common  characters,  but  without  concluding  from  them 
to  unknown,  may,  I think,  with  strict  logical  correctness,  be  termed  a De- 
scription ; nor  do  I know  in  what  other  way  things  can  ever  be  described. 
My  position,  however,  does  not  depend  on  the  employment  of  that  partic- 
ular word;  I am  quite  content  to  use  Dr.  Whewell’s  term  Colligation,  or 
the  more  general  phrases,  “ mode  of  representing,  or  of  expressing,  phe- 
nomena:” provided  it  be  clearly  seen  that  the  process  is  not  Induction,  but 
something  radically  different. 


GROUND  OF  INDUCTION. 


223 


What  more  may  usefully  be  said  on  the  subject  of  Colligation,  or  of  the 
correlative  expression  invented  by  Dr.  Whewell,  the  Explication  of  Con- 
ceptions, and  generally  on  the  subject  of  ideas  and  mental  representations 
as  connected  with  the  study  of  facts,  will  find  a more  appropriate  place  in 
the  Fourth  Book,  on  the  Operations  Subsidiary  to  Induction:  to  which  I 
must  refer  the  reader  for  the  removal  of  any  difficulty  which  the  present 
discussion  may  have  left. 


CHAPTER  III. 

OF  THE  GROUND  OF  INDUCTION. 

§ 1.  Induction  properly  so  called,  as  distinguished  from  those  mental 
operations,  sometimes,  though  improperly,  designated  by  the  name,  which  I 
have  attempted  in  the  preceding  chapter  to  characterize,  may,  then,  be  sum- 
marily defined  as  Generalization  from  Experience.  It  consists  in  inferring 
from  some  individual  instances  in  which  a phenomenon  is  observed  to  oc- 
cur, that  it  occurs  in  all  instances  of  a certain  class  ; namely,  in  all  which 
resemble,  the  former,  in  what  are  regarded  as  the  material  circumstances. 

In  what  way  the  material  circumstances  are  to  be  distinguished  from 
those  which  are  immaterial,  or  why  some  of  the  circumstances  are  material 
and  others  not  so,  we  are  not  yet  ready  to  point  out.  We  must  first  ob- 
serve, that  there  is  a principle  implied  in  the  very  statement  of  what  Induc- 
tion is;  an  assumption  with  regard  to  the  course  of  nature  and  the  order 
of  the  universe;  namely,  that  there  are  such  things  in  nature  as  parallel 
cases;  that  what  happens  once,  will,  under  a sufficient  degree  of  similarity 
of  circumstances,  happen  again,  and  not  only  again,  but  as  often  as  the 
same  circumstances  recur.  This,  I say,  is  an  assumption,  involved  in  every 
case  of  induction.  And,  if  we  consult  the  actual  course  of  nature,  we  find 
that  the  assumption  is  warranted.  The  universe,  so  far  as  known  to  us,  is 
so  constituted,  that  whatever  is  true  in  any  one  case,  is  true  in  all  cases  of 
a certain  description ; the  only  difficulty  is,  to  find  what  description. 

This  universal  fact,  which  is  our  warrant  for  all  inferences  from  experi- 
ence, has  been  described  by  different  philosophers  in  different  forms  of  lan- 
guage: that  the  course  of  nature  is  uniform;  that  the  universe  is  governed 
by  general  laws;  and  the  like.  One  of  the  most  usual  of  these  modes  of 
expression,  but  also  one  of  the  most  inadequate,  is  that  which  has  been 
brought  into  familiar  use  by  the  metaphysicians  of  the  school  of  Reid 
and  Stewart.  The  disposition  of  the  human  mind  to  generalize  from  ex- 
perience— a propensity  considered  by  these  philosophers  as  an  instinct  of 
our  nature — they  usually  describe  under  some  such  name  as  “ our  intuitive 
conviction  that  the  future  will  resemble  the  past.”  Now  it  has  been  well 
pointed  out  by  Mr.  Bailey,*  that  (whether  the  tendency  be  or  not  an  orig- 
inal and  ultimate  element  of  our  nature),  Time,  in  its  modifications  of  past, 
present,  and  future,  has  no  concern  either  with  the  belief  itself,  or  with  the 
grounds  of  it.  We  believe  that  fire  will  burn  to-morrow,  because  it  burned 
to-day  and  yesterday;  but  we  believe,  on  precisely  the  same  grounds,  that 
it  burned  before  we  were  born,  and  that  it  burns  this  very  day  in  Cochin- 
China.  It  is  not  from  the  past  to  the  future,  as  past  and  future,  that  we 


Essays  on  the  Pursuit  of  Truth, 


224 


INDUCTION. 


infer,  but  from  the  known  to  the  unknown;  from  facts  observed  to  facts 
unobserved ; from  what  we  have  perceived,  or  been  directly  conscious  of, 
to  what  has  not  come  within  our  experience.  In  this  last  predicament  is 
the  whole  region  of  the  future ; but  also  the  vastly  greater  portion  of  the 
present  and  of  the  past. 

W hatevcr  be  the  most  proper  mode  of  expressing  it,  the  proposition  that 
the  course  of  nature  is  uniform,  is  the  fundamental  principle,  or  general  ax- 
iom, of  Induction.  It  would  yet  be  a great  error  to  offer  this  large  gener- 
alization as  any  explanation  of  the  inductive  process.  On  the  contrary,  I 
hold  it  to  be  itself  an  instance  of  induction,  and  induction  by  no  means  of 
the  most  obvious  kind.  Far  from  being  the  first  induction  we  make,  it  is 
one  of  the  last,  or  at  all  events  one  of  those  which  are  latest  in  attaining 
strict  philosophical  accuracy.  As  a general  maxim,  indeed,  it  has  scarcely 
entered  into  the  minds  of  any  but  philosophers;  nor  even  by  them,  as  we 
shall  have  many  opportunities  of  remarking,  have  its  extent  and  limits  been 
always  very  justly  conceived.  The  truth  is,  that  this  great  generalization 
is  itself  founded  on  prior  generalizations.  The  obscurer  laws  of  nature 
were  discovered  by  means  of  it,  but  the  more  obvious  ones  must  have 
been  understood  and  assented  to  as  general  truths  before  it  was  ever  heard 
of.  We  should  never  have  thought  of  affirming  that  all  phenomena  take 
place  according  to  general  laws,  if  we  had  not  first  arrived,  in  the  case  of  a 
great  multitude  of  phenomena,  at  some  knowledge  of  the  laws  themselves ; 
which  could  be  done  no  otherwise  than  by  induction.  In  what  sense,  then, 
can  a principle,  which  is  so  far  from  being  our  earliest  induction,  be  re- 
garded as  our  warrant  for  all  the  others?  In  the  only  sense,  in  which  (as 
we  have  already  seen)  the  general  propositions  which  we  place  at  the  head 
of  our  reasonings  when  rve  throw  them  into  syllogisms,  ever  really  contrib- 
ute to  their  validity.  As  Archbishop  Whately  remarks,  every  induction  is 
a syllogism  with  the  major  premise  suppressed;  or  (as  I prefer  expressing 
it)  every  induction  may  be  thrown  into  the  form  of  a syllogism,  by  supply- 
ing a major  premise.  If  this  be  actually  done,  the  principle  which  we  are 
now  considering,  that  of  the  uniformity  of  the  course  of  nature,  will  appear 
as  the  ultimate  major  premise  of  all  inductions,  and  will,  therefore,  stand  to 
all  inductions  in  the  relation  in  which,  as  has  been  shown  at  so  much  length, 
the  major  proposition  of  a syllogism  always  stands  to  the  conclusion;  not 
contributing  at  all  to  prove  it,  but  being  a necessary  condition  of  its  being 
proved;  since  no  conclusion  is  proved,  for  which  there  can  not  be  found  a 
true  major  premise.* 

* In  the  first  edition  a note  was  appended  at  this  place,  containing  some  criticism  on  Arch- 
bishop Whately ’s  mode  of  conceiving  the  relation  between  Syllogism  and  Induction.  In  a 
subsequent  issue  of  his  Logic , the  Archbishop  made  a reply  to  the  criticism,  which  induced 
me  to  cancel  part  of  the  note,  incorporating  the  remainder  in  the  text.  In  a still  later  edi- 
tion, the  Archbishop  observes  in  a tone  of  something  like  disapprobation,  that  the  objections, 
“ doubtless  from  their  being  fully  answered  and  found  untenable,  were  silently  suppressed,” 
and  that  hence  he  might  appear  to  some  of  his  readers  to  be  combating  a shadow.  On  this 
latter  point,  the  Archbishop  need  give  himself  no  uneasiness.  His  readers,  I make  bold  to 
say,  will  fully  credit  his  mere  affirmation  that  the  objections  have  actually  been  made. 

But  as  he  seems  to  think  that  what  he  terms  the  suppression  of  the  objections  ought  not  to 
have  been  made  “ silently,”  I now  break  that  silence,  and  state  exactly  what  it  is  that  I sup- 
pressed, and  why.  I suppressed  that  alone  which  might  be  regarded  as  personal  criticism  on 
the  Archbishop.  I had  imputed  to  him  the  having  omitted  to  ask  himself  a particular  ques- 
tion. I found  that  he  had  asked  himself  the  question,  and  could  give  it  an  answer  consistent 
with  his  own  theorv.  I had  also,  within  the  compass  of  a parenthesis,  hazarded  some  re- 
marks on  certain  general  characteristics  of  Archbishop  Whately  as  a philosopher.  These  re- 
marks, though  their  tone,  I hope,  was  neither  disrespectful  nor  arrogant,  I felt,  on  reconsider- 
ation, that  I was  hardly  entitled  to  make;  least  of  all,  when  the  instance  which  I had  re- 


GROUND  OF  INDUCTION. 


225 


The  statement,  that  the  uniformity  of  the  course  of  nature  is  the  ulti- 
mate major  premise  in  all  cases  of  induction,  may  be  thought  to  require 
some  explanation.  The  immediate  major  premise  in  every  inductive  argu- 
ment, it  certainly  is  not.  Of  that,  Archbishop  Whately’s  must  be  held  to 
be  the  correct  account.  The  induction,  “ John,  Peter,  etc.,  are  mortal,  there- 
fore all  mankind  are  mortal,”  may,  as  he  justly  says,  be  thrown  into  a syl- 
logism by  prefixing  as  a major  premise  (what  is  at  any  rate  a necessary 
condition  of  the  validity  of  the  argument),  namely,  that  what  is  true  of 
John,  Peter,  etc.,  is  true  of  all  mankind.  But  how  came  we  by  this  ma- 
jor premise?  It  is  not  self-evident;  nay, in  all  cases  of  unwarranted  gen- 
eralization, it  is  not  true.  How,  then,  is  it  arrived  at  ? Necessarily  either 
by  induction  or  ratiocination;  and  if  by  induction,  the  process, like  all  oth- 
er inductive  arguments,  may  be  thrown  into  the  form  of  a syllogism.  This 
previous  syllogism  it  is,  therefore,  necessary  to  construct.  There  is,  in  the 
long  run,  only  one  possible  construction.  The  real  proof  that  what  is  true 
of  John,  Peter,  etc.,  is  true  of  all  mankind,  can  only  be,  that  a different  sup- 
position would  be  inconsistent  with  the  uniformity  which  we  know  to  exist 
in  the  course  of  nature.  Whether  there  would  be  this  inconsistency  or  not, 
may  be  a matter  of  long  and  delicate  inquiry;  but  unless  there  would,  we 
have  no  sufficient  ground  for  the  major  of  the  inductive  syllogism.  It 
hence  appears,  that  if  we  throw  the  whole  course  of  any  inductive  argu- 
ment into  a series  of  syllogisms,  we  shall  arrive  by  more  or  fewer  steps  at 
an  ultimate  syllogism,  which  will  have  for  its  major  premise  the  principle, 
or  axiom,  of  the  uniformity  of  the  course  of  nature.* 

It  was  not  to  be  expected  that  in  the  case  of  this  axiom,  any  more  than 
of  other  axioms,  there  should  be  unanimity  among  thinkers  with  respect  to 
the  grounds  on  which  it  is  to  be  received  as  true.  I have  already  stated 
that  I regard  it  as  itself  a generalization  from  experience.  Others  hold  it 
to  be  a principle  which,  antecedently  to  any  verification  by  experience,  we 

garded  as  an  illustration  of  them,  failed,  as  I now  saw,  to  bear  them  out.  The  real  matter  at 
the  bottom  of  the  whole  dispute,  the  different  view  we  take  of  the  function  of  the  major  prem- 
ise, remains  exactly  where  it  was  ; and  so  far  was  I from  thinking  that  my  opinion  had 
been  fully  “answered”  and  was  “untenable,”  that  in  the  same  edition  in  which  I canceled 
the  note,  I not  only  enforced  the  opinion  by  further  arguments,  but  answered  (though  without 
naming  him)  those  of  the  Archbishop. 

For  not  having  made  this  statement  before,  I do  not  think  it  needful  to  apologize.  It  would 
be  attaching  very  great  importance  to  one's  smallest  sayings,  to  think  a formal  retractation  req- 
uisite every  time  that  one  falls  into  an  error.  Nor  is  Archbishop  Whately's  well-earned  fame 
of  so  tender  a quality  as  to  require  that  in  withdrawing  a slight  criticism  on  him  I should  have 
been  bound  to  offer  a public  amende  for  having  made  it, 

* But  though  it  is  a condition  of  the  validity  of  every  induction  that  there  be  uniformity  in 
the  course  of  nature,  it  is  not  a necessary  condition  that  the  uniformity  should  pervade  all  na- 
ture. It  is  enough  that  it  pervades  the  particular  class  of  phenomena  to  which  the  induction 
relates.  An  induction  concerning  the  motions  of  the  planets,  or  the  properties  of  the  magnet, 
would  not  be  vitiated  though  we  were  to  suppose  that  wind  and  weather  are  the  sport  of 
chance,  provided  it  be  assumed  that  astronomical  and  magnetic  phenomena  are  under  the 
dominion  of  general  laws.  Otherwise  the  early  experience  of  mankind  would  have  rested  on 
a very  weak  foundation ; for  in  the  infancy  of  science  it  could  not  be  known  that  all  phe- 
nomena are  regular  in  their  course. 

Neither  would  it  be  correct  to  say  that  every  induction  by  which  we  infer  any  truth,  implies 
the  general  fact  of  uniformity  as  foreknown , even  in  reference  to  the  kind  of  phenomena  con- 
cerned. It  implies,  either  that  this  general  fact  is  already  known,  or  that  rye  may  now  know 
it : as  the  conclusion,  the  Duke  of  Wellington  is  mortal,  drawn  from  the  instances  A,  B,  and 
C,  implies  either  that  we  have  already  concluded  all  men  to  be  mortal,  or  that  we  are  now  en- 
titled to  do  so  from  the  same  evidence.  A vast  amount  of  confusion  and  paralogism  respect- 
ing the  grounds  of  Induction  would  be  dispelled  by  keeping  in  view  these  simple  consider- 
ations. 


15 


226 


INDUCTION. 


are  compelled  by  the  constitution  of  our  thinking  faculty  to  assume  as  true. 
Having  so  recently,  and  at  so  much  length,  combated  a similar  doctrine  as 
applied  to  the  axioms  of  mathematics,  by  arguments  which  are  in  a great 
measure  applicable  to  the  present  case,  I shall  defer  the  more  particular 
discussion  of  this  controverted  point  in  regard  to  the  fundamental  axiom 
of  induction,  until  a more  advanced  period  of  our  inquiry.*  At  present  it 
is  of  more  importance  to  understand  thoroughly  the  import  of  the  axiom 
itself.  For  the  proposition,  that  the  course  of  nature  is  uniform,  possesses 
rather  the  brevity  suitable  to  popular,  than  the  precision  requisite  in  phil- 
osophical language:  its  terms  require  to  be  explained,  and  a stricter  than 
their  ordinary  signification  given  to  them,  before  the  truth  of  the  assertion 
can  be  admitted. 

§ 2.  Every  person’s  consciousness  assures  him  that  he  does  not  always 
expect  uniformity  in  the  course  of  events;  he  does  not  always  believe  that 
the  unknown  will  be  similar  to  the  known,  that  the  future  will  resemble  the 
past.  Nobody  believes  that  the  succession  of  rain  and  fine  weather  will  be 
the  same  in  every  future  year  as  in  the  present.  Nobody  expects  to  have 
the  same  dreams  repeated  every  night.  On  the  contrary,  every  body  men- 
tions it  as  something  extraordinary,  if  the  course  of  nature  is  constant,  and 
resembles  itself,  in  these  particulars.  To  look  for  constancy  where  con- 
stancy is  not  to  be  expected,  as  for  instance  that  a day  which  has  once 
brought  good  fortune  will  always  be  a fortunate  day,  is  justly  accounted 
superstition. 

The  course  of  nature,  in  truth,  is  not  only  uniform,  it  is  also  infinitely  va- 
rious. Some  phenomena  are  always  seen  to  recur  in  the  very  same  combi- 
nations in  which  we  met  with  them  at  first;  others  seem  altogether  capri- 
cious; while  some,  which  we  had  been  accustomed  to  regard  as  bound 
down  exclusively  to  a particular  set  of  combinations,  we  unexpectedly  find 
detached  from  some  of  the  elements  with  which  we  had  hitherto  found 
them  conjoined,  and  united  to  others  of  quite  a contrary  description.  To 
an  inhabitant  of  Central  Africa,  fifty  years  ago,  no  fact  probably  appeared 
to  rest  on  more  uniform  experience  than  this,  that  all  human  beings  are 
black.  To  Europeans,  not  many  years  ago,  the  proposition,  All  swans  are 
white,  appeared  an  equally  unequivocal  instance  of  uniformity  in  the  course 
of  nature.  Further  experience  has  proved  to  both  that  they  were  mistaken; 
but  they  had  to  wait  fifty  centuries  for  this  experience.  During  that  long 
time,  mankind  believed  in  a uniformity  of  the  course  of  nature  where  no 
such  uniformity  really  existed. 

According  to  the  notion  which  the  ancients  entertained  of  induction,  the 
foregoing  were  cases  of  as  legitimate  inference  as  any  inductions  whatever. 
In  these  two  instances,  in  which,  the  conclusion  being  false,  the  ground  of 
inference  must  have  been  insufficient,  there  was,  nevertheless,  as  much 
ground  for  it  as  this  conception  of  induction  admitted  of.  The  induction 
of  the  ancients  has  been  well  described  by  Bacon,  under  the  name  of  “In- 
ductio  per  enumerationem  simplicem,  ubi  non  reperitur  instantia  contradic- 
toria.”  It  consists  in  ascribing  the  character  of  general  truths  to  all  prop- 
ositions which  are  true  in  every  instance  that  we  happen  to  know  of.  This 
is  the  kind  of  induction  which  is  natural  to  the  mind  when  unaccustomed 
to  scientific  methods.  The  tendency,  which  some  call  an  instinct,  and 
which  others  account  for  by  association,  to  infer  the  future  from  the  past, 


Infra,  chap.  xxi. 


GROUND  OF  INDUCTION. 


227 


the  known  from  the  unknown,  is  simply  a habit  of  expecting  that  what  has 
been  found  true  once  or  several  times,  and  never  yet  found  false,  will  be 
found  true  again.  Whether  the  instances  are  few  or  many,  conclusive  or 
inconclusive,  does  not  much  affect  the  matter : these  are  considerations 
which  occur  only  on  reflection  ; the  unprompted  tendency  of  the  mind  is  to 
generalize  its  experience,  provided  this  points  all  in  one  direction  ; provided 
no  other  experience  of  a conflicting  character  comes  unsought.  The  notion 
of  seeking  it,  of  experimenting  for  it,  of  interrogating  nature  (to  use  Ba- 
con’s expression)  is  of  much  later  growth.  The  observation  of  nature,  by 
uncultivated  intellects,  is  purely  passive : they  accept  the  facts  which  pre- 
sent themselves,  without  taking  the  trouble  of  searching  for  more : it  is  a 
superior  mind  only  which  asks  itself  what  facts  are  needed  to  enable  it  to 
come  to  a safe  conclusion,  and  then  looks  out  for  these. 

But  though  we  have  always  a propensity  to  generalize  from  unvarying 
experience,  we  are  not  always  warranted  in  doing  so.  Before  we  can  be 
at  liberty  to  conclude  that  something  is  universally  true  because  we  have 
never  known  an  instance  to  the  contrary,  we  must  have  reason  to  believe 
that  if  there  were  in  nature  any  instances  to  the  contrary,  we  should  have 
known  of  them.  This  assurance, in  the  great  majority  of  cases, we  cannot 
have,  or  can  have  only  in  a very  moderate  degree.  The  possibility  of  hav- 
ing it,  is  the  foundation  on  which  we  shall  see  hereafter  that  induction  by 
simple  enumeration  may  in  some  remarkable  cases  amount  practically  to 
proof.*  No  such  assurance,  however,  can  be  had,  on  any  of  the  ordinary 
subjects  of  scientific  inquiry.  Popular  notions  are  usually  founded  on  in- 
duction by  simple  enumeration ; in  science  it  carries  us  but  a little  way. 
We  are  forced  to  begin  with  it;  we  must  often  rely  on  it  provisionally,  in 
the  absence  of  means  of  more  searching  investigation.  But,  for  the  accu- 
rate study  of  nature,  we  require  a surer  and  a more  potent  instrument. 

It  was,  above  all,  by  pointing  out  the  insufficiency  of  this  rude  and  loose 
conception  of  Induction,  that  Bacon  merited  the  title  so  generally  awarded 
to  him,  of  Founder  of  the  Inductive  Philosophy.  The  value  of  his  own  con- 
tributions to  a more  philosophical  theory  of  the  subject  has  certainly  been 
exaggerated.  Although  (along  with  some  fundamental  errors)  his  writings 
contain,  more  or  less  fully  developed,  several  of  the  most  important  princi- 
ples of  the  Inductive  Method,  physical  investigation  has  now  far  outgrown 
the  Baconian  conception  of  Induction.  Moral  and  political  inquiry,  indeed, 
are  as  yet  far  behind  that  conception.  The  current  and  approved  modes 
of  reasoning  on  these  subjects  are  still  of  the  same  vicious  description 
against  which  Bacon  protested ; the  method  almost  exclusively  employed 
by  those  professing  to  treat  such  matters  inductively,  is  the  very  inductio 
per  enumerationem  simplicem  which  he  condemns;  and  the  experience 
which  we  hear  so  confidently  appealed  to  by  all  sects,  parties,  and  interests, 
is  still,  in  his  own  emphatic  words,  mera  palpatio. 

§ 3.  In  order  to  a better  understanding  of  the  problem  which  the  logi- 
cian must  solve  if  he  would  establish  a scientific  theory  of  Induction,  let  us 
compare  a few  cases  of  incorrect  inductions  with  others  which  are  acknowl- 
edged to  be  legitimate.  Some,  we  know,  which  were  believed  for  centuries 
to  be  correct,  were  nevertheless  incorrect.  That  all  swans  ai’e  white,  can 
not  have  been  a good  induction,  since  the  conclusion  has  turned  out  errone- 
ous. The  experience,  however,  on  which  the  conclusion  rested,  was  genu- 


Infra,  chap,  xxi.,  xxii. 


228 


INDUCTION. 


ine.  From  the  earliest  records,  the  testimony  of  the  inhabitants  of  the 
known  world  was  unanimous  on  the  point.  The  uniform  experience,  there- 
fore, of  the  inhabitants  of  the  known  world,  agreeing  in  a common  result, 
without  one  known  instance  of  deviation  from  that  result,  is  not  always 
sufficient  to  establish  a general  conclusion. 

But  let  us  now  turn  to  an  instance  apparently  not  very  dissimilar  to  this. 
Mankind  were  wrong,  it  seems,  in  concluding  that  all  swans  were  white: 
are  we  also  wrong,  when  we  conclude  that  all  men’s  heads  grow  above  their 
shoulders,  and  never  below,  in  spite  of  the  conflicting  testimony  of  the  natu- 
ralist Pliny  ? As  there  were  black  swans,  though  civilized  people  had  exist- 
ed for  three  thousand  years  on  the  earth  without  meeting  with  them,  may 
there  not  also  be  “ men  whose  heads  do  grow  beneath  their  shoulders,”  not- 
withstanding a rather  less  perfect  unanimity  of  negative  testimony  from 
observers  ? Most  persons  would  answer  ISTo ; it  was  more  credible  that  a 
bird  should  vary  in  its  color,  than  that  men  should  vary  in  the  relative  po- 
sition of  their  principal  organs.  And  there  is  no  doubt  that  in  so  saying 
they  would  be  right : but  to  say  why  they  are  right,  would  be  impossible, 
without  entering  more  deeply  than  is  usually  done,  into  the  true  theory  of 
Induction. 

Again,  there  are  cases  in  which  we  reckon  with  the  most  unfailing  confi- 
dence upon  uniformity,  and  other  cases  in  which  we  do  not  count  upon  it 
at  all.  In  some  we  feel  complete  assurance  that  the  future  will  resemble  the 
past,  the  unknown  be  precisely  similar  to  the  known.  In  others,  however 
invariable  may  be  the  result  obtained  from  the  instances  which  have  been 
observed,  we  draw  from  them  no  more  than  a very  feeble  presumption  that 
the  like  result  will  hold  in  all  other  cases.  That  a straight  line  is  the  short- 
est distance  between  two  points,  we  do  not  doubt  to  be  true  even  in  the  re- 
gion of  the  fixed  stars.*  When  a chemist  announces  the  existence  and 
properties  of  a newly-discovered  substance,  if  we  confide  in  his  accuracy, 
we  feel  assured  that  the  conclusions  he  has  arrived  at  will  hold  universally, 
though  the  induction  be  founded  but  on  a single  instance.  We  do  not 
withhold  our  assent,  waiting  for  a repetition  of  the  experiment;  or  if  we 
do,  it  is  from  a doubt  whether  the  one  experiment  was  properly  made,  not 
whether  if  properly  made  it  would  be  conclusive.  Here,  then,  is  a general 
law  of  nature,  inferred  without  hesitation  from  a single  instance ; a uni- 
versal proposition  from  a singular  one.  Now  mark  another  case,  and  con- 
trast it  with  this.  Not  all  the  instances  which  have  been  observed  since 
the  beginning  of  the  world,  in  support  of  the  general  proposition  that  all 
crows  are  black,  would  be  deemed  a sufficient  presumption  of  the  truth  of 
the  proposition,  to  outweigh  the  testimony  of  one  unexceptionable  witness 
who  should  affirm  that  in  some  region  of  the  earth  not  fully  explored,  he 
had  caught  and  examined  a crow,  and  had  found  it  to  be  gray. 

Why  is  a single  instance,  in  some  cases,  sufficient  for  a complete  induc- 
tion, while  in  others,  myriads  of  concurring  instances,  without  a single  ex- 
ception known  or  presumed,  go  such  a very  little  way  toward  establishing 
a universal  proposition  ? Whoever  can  answer  this  question  knows  more 
of  the  philosophy  of  logic  than  the  wisest  of  the  ancients,  and  has  solved 
the  problem  of  induction. 

* In  strictness,  wherever  the  present  constitution  of  space  exists ; which  we  have  ample 
reason  to  believe  that  it  does  in  the  region  of  the  fixed  stars. 


LAWS  OF  NATURE. 


229 


CHAPTER  IY. 

OF  LAWS  OF  NATURE. 

§ 1.  In  the  contemplation  of  that  uniformity  in  the  course  of  nature, 
which  is  assumed  iu  every  inference  from  experience,  one  of  the  first  ob- 
servations that  present  themselves  is,  that  the  uniformity  in  question  is  not 
properly  uniformity,  but  uniformities.  The  general  regularity  results  from 
the  co-existence  of  partial  regularities.  The  course  of  nature  in  general  is 
constant,  because  the  course  of  each  of  the  various  phenomena  that  com- 
pose it  is  so.  A certain  fact  invariably  occurs  whenever  certain  circum- 
stances are  present,  and  does  not  occur  when  they  are  absent;  the  like  is 
true  of  another  fact;  and  so  on.  From  these  separate  threads  of  connec- 
tion between  parts  of  the  great  whole  which  we  term  nature,  a general  tis- 
sue of  connection  unavoidably  weaves  itself,  by  which  the  whole  is  held  to- 
gether. If  A is  always  accompanied  by  D,  B by  E,  and  C by  F,  it  follows 
that  A B is  accompanied  by  D E,  A C by  D F,  B C by  E F,  and  finally  A 
B C by  D E F ; and  thus  the  general  character  of  regularity  is  produced, 
which,  along  with  and  in  the  midst  of  infinite  diversity,  pervades  all  nature. 

The  first  point,  therefore,  to  be  noted  in  regard  to  what  is  called  the  uni- 
formity of  the  course  of  nature,  is,  that  it  is  itself  a complex  fact,  com- 
pounded of  all  the  separate  uniformities  which  exist  in  respect  to  single 
phenomena.  These  various  uniformities,  when  ascertained  by  what  is  re- 
garded as  a sufficient  induction,  we  call,  in  common  parlance,  Laws  of  Na- 
ture. Scientifically  speaking,  that  title  is  employed  in  a more  restricted 
sense,  to  designate  the  uniformities  when  reduced  to  their  most  simple  ex- 
pression. Thus  in  the  illustration  already  employed,  there  were  seven  uni- 
formities ; all  of  which,  if  considered  sufficiently  certain,  would,  in  the  more 
lax  application  of  the  term,  be  called  laws  of  nature.  But  of  the  seven, 
three  alone  are  properly  distinct  and  independent : these  being  presup- 
posed, the  others  follow  of  course.  The  first  three,  therefore,  according  to 
the  stricter  acceptation,  are  called  laws  of  nature;  the  remainder  not;  be- 
cause they  are  in  truth  mere  cases  of  the  first  three ; virtually  included  in 
them  ; said,  therefore,  to  result  from  them  : whoever  affirms  those  three  has 
already  affirmed  all  the  rest. 

To  substitute  real  examples  for  symbolical  ones,  the  following  are  three 
uniformities,  or  call  them  laws  of  nature:  the  law  that  air  has  weight,  the 
law  that  pressure  on  a fluid  is  propagated  equally  in  all  directions,  and  the 
law  that  pressure  in  one  direction,  not  opposed  by  equal  pressure  in  the 
contrary  direction,  produces  motion,  which  does  not  cease  until  equilibrium 
is  restored.  From  these  three  uniformities  we  should  be  able  to  predict 
another  uniformity,  namely,  the  rise  of  the  mercury  in  the  Torricellian 
tube.  This,  in  the  stricter  use  of  the  phrase,  is  not  a law  of  nature.  It  is 
the  result  of  laws  of  nature.  It  is  a case  of  each  and  every  one  of  the 
three  laws : and  is  the  only  occurrence  by  which  they  could  all  be  fulfilled. 
If  the  mercury  were  not  sustained  in  the  barometer,  and  sustained  at  such 
a height  that  the  column  of  mercury  were  equal  in  weight  to  a column  of 
the  atmosphere  of  the  same  diameter ; here  would  be  a case,  either  of  the 


230 


INDUCTION. 


air  not  pressing  upon  the  surface  of  the  mercury  with  the  force  which  is 
called  its  weight,  or  of  the  downward  pressure  on  the  mercury  not  being 
propagated  equally  in  an  upward  direction,  or  of  a body  pressed  in  one  di- 
rection and  not  in  the  direction  opposite,  either  not  moving  in  the  direction 
in  which  it  is  pressed,  or  stopping  before  it  had  attained  equilibrium.  If 
we  knew,  therefore,  the  three  simple  laws,  but  had  never  tried  the  Torricel- 
lian experiment,  we  might  deduce  its  result  from  those  laws.  The  known 
weight  of  the  air,  combined  with  the  position  of  the  apparatus,  would 
bring  the  mercury  within  the  first  of  the  three  inductions;  the  first  induc- 
tion would  bring  it  within  the  second,  and  the  second  within  the  third,  in 
the  manner  which  we  characterized  in  treating  of  Ratiocination.  We  should 
thus  come  to  know  the  more  complex  uniformity,  independently  of  specific 
experience,  through  our  knowledge  of  the  simpler  ones  from  which  it  results; 
though,  for  reasons  which  will  appear  hereafter,  verification  by  specific  ex- 
perience would  still  be  desirable,  and  might  possibly  be  indispensable. 

Complex  uniformities  which,  like  this,  are  mere  cases  of  simpler  ones, 
and  have,  therefore,  been  virtually  affirmed  in  affirming  those,  may  with 
propriety  be  called  laics,  but  can  scarcely,  in  the  strictness  of  scientific 
speech,  be  termed  Laws  of  Nature.  It  is  the  custom  in  science,  wherever 
regularity  of  any  kind  can  be  traced,  to  call  the  general  proposition  which 
expresses  the  nature  of  that  regularity,  a law ; as  when,  in  mathematics, 
we  speak  of  the  law  of  decrease  of  the  successive  terms  of  a converging 
series.  But  the  expression  law  of  nature  has  generally  been  employed 
with  a sort  of  tacit  reference  to  the  original  sense  of  the  word  law,  namely, 
the  expression  of  the  will  of  a superior.  When,  therefore,  it  appeared  that 
any  of  the  uniformities  which  were  observed  in  nature,  would  result  spon- 
taneously from  certain  other  uniformities,  no  separate  act  of  creative  will 
being  supposed  necessary  for  the  production  of  the  derivative  uniformities, 
these  have  not  usually  been  spoken  of  as  laws  of  nature.  According  to 
one  mode  of  expression,  the  question,  What  are  the  laws  of  nature  ? may 
be  stated  thus:  What  are  the  fewest  and  simplest  assumptions, which  be- 
ing granted,  the  whole  existing  order  of  nature  would  result  ? Another 
mode  of  stating  it  would  be  thus:  What  are  the  fewest  general  proposi- 
tions from  which  all  the  uniformities  which  exist  in  the  universe  might  be 
deductively  inferred? 

Every  great  advance  which  marks  an  epoch  in  the  progress  of  science, 
has  consisted  in  a step  made  toward  the  solution  of  this  problem.  Even  a 
simple  colligation  of  inductions  already  made,  without  any  fresh  extension 
of  the  inductive  inference,  is  already  an  advance  in  that  direction.  When 
Ivepler  expressed  the  regularity  which  exists  in  the  observed  motions  of 
the  heavenly  bodies,  by  the  three  general  propositions  called  his  laws,  he, 
in  so  doing,  pointed  out  three  simple  suppositions  which,  instead  of  a much 
greater  number,  would  suffice  to  construct  the  whole  scheme  of  the  heav- 
enly motions,  so  far  as  it  was  known  up  to  that  time.  A similar  and  still 
greater  step  was  made  when  these  laws,  which  at  first  did  not  seem  to  be 
included  in  any  more  general  truths,  were  discovered  to  be  cases  of  the 
three  laws  of  motion,  as  obtaining  among  bodies  which  mutually  tend  to- 
ward one  another  with  a certain  force,  and  have  had  a certain  instantaneous 
impulse  originally  impressed  upon  them.  After  this  great  discovery,  Kep- 
ler’s three  propositions,  though  still  called  laws,  would  hardly,  by  any  per- 
son accustomed  to  use  language  with  precision,  be  termed  laws  of  nature : 
that  phrase  would  be  reserved  for  the  simpler  and  more  general  laws  into 
which  Newton  is  said  to  have  resolved  them. 


LAWS  OF  NATURE. 


231 


According  to  this  language,  every  well-grounded  inductive  generaliza- 
tion is  either  a law  of  nature,  or  a result  of  laws  of  nature,  capable,  if  those 
laws  are  known,  of  being  predicted  from  them.  And  the  problem  of  In- 
ductive Logic  may  be  summed  up  in  two  questions : how  to  ascertain  the 
laws  of  nature;  and  how,  after  having  ascertained  them,  to  follow  them 
into  their  results.  On  the  other  hand,  we  must  not  suffer  ourselves  to  im- 
agine that  this  mode  of  statement  amounts  to  a real  analysis,  or  to  any 
thing  but  a mere  verbal  transformation  of  the  problem ; for  the  expression, 
Laws  of  Nature,  means  nothing  but  the  uniformities  which  exist  among 
natural  phenomena)  or,  in  other  words,  the  results  of  induction),  when  re- 
duced to  their  simplest  expression.  It  is,  however,  something  to  have  ad- 
vanced so  far,  as  to  see  that  the  study  of  nature  is  the  study  of  laws,  not  a 
law;  of  uniformities, in  the  plural  number:  that  the  different  natural  phe- 
nomena have  their  separate  rules  or  modes  of  taking  place,  which,  though 
much  intermixed  and  entangled  with  one  another,  may,  to  a certain  extent, 
be  studied  apart:  that  (to  resume  our  former  metaphor)  the  regularity 
which  exists  in  nature  is  a web  composed  of  distinct  threads,  and  only  to 
be  understood  by  tracing  each  of  the  threads  separately;  for  which  pur- 
pose it  is  often  necessary  to  unravel  some  portion  of  the  web,  and  exhibit 
the  fibres  apart.  The  rules  of  experimental  inquiry  are  the  contrivances 
for  unraveling  the  web. 

§ 2.  In  thus  attempting  to  ascertain  the  general  order  of  nature  by  as- 
certaining the  particular  order  of  the  occurrence  of  each  one  of  the  phe- 
nomena of  nature,  the  most  scientific  proceeding  can  be  no  more  than  an  im- 
proved form  of  that  which  was  primitively  pursued  by  the  human  under- 
standing, while  undirected  by  science.  When  mankind  first  formed  the 
idea  of  studying  phenomena  according  to  a stricter  and  surer  method  than 
that  which  they  had  in  the  first  instance  spontaneously  adopted,  they  did 
not,  conformably  to  the  well-meant  but  impracticable  precept  of  Descartes, 
set  out  from  the  supposition  that  nothing  had  been  already  ascertained. 
Many  of  the  uniformities  existing  among  phenomena  are  so  constant,  and 
so  open  to  observation,  as  to  force  themselves  upon  involuntary  recognition. 
Some  facts  are  so  perpetually  and  familiarly  accompanied  by  certain  oth- 
ers, that  mankind  learned,  as  children  learn,  to  expect  the  one  where  they 
found  the  other,  long  before  they  knew  how  to  put  their  expectation  into 
words  by  asserting,  in  a proposition,  the  existence  of  a connection  between 
those  phenomena.  No  science  was  needed  to  teach  that  food  nourishes, 
that  water  drowns,  or  quenches  thirst,  that  the  sun  gives  light  and  heat, 
that  bodies  fall  to  the  ground.  The  first  scientific  inquirers  assumed  these 
and  the  like  as  known  truths,  and  set  out  from  them  to  discover  others 
which  were  unknown:  nor  were  they  wrong  in  so  doing, subject, however, 
as  they  afterward  began  to  see,  to  an  ulterior  revision  of  these  spontaneous 
generalizations  themselves,  when  the  progress  of  knowledge  pointed  out 
limits  to  them,  or  showed  their  truth  to  be  contingent  on  some  circum- 
stance not  originally  attended  to.  It  will  appear,  I think,  from  the  subse- 
quent part  of  our  inquiry,  that  there  is  no  logical  fallacy  in  this  mode  of 
proceeding  ; but  we  may  see  already  that  any  other  mode  is  rigorously  im- 
practicable: since  it  is  impossible  to  frame  any  scientific  method  of  induc- 
tion, or  test  of  the  correctness  of  inductions,  unless  on  the  hypothesis  that 
some  inductions  deserving  of  reliance  have  been  already  made. 

Let  us  revert,  for  instance,  to  one  of  our  former  illustrations,  and  con- 
sider why  it  is  that,  with  exactly  the  same  amount  of  evidence,  both  nega- 


232 


INDUCTION. 


tive  and  positive,  we  did  not  reject  the  assertion  that  there  are  black 
swans,  while  we  should  refuse  credence  to  any  testimony  which  asserted 
that  there  were  men  wearing  their  heads  underneath  their  shoulders.  The 
first  assertion  was  more  credible  than  the  latter.  But  why  more  credible? 
So  long  as  neither  phenomenon  had  been  actually  witnessed,  what  reason 
was  there  for  finding  the  one  harder  to  be  believed  than  the  other?  Ap- 
parently because  there  is  less  constancy  in  the  colors  of  animals,  than  in 
the  general  structure  of  their  anatomy.  But  how  do  we  know  this? 
Doubtless,  from  experience.  It  appears,  then,  that  we  need  experience  to 
inform  us,  in  what  degree,  and  in  what  cases,  or  sorts  of  cases,  experience 
is  to  be  relied  on.  Experience  must  be  consulted  in  order  to  learn  from  it 
under  what  circumstances  arguments  from  it  will  be  valid.  We  have  no 
ulterior  test  to  which  we  subject  experience  in  general;  but  we  make  ex- 
perience its  own  test.  Experience  testifies,  that  among  the  uniformities 
which  it  exhibits  or  seems  to  exhibit,  some  are  more  to  be  relied  on  than 
others;  and  uniformity,  therefore,  may  be  presumed,  from  any  given  num- 
ber of  instances,  with  a greater  degree  of  assurance,  in  proportion  as  the 
case  belongs  to  a class  in  which  the  uniformities  have  hitherto  been  found 
more  uniform. 

This  mode  of  correcting  one  generalization  by  means  of  another,  a nar- 
rower generalization  by  a wider,  which  common  sense  suggests  and  adopts 
in  practice,  is  the  real  type  of  scientific  Induction.  All  that  art  can  do  is 
but  to  give  accuracy  and  precision  to  this  process,  and  adapt  it  to  all  va- 
rieties of  cases,  without  any  essential  alteration  in  its  principle. 

There  are  of  course  no  means  of  applying  such  a test  as  that  above  de- 
scribed, unless  we  already  possess  a general  knowledge  of  the  prevalent 
character  of  the  uniformities  existing  throughout  nature.  The  indispen- 
sable foundation,  therefore,  of  a scientific  formula  of  induction,  must  be  a 
survey  of  the  inductions  to  which  mankind  have  been  conducted  in  unsci- 
entific practice  ; with  the  special  purpose  of  ascertaining  what  kinds  of 
uniformities  have  been  found  perfectly  invariable,  pervading  all  nature, 
and  what  are  those  which  have  been  found  to  vary  with  difference  of  time, 
place,  or  other  changeable  circumstances. 

§ 3.  The  necessity  of  such  a survey  is  confirmed  by  the  consideration, 
that  the  stronger  inductions  are  the  touch-stone  to  which  we  always  en- 
deavor to  bring  the  weaker.  If  we  find  any  means  of  deducing  one  of 
the  less  strong  inductions  from  stronger  ones,  it  acquires,  at  once,  all  the 
strength  of  those  from  which  it  is  deduced  ; and  even  adds  to  that  strength  ; 
since  the  independent  experience  on  which  the  weaker  induction  previously 
rested,  becomes  additional  evidence  of  the  truth  of  the  better  established 
law  in  which  it  is  now  found  to  be  included.  We  may  have  inferred,  from 
historical  evidence,  that  the  uncontrolled  power  of  a monarch,  of  an  aris- 
tocracy, or  of  the  majority,  will  often  be  abused  : but  we  are  entitled  to 
rely  on  this  generalization  with  much  greater  assurance  when  it  is  shown 
to  be  a corollary  from  still  better  established  facts ; the  very  low  degree 
of  elevation  of  character  ever  yet  attained  by  the  average  of  mankind,  and 
the  little  efficacy,  for  the  most  part,  of  the  modes  of  education  hitherto 
practiced,  in  maintaining  the  predominance  of  reason  and  conscience  over 
the  selfish  propensities.  It  is  at  the  same  time  obvious  that  even  these 
more  general  facts  derive  an  accession  of  evidence  from  the  testimony 
which  history  bears  to  the  effects  of  despotism.  The  strong  induction  be- 
comes still  stronger  when  a weaker  one  has  been  bound  up  with  it. 

On  the  other  hand,  if  an  induction  conflicts  with  stronger  inductions, 


LAWS  OF  NATURE. 


233 


or  with  conclusions  capable  of  being  correctly  deduced  from  them,  then, 
unless  on  reconsideration  it  should  appear  that  some  of  the  stronger  induc- 
tions have  been  expressed  with  greater  universality  than  their  evidence 
warrants,  the  weaker  one  must  give  way.  The  opinion  so  long  prevalent 
that  a comet,  or  any  other  unusual  appearance  in  the  heavenly  regions,  was 
the  precursor  of  calamities  to  mankind,  or  to  those  at  least  who  witnessed 
it;  the  belief  in  the  veracity  of  the  oracles  of  Delphi  or  Dodona;  the  reli- 
ance on  astrology,  or  on  the  weather-prophecies  in  almanacs,  were  doubt- 
less inductions  supposed  to  be  grounded  on  experience:*  and  faith  in  such 
delusions  seems  quite  capable  of  holding  out  against  a great  multitude  of 
failures,  provided  it  be  nourished  by  a reasonable  number  of  casual  coinci- 
dences between  the  prediction  and  the  event.  What  has  really  put  an  end 
to  these  insufficient  inductions,  is  their  inconsistency  with  the  stronger  in- 
ductions, subsequently  obtained  by  scientific  inquiry,  respecting  the  causes 
on  which  terrestrial  events  really  depend ; and  where  those  scientific  truths 
have  not  yet  penetrated,  the  same  or  similar  delusions  still  prevail. 

It  may  be  affirmed  as  a general  principle,  that  all  inductions,  whether 
strong  or  weak,  which  can  be  connected  by  ratiocination,  are  confirmatory 
of  one  another ; while  any  which  lead  deductively  to  consequences  that  are 
incompatible,  become  mutually  each  other’s  test,  showing  that  one  or  other 
must  be  given  up,  or  at  least  more  guardedly  expressed.  In  the  case  of 
inductions  which  confirm  each  other,  the  one  which  becomes  a conclusion 
from  ratiocination  rises  to  at  least  the  level  of  certainty  of  the  weakest  of 
those  from  which  it  is  deduced;  while  in  general  all  are  more  or  less  in- 
creased in  certainty.  Thus  the  Torricellian  experiment,  though  a mere 
case  of  three  more  general  laws,  not  only  strengthened  greatly  the  evidence 
on  which  those  laws  rested,  but  converted  one  of  them  (the  weight  of  the 
atmosphere)  from  a still  doubtful  generalization  into  a completely  estab- 
lished doctrine. 

If,  then,  a survey  of  the  uniformities  which  have  been  ascertained  to  ex- 
ist in  nature,  should  point  out  some  which,  as  far  as  any  human  purpose  re- 
quires certainty,  may  be  considered  quite  certain  and  quite  universal ; then 
by  means  of  these  uniformities  we  may  be  able  to  raise  multitudes  of  other 
inductions  to  the  same  point  in  the  scale.  For  if  we  can  show,  with  re- 

* Dr.  Whewell  (Phil,  of  Discov.,  p.  246)  will  not  nllow  these  and  similar  erroneous  judg- 
ments to  be  called  inductions;  inasmuch  as  such  superstitious  fancies  “were  not  collected 
from  the  facts  by  seeking  a law  of  their  occurrence,  but  were  suggested  by  an  imagination  of 
the  anger  of  superior  powers,  shown  by  such  deviations  from  the  ordinary  course  of  nature.” 
I conceive  the  question  to  be,  not  in  what  manner  these  notions  were  at  first  suggested,  but 
by  what  evidence  they  have,  from  time  to  time,  been  supposed  to  be  substantiated.  If  the  be- 
lievers in  these  erroneous  opinions  had  been  put  on  their  defense,  they  would  have  referred 
to  experience : to  the  comet  which  preceded  the  assassination  of  Julius  Cajsar,  or  to  oracles 
and  other  prophecies  known  to  have  been  fulfilled.  It  is  by  such  appeals  to  facts  that  all 
analogous  superstitions,  even  in  our  day,  attempt  to  justify  themselves ; the  supposed  evi- 
dence of  experience  is  necessary  to  their  hold  on  the  mind.  I quite  admit  that  the  influence 
of  such  coincidences  would  not  be  what  it  is,  if  strength  were  not  lent  to  it  by  an  antecedent 
presumption  ; but  this  is  not  peculiar  to  such  cases ; preconceived  notions  of  probability  form 
part  of  the  explanation  of  many  other  cases  of  belief  on  insufficient  evidence.  The  a priori 
prejudice  does  not  prevent  the  erroneous  opinion  from  being  sincerely  regarded  as  a legiti- 
mate conclusion  from  experience ; though  it  improperly  predisposes  the  mind  to  that  inter- 
pretation of  experience. 

Thus  much  in  defense  of  the  sort  of  examples  objected  to.  But  it  would  be  easy  to  pro- 
duce instances,  equally  adapted  to  the  purpose,  and  in  which  no  antecedent  prejudice  is  at  all 
concerned.  “For  many  ages,”  says  Archbishop  Whately,  “all  farmers  and  gardeners  were 
firmly  convinced — and  convinced  of  their  knowing  it  by  experience — that  the  crops  would 
never  turn  out  good  unless  the  seed  were  sown  during  the  increase  of  the  moon.”  This  was 
induction,  but  bad  induction;  just  as  a vicious  syllogism  is  reasoning,  but  bad  reasoning. 


234 


INDUCTION. 


spect  to  any  inductive  inference,  that  either  it  must  be  true,  or  one  of  these 
certain  and  universal  inductions  must  admit  of  an  exception  ; the  former 
generalization  will  attain  the  same  certainty,  and  indefeasibleness  within 
the  bounds  assigned  to  it,  which  are  the  attributes  of  the  latter.  It  will 
be  proved  to  be  a law ; and  if  not  a result  of  other  and  simpler  laws,  it  will 
be  a law  of  nature. 

There  are  such  certain  and  universal  inductions ; and  it  is  because  there 
are  such,  that  a Logic  of  Induction  is  possible. 


CHAPTER  Y. 

OF  THE  LAW  OF  UNIVERSAL  CAUSATION. 

§ 1.  The  phenomena  of  nature  exist  in  two  distinct  relations  to  one  an- 
other ; that  of  simultaneity,  and  that  of  succession.  Every  phenomenon  is 
related,  in  a uniform  manner,  to  some  phenomena  that  co-exist  with  it,  and 
to  some  that  have  preceded  and  will  follow  it. 

Of  the  uniformities  which  exist  among  synchronous  phenomena,  the  most 
important,  on  every  account,  are  the  laws  of  number;  and  next  to  them 
those  of  space,  or,  in  other  words,  of  extension  and  figure.  The  laws  of 
number  are  common  to  synchronous  and  successive  phenomena.  That  two 
and  two  make  four,  is  equally  true  whether  the  second  two  follow  the  first 
two  or  accompany  them.  It  is  as  true  of  days  and  years  as  of  feet  and 
inches.  The  laws  of  extension  and  figure  (in  other  words,  the  theorems 
of  geometry,  from  its  lowest  to  its  highest  branches)  are,  on  the  contrary, 
laws  of  simultaneous  jihenomena  only.  The  various  parts  of  space,  and  of 
the  objects  which  are  said  to  fill  space,  co-exist ; and  the  unvarying  laws 
which  are  the  subject  of  the  science  of  geometry,  are  an  expression  of  the 
mode  of  their  co-existence. 

This  is  a class  of  laws,  or  in  other  words,  of  uniformities,  for  the  com- 
prehension and  proof  of  which  it  is  not  necessary  to  suppose  any  lapse  of 
time,  any  variety  of  facts  or  events  succeeding  one  another.  The  proposi- 
tions of  geometry  are  independent  of  the  succession  of  events.  All  things 
which  possess  extension,  or,  in  other  words,  which  fill  space,  are  subject  to 
geometrical  laws.  Possessing  extension,  they  possess  figure ; possessing 
figure,  they  must  possess  some  figure  in  particular,  and  have  all  the  proper- 
ties which  geometry  assigns  to  that  figure.  If  one  body  be  a sphere  and 
another  a cylinder,  of  equal  height  and  diameter,  the  one  will  be  exactly 
two-thirds  of  the  other,  let  the  nature  and  quality  of  the  material  be  what 
it  will.  Again,  each  body,  and  each  point  of  a body,  must  occupy  some 
place  or  position  among  other  bodies ; and  the  position  of  two  bodies  rela- 
tively to  each  other,  of  whatever  nature  the  bodies  be,  may  be  unerringly 
inferred  from  the  position  of  each  of  them  relatively  to  any  third  body. 

In  the  laws  of  number,  then,  and  in  those  of  space,  we  recognize  in  the 
most  unqualified  manner,  the  rigorous  universality  of  which  we  are  in 
quest.  Those  laws  have  been  in  all  ages  the  type  of  certainty,  the  standard 
of  comparison  for  all  inferior  degrees  of  evidence.  Their  invariability  is  so 
perfect,  that  it  renders  us  unable  even  to  conceive  any  exception  to  them ; 
and  philosophers  have  been  led,  though  (as  I have  endeavored  to  show)  er- 
roneously, to  consider  their  evidence  as  lying  not  in  experience,  but  in  the 
original  constitution  of  the  intellect.  If,  therefore,  from  the  laws  of  space 
and  number,  we  were  able  to  deduce  uniformities  of  any  other  description, 


LAW  OF  CAUSATION. 


235 


this  would  be  conclusive  evidence  to  us  that  those  other  uniformities  pos- 
sessed the  same  rigorous  certainty.  But  this  we  can  not  do.  From  laws 
of  space  and  number  alone,  nothing  can  be  deduced  but  laws  of  space  and 
number. 

Of  all  truths  relating  to  phenomena,  the  most  valuable  to  us  are  those 
which  relate  to  the  order  of  their  succession.  On  a knowledge  of  these  is 
founded  every  reasonable  anticipation  of  future  facts,  and  whatever  power 
we  possess  of  influencing  those  facts  to  our  advantage.  Even  the  laws  of 
geometry  are  chiefly  of  practical  importance  to  us  as  being  a portion  of  the 
premises  from  which  the  order  of  the  succession  of  phenomena  may  be  in- 
ferred. Inasmuch  as  the  motion  of  bodies,  the  action  of  forces,  and  the 
propagation  of  influences  of  all  sorts,  take  place  in  certain  lines  and  over 
definite  spaces,  the  properties  of  those  lines  and  spaces  are  an  important 
part  of  the  laws  to  which  those  phenomena  are  themselves  subject.  Again, 
motions,  forces,  or  other  influences,  and  times,  are  numerable  quantities ; 
and  the  properties  of  number  are  applicable  to  them  as  to  all  other  things. 
But  though  the  laws  of  number  and  space  are  important  elements  in  the 
ascertainment  of  uniformities  of  succession,  they  can  do  nothing  toward  it 
when  taken  by  themselves.  They  can  only  be  made  instrumental  to  that 
purpose  when  we  combine  with  them  additional  premises,  expressive  of 
uniformities  of  succession  already  known.  By  taking,  for  instance,  as 
premises  these  propositions,  that  bodies  acted  upon  by  an  instantaneous 
force  move  with  uniform  velocity  in  straight  lines ; that  bodies  acted  upon 
by  a continuous  force  move  with  accelerated  velocity  in  straight  lines ; and 
that  bodies  acted  upon  by  two  forces  in  different  directions  move  in  the 
diagonal  of  a parallelogram,  whose  sides  represent  the  direction  and  quan- 
tity of  those  forces ; we  may  by  combining  these  truths  with  propositions 
relating  to  the  properties  of  straight  lines  and  of  parallelograms  (as  that  a 
triangle  is  half  a parallelogram  of  the  same  base  and  altitude),  deduce  an- 
other important  uniformity  of  succession,  viz.,  that  a body  moving  round 
a centre  of  force  describes  areas  jmoportional  to  the  times.  But  unless 
there  had  been  laws  of  succession  in  our  premises,  there  could  have  been 
no  truths  of  succession  in  our  conclusions.  A similar  remark  might  be 
extended  to  every  other  class  of  phenomena  really  peculiar ; and,  had  it 
been  attended  to,  would  have  prevented  many  chimerical  attempts  at  dem- 
onstrations of  the  indemonstrable,  and  explanations  which  do  not  explain. 

It  is  not,  therefore,  enough  for  us  that  the  laws  of  space,  which  are  only 
laws  of  simultaneous  phenomenon,  and  the  laws  of  number,  which  though 
true  of  successive  phenomena  do  not  relate  to  their  succession,  possess  the 
rigorous  certainty  and  universality  of  which  we  are  in  search.  We  must 
endeavor  to  find  some  law  of  succession  which  has  those  same  attributes, 
and  is  therefore  fit  to  be  made  the  foundation  of  processes  for  discovering, 
and  of  a test  for  verifying,  all  other  uniformities  of  succession.  This  fun- 
damental law  must  resemble  the  truths  of  geometry  in  their  most  remark- 
able peculiarity,  that  of  never  being,  in  any  instance  whatever,  defeated  or 
suspended  by  any  change  of  circumstances. 

ISTow  among  all  those  uniformities  in  the  succession  of  phenomena,  which 
common  observation  is  sufficient  to  bring  to  light,  there  are  very  few  which 
have  any,  even  apparent,  pretension  to  this  rigorous  indefeasibility  : and  of 
those  few,  one  only  has  been  found  capable  of  completely  sustaining  it.  In 
that  one,  however,  we  recognize  a law  which  is  universal  also  in  another 
sense ; it  is  co-extensive  with  the  entire  field  of  successive  phenomena,  all 
instances  whatever  of  succession  being  examples  of  it.  This  law  is  the 


236 


INDUCTION. 


Law  of  Causation.  The  truth  that  every  fact  which  has  a beginning  has  a 
cause,  is  co-extensive  with  human  experience. 

This  generalization  may  appear  to  some  minds  not  to  amount  to  much, 
since  after  all  it  asserts  only  this:  “it  is  a law,  that  every  event  depends 
on  some  law “ it  is  a law,  that  there  is  a law  for  every  thing.”  We  must 
not,  however,  conclude  that  the  generality  of  the  principle  is  merely  verbal ; 
it  will  be  found  on  inspection  to  be  no  vague  or  unmeaning  assertion,  but 
a most  important  and  really  fundamental  truth. 

§ 2.  The  notion  of  Cause  being  the  root  of  the  whole  theory  of  Induc- 
tion, it  is  indispensable  that  this  idea  should,  at  the  very  outset  of  our  in 
quiry,  be,  with  the  utmost  practicable  degree  of  precision,  fixed  and  deter- 
mined. If,  indeed,  it  were  necessary  for  the  purpose  of  inductive  logic 
that  the  strife  should  be  quelled,  which  has  so  long  raged  among  the  differ- 
ent schools  of  metaphysicians,  respecting  the  origin  and  analysis  of  our  idea 
of  causation;  the  promulgation,  or  at  least  the  general  reception,  of  a true 
theory  of  induction,  might  be  considered  desperate  for  a long  time  to  come. 
But  the  science  of  the  Investigation  of  Truth  by  means  of  Evidence,  is 
happily  independent  of  many  of  the  controversies  which  perplex  the  sci- 
ence of  the  ultimate  constitution  of  the  human  mind,  and  is  under  no  ne- 
cessity of  pushing  the  analysis  of  mental  phenomenon  to  that  extreme 
limit  which  alone  ought  to  satisfy  a metaphysician. 

I premise,  then,  that  when  in  the  course  of  this  inquiry  I speak  of  the 
cause  of  any  phenomenon,  I do  not  mean  a cause  which  is  not  itself  a phe- 
nomenon ; I make  no  research  into  the  ultimate  or  ontological  cause  of 
any  thing.  To  adopt  a distinction  familiar  in  the  writings  of  the  Scotch 
metaphysicians,  and  especially  of  Reid,  the  causes  with  which  I concern 
myself  are  not  efficient,  but  physical  causes.  They  are  causes  in  that  sense 
alone,  in  which  one  physical  fact  is  said  to  be  the  cause  of  another.  Of 
the  efficient  causes  of  phenomena,  or  whether  any  such  causes  exist  at  all, 
I am  not  called  upon  to  give  an  opinion.  The  notion  of  causation  is  deem- 
ed, by  the  schools  of  metaphysics  most  in  vogue  at  the  present  moment,  to 
imply  a mysterious  and  most  powerful  tie,  such  as  can  not,  or  at  least  does 
not,  exist  between  any  physical  fact  and  that  other  physical  fact  on  which 
it  is  invariably  consequent,  and  which  is  popularly  termed  its  cause : and 
thence  is  deduced  the  supposed  necessity  of  ascending  higher,  into  the  es- 
sences and  inherent  constitution  of  things,  to  find  the  true  cause,  the  cause 
which  is  not  only  followed  by,  but  actually  produces,  the  effect.  No  such 
necessity  exists  for  the  purposes  of  the  present  inquiry,  nor  will  any  such 
doctrine  be  found  in  the  following  pages.  The  only  notion  of  a cause, 
which  the  theory  of  induction  requires,  is  such  a notion  as  can  be  gained 
from  experience.  The  Law  of  Causation,  the  recognition  of  which  is  the 
main  pillar  of  inductive  science,  is  but  the  familiar  truth,  that  invariability 
of  succession  is  found  by  observation  to  obtain  between  every  fact  in  na- 
ture and  some  other  fact  which  has  preceded  it;  independently  of  all  con- 
siderations respecting  the  ultimate  mode  of  production  of  phenomena,  and 
of  every  other  question  regarding  the  nature  of  “ Things  in  themselves.” 

Between  the  phenomena,  then,  which  exist  at  any  instant,  and  the  phe- 
nomena which  exist  at  the  succeeding  instant,  there  is  an  invariable  order 
of  succession ; and,  as  we  said  in  speaking  of  the  general  uniformity  of  the 
course  of  nature,  this  web  is  composed  of  separate  fibres ; this  collective 
order  is  made  up  of  particular  sequences,  obtaining  invariably  among  the 
separate  parts.  To  certain  facts,  certain  facts  always  do,  and,  as  we  be- 


LAW  or  CAUSATION. 


237 


lieve,  will  continue  to,  succeed.  The  invariable  antecedent  is  termed  the 
cause;  the  invariable  consequent,  the  effect.  And  the  universality  of  the 
law  of  causation  consists  in  this,  that  every  consequent  is  connected  in  this 
manner  with  some  particular  antecedent,  or  set  of  antecedents.  Let  the 
fact  be  what  it  may,  if  it  has  begun  to  exist,  it  was  preceded  by  some  fact 
or  facts,  with  which  it  is  invariably  connected.  For  every  event  there  ex- 
ists some  combination  of  objects  or  events,  some  given  concurrence  of  cir- 
cumstances, positive  and  negative,  the  occurrence  of  which  is  always  fol- 
lowed by  that  phenomenon.  We  may  not  have  found  out  what  this  con- 
currence of  circumstances  may  be ; but  we  never  doubt  that  there  is  such 
a one,  and  that  it  never  occurs  without  having  the  phenomenon  in  question 
as  its  effect  or  consequence.  On  the  universality  of  this  truth  depends  the 
possibility  of  reducing  the  inductive  process  to  rules.  The  undoubted  as- 
surance we  have  that  there  is  a law  to  be  found  if  we  only  knew  how  to 
find  it,  will  be  seen  presently  to  be  the  source  from  which  the  canons  of 
the  Inductive  Logic  derive  their  validity. 

§ 3.  It  is  seldom,  if  ever,  between  a consequent  and  a single  antecedent, 
that  this  invariable  sequence  subsists.  It  is  usually  between  a consequent 
and  the  sum  of  several  antecedents ; the  concurrence  of  all  of  them  being 
requisite  to  produce,  that  is,  to  be  certain  of  being  followed  by,  the  conse- 
quent. In  such  cases  it  is  very  common  to  single  out  one  only  of  the  an- 
tecedents under  the  denomination  of  Cause,  calling  the  others  merely  Con- 
ditions. Tims,  if  a person  eats  of  a particular  dish,  and  dies  in  consequence, 
that  is,  would  not  have  died  if  he  had  not  eaten  of  it,  people  would  be  apt 
to  say  that  eating  of  that  dish  was  the  cause  of  his  death.  There  needs 
not,  however,  be  any  invariable  connection  between  eating  of  the  dish  and 
death ; but  there  certainly  is,  among  the  circumstances  which  took  place, 
some  combination  or  other  on  which  death  is  invariably  consequent : as, 
for  instance,  the  act  of  eating  of  the  dish,  combined  with  a particular  bod- 
ily constitution,  a particular  state  of  present  health,  and  perhaps  even  a 
certain  state  of  the  atmosphere;  the  whole  of  which  circumstances  per- 
haps constituted  in  this  particular  case  the  conditions  of  the  phenomenon, 
or,  in  other  words,  the  set  of  antecedents  which  determined  it,  and  but  for 
which  it  would  not  have  happened.  The  real  Cause,  is  the  whole  of  these 
antecedents ; and  we  have,  philosophically  speaking,  no  right  to  give  the 
name  of  cause  to  one  of  them,  exclusively  of  the  others.  What,  in  the 
case  we  have  supposed,  disguises  the  incorrectness  of  the  expression,  is 
this:  that  the  various  conditions,  except  the  single  one  of  eating  the  food, 
were  not  events  (that  is,  instantaneous  changes,  or  successions  of  instan- 
taneous changes)  but  states,  possessing  more  or  less  of  permanency ; and 
might  therefore  have  preceded  the  effect  by  an  indefinite  length  of  dura- 
tion, for  want  of  the  event  which  was  requisite  to  complete  the  required 
concurrence  of  conditions : w’hile  as  soon  as  that  event,  eating  the  food, 
occurs,  no  other  cause  is  waited  for,  but  the  effect  begins  immediately  to 
take  place : and  hence  the  appearance  is  presented  of  a more  immediate 
and  close  connection  between  the  effect  and  that  one  antecedent,  than  be- 
tween the  effect  and  the  remaining  conditions.  But  though  we  may  think 
proper  to  give  the  name  of  cause  to  that  one  condition,  the  fulfillment  of 
which  completes  the  tale,  and  brings  about  the  effect  without  further  de- 
lay ; this  condition  has  really  no  closer  relation  to  the  effect  than  any  of 
the  other  conditions  has.  All  the  conditions  were  equally  indispensable  to 
the  production  of  the  consequent ; and  the  statement  of  the  cause  is  incom- 


23S 


INDUCTION. 


plete,  unless  in  some  shape  or  other  we  introduce  them  all.  A man  takes 
mercury,  goes  out-of-doors,  and  catches  cold.  We  say,  perhaps,  that  the 
cause  of  his  taking  cold  was  exposure  to  the  air.  It  is  clear,  however, 
that  his  having  taken  mercury  may  have  been  a necessary  condition  of 
his  catching  cold;  and  though  it  might  consist  with  usage  to  say  that  the 
cause  of  his  attack  was  exposure  to  the  air,  to  be  accurate  we  ought  to 
say  that  the  cause  was  exposure  to  the  air  while  under  the  effect  of  mer- 
cury. 

If  we  do  not,  when  aiming  at  accuracy,  enumerate  all  the  conditions,  it 
is  only  because  some  of  them  will  in  most  cases  be  understood  without 
being  expressed,  or  because  for  the  purpose  in  view  they  may  without 
detriment  be  overlooked.  For  example,  when  we  say,  the  cause  of  a man’s 
death  was  that  his  foot  slipped  in  climbing  a ladder,  we  omit  as  a thing 
unnecessary  to  be  stated  the  circumstance  of  his  weight,  though  quite  as 
indispensable  a condition  of  the  effect  which  took  place.  When  we  say 
that  the  assent  of  the  crown  to  a bill  makes  it  law,  we  mean  that  the  as- 
sent, being  never  given  until  all  the  other  conditions  are  fulfilled,  makes  up 
the  sum  of  the  conditions,  though  no  one  now  regards  it  as  the  principal 
one.  When  the  decision  of  a legislative  assembly  has  been  determined 
by  the  casting  vote  of  the  chairman,  we  sometimes  say  that  this  one  person 
was  the  cause  of  all  the  effects  which  resulted  from  the  enactment.  Yet 
we  do  not  really  suppose  that  his  single  vote  contributed  more  to  the  re- 
sult than  that  of  any  other  person  who  voted  in  the  affirmative ; but,  for 
the  purpose  we  have  in  view,  which  is  to  insist  on  his  individual  responsi- 
bility, the  part  which  any  other  person  had  in  the  transaction  is  not  ma- 
terial. 

In  all  these  instances  the  fact  which  was  dignified  with  the  name  of 
cause,  was  the  one  condition  which  came  last  into  existence.  But  it  must 
not  be  supposed  that  in  the  employment  of  the  term  this  or  any  other  rule 
is  always  adhered  to.  Nothing  can  better  show  the  absence  of  any  scien- 
tific ground  for  the  distinction  between  the  cause  of  a phenomenon  and  its 
conditions,  than  the  capricious  manner  in  which  we  select  from  among  the 
conditions  that  which  we  choose  to  denominate  the  cause.  However  nu- 
merous the  conditions  may  be,  there  is  hardly  any  of  them  which  may  not, 
according  to  the  purpose  of  our  immediate  discourse,  obtain  that  nominal 
pre-eminence.  This  will  be  seen  by  analyzing  the  conditions  of  some  one 
familiar  phenomenon.  For  example,  a stone  thrown  into  water  falls  to  the 
bottom.  What  are  the  conditions  of  this  event?  In  the  first  place  there 
must  be  a stone,  and  water,  and  the  stone  must  be  thrown  into  the  water ; 
but  these  suppositions  forming  part  of  the  enunciation  of  the  phenomenon 
itself,  to  include  them  also  among  the  conditions  would  be  a vicious  tautol- 
ogy ; and  this  class  of  conditions,  therefore,  have  never  received  the  name 
of  cause  from  any  but  the  Aristotelians,  by  whom  they  were  called  the  ma- 
terial cause,  causa  materialis.  The  next  condition  is,  there  must  be  an 
earth  : and  accordingly  it  is  often  said,  that  the  fall  of  a stone  is  caused  by 
the  earth  ; or  by  a power  or  property  of  the  earth,  or  a force  exerted  by  the 
earth,  all  of  which  are  merely  roundabout  ways  of  saying  that  it  is  caused 
by  the  earth  ; or,  lastly,  the  earth’s  attraction ; which  also  is  only  a technical 
mode  of  saying  that  the  earth  causes  the  motion,  with  the  additional  pai-- 
ticularity  that  the  motion  is  toward  the  earth,  which  is  not  a character  of 
the  cause,  but  of  the  effect.  Let  us  now  pass  to  another  condition.  It  is 
not  enough  that  the  earth  should  exist;  the  body  must  be  within  that  dis- 
tance from  it,  in  which  the  earth’s  attraction  preponderates  over  that  of  any 


LAW  OF  CAUSATION. 


239 


other  body.  Accordingly  we  may  say,  and  the  expression  would  be  con- 
fessedly correct,  that  the  cause  of  the  stone’s  falling  is  its  being  within  the 
sphere  of  the  earth’s  attraction.  We  proceed  to  a further  condition.  The 
stone  is  immersed  in  water:  it  is  therefore  a condition  of  its  reaching  the 
ground,  that  its  specific  gravity  exceed  that  of  the  surrounding  fluid,  or  in 
other  words  that  it  surpass  in  weight  an  equal  volume  of  water.  Accord- 
ingly any  one  would  be  acknowledged  to  speak  correctly  who  said,  that  the 
cause  of  the  stone’s  going  to  the  bottom  is  its  exceeding  in  specific  gravity 
the  fluid  in  which  it  is  immersed. 

Thus  we  see  that  each  and  every  condition  of  the  phenomenon  may  be 
taken  in  its  turn,  and,  with  equal  propriety  in  common  parlance,  but  with 
equal  impropriety  in  scientific  discourse,  may  be  spoken  of  as  if  it  were  the 
entire  cause.  And  in  practice,  that  particular  condition  is  usually  styled 
the  cause,  whose  share  in  the  matter  is  superficially  the  most  conspicuous, 
or  whose  requisiteness  to  the  production  of  the  effect  we  happen  to  be  in- 
sisting on  at  the  moment.  So  great  is  the  force  of  this  last  consideration, 
that  it  sometimes  induces  us  to  give  the  name  of  cause  even  to  one  of  the 
negative  conditions.  We  say,  for  example,  The  army  was  surprised  be- 
cause the  sentinel  was  off  his  post.  But  since  the  sentinel’s  absence  was 
not  what  created  the  enemy,  or  put  the  soldiers  asleep,  how  did  it  cause 
them  to  be  surprised  ? All  that  is  really  meant  is,  that  the  event  would 
not  have  happened  if  he  had  been  at  his  duty.  His  being  off  his  post  was 
no  producing  cause,  but  the  mere  absence  of  a preventing  cause : it  was 
simply  equivalent  to  his  non-existence.  From  nothing,  from  a mere  nega- 
tion, no  consequences  can  proceed.  All  effects  are  connected,  by  the  law 
of  causation,  with  some  set  of  positive  conditions;  negative  ones,  it  is  true, 
being  almost  always  required  in  addition.  In  other  words,  every  fact  or 
phenomenon  which  has  a beginning,  invariably  arises  when  some  certain 
combination  of  positive  facts  exists,  provided  certain  other  positive  facts 
do  not  exist. 

There  is,  no  doubt,  a tendency  (which  our  first  example,  that  of  death 
from  taking  a particular  food,  sufficiently  illustrates)  to  associate  the  idea 
of  causation  with  the  proximate  antecedent  event,  rather  than  with  any  of 
the  antecedent  states,  or  permanent  facts,  which  may  happen  also  to  be 
conditions  of  the  phenomenon  ; the  reason  being  that  the  event  not  only 
exists,  but  begins  to  exist  immediately  previous ; while  the  other  condi- 
tions may  have  pre-existed  for  an  indefinite  time.  And  this  tendency 
shows  itself  very  visibly  in  the  different  logical  fictions  which  are  resorted 
to,  even  by  men  of  science,  to  avoid  the  necessity  of  giving  the  name  of 
cause  to  any  thing  which  had  existed  for  an  indeterminate  length  of  time 
before  the  effect.  Thus,  rather  than  say  that  the  earth  causes  the  fall  of 
bodies,  they  ascribe  it  to  a force  exerted  by  the  earth,  or  an  attraction  by 
the  earth,  abstractions  which  they  can  represent  to  themselves  as  exhausted 
by  each  effort,  and  therefore  constituting  at  each  successive  instant  a fresh 
fact,  simultaneous  with,  or  only  immediately  preceding,  the  effect.  Inas- 
much as  the  coming  of  the  circumstance  which  completes  the  assemblage 
of  conditions,  is  a change  or  event,  it  thence  happens  that  an  event  is  al- 
ways the  antecedent  in  closest  apparent  proximity  to  the  consequent:  and 
this  may  account  for  the  illusion  which  disposes  us  to  look  upon  the  prox- 
imate event  as  standing  more  peculiarly  in  the  position  of  a cause  than  any 
of  the  antecedent  states.  But  even  this  peculiarity,  of  being  in  closer  prox- 
imity to  the  effect  than  any  other  of  its  conditions,  is,  as  we  have  already 
seen,  far  from  being  necessary  to  the  common  notion  of  a cause;  with 


240 


INDUCTION. 


which  notion,  on  the  contrary,  any  one  of  the  conditions,  either  positive  or 
negative,  is  found,  on  occasion,  completely  to  accord.* 

* The  assertion,  that  any  and  every  one  of  the  conditions  of  a phenomenon  may  be  and  is.  on 
some  occasions  and  for  some  purposes,  spoken  of  as  the  cause,  has  been  disputed  by  an  intel- 
ligent reviewer  of  this  work  in  the  Prospective  Review  (the  predecessor  of  the  justly  esteemed 
National  Review),  who  maintains  that  “we  always  apply  the  word  cause  rather  to  that  ele- 
ment in  the  antecedents  which  exercises  force,  and  which  would  tend  at  all  times  to  produce 
the  same  or  a similar  effect  to  that  which,  under  certain  conditions,  it  would  actually  pro- 
duced’ And  he  says,  that  “ every  one  would  feel”  the  expression,  that  the  cause  of  a surprise 
was  the  sentinel’s  being  off  his  post,  to  be  incorrect ; but  that  the  “allurement  or  force  which 
drew  him  off  his  post,  might  be  so  called,  because  in  doing  so  it  removed  a resisting  power 
which  would  have  prevented  the  surprise.”  I can  not  think  that  it  would  be  wrong  to  sav, 
that  the  event  took  place  because  the  sentinel  was  absent,  and  yet  right  to  say  that  it  took 
place  because  he  was  bribed  to  be  absent.  Since  the  only  direct  effect  of  the  bribe  was  his 
absence,  the  bribe  could  be  called  the  remote  cause  of  the  surprise,  only  on  the  supposition 
that  the  absence  was  the  proximate  cause;  nor  does  it  seem  to  me  that  any  one  (who  had 
not  a theory  to  support)  would  use  the  one  expression  and  reject  the  other. 

The  reviewer  observes,  that  when  a person  dies  of  poison,  his  possession  of  bodily  organs  is 
a necessary  condition,  but  that  no  one  would  ever  speak  of  it  as  the  cause.  I admit  the  fact; 
but  I believe  the  reason  to  be,  that  the  occasion  could  never  arise  for  so  speaking  of  it ; for 
when  in  the  inaccuracy  of  common  discourse  we  are  led  to  speak  of  some  one  condition  of  a 
phenomenon  as  its  cause,  the  condition  so  spoken  of  is  always  one  which  it  is  at  least  possi- 
ble that  the  hearer  may  require  to  be  informed  of.  The  possession  of  bodily  organs  is  a 
known  condition,  and  to  give  that  as  the  answer,  when  asked  the  cause  of  a person’s  death, 
would  not  supply  the  information  sought.  Once  conceive  that  a doubt  could  exist  as  to  his 
having  bodily  organs,  or  that  he  were  to  be  compared  with  some  being  who  had  them  not, 
and  cases  may  be  imagined  in  which  it  might  be  said  that  his  possession  of  them  was  the 
cause  of  his  death.  If  Faust  and  Mephistopheles  together  took  poison,  it  might  be  said  that 
Faust  died  because  he  was  a human  being,  and  had  a body,  while  Mephistopheles  survived 
because  he  was  a spirit. 

It  is  for  the  same  reason  that  no  one  (as  the  reviewer  remarks)  “calls  the  cause  of  a leap, 
the  muscles  or  sinews  of  the  body,  though  they  are  necessary  conditions ; nor  the  cause  of  a 
self-sacrifice,  the  knowledge  which  was  necessary  for  it ; nor  the  cause  of  writing  a book,  that 
a man  has  time  for  it,  which  is  a necessary  condition.”  These  conditions  (besides  that  they 
are  antecedent  states,  and  not  proximate  antecedent  events,  and  are  therefore  never  the  con- 
ditions in  closest  apparent  proximity  to  the  effect)  are  all  of  them  so  obviously  implied,  that  it 
is  hardly  possible  there  should  exist  that  necessity  for  insisting  on  them,  which  alone  gives 
occasion  for  speaking  of  a single  condition  as  if  it  were  the  cause.  Wherever  this  necessity 
exists  in  regard  to  some  one  condition,  and  does  not  exist  in  regard  to  any  other,  I conceive 
that  it  is  consistent  with  usage,  when  scientific  accuracy  is  not  aimed  at,  to  apply  the  name 
cause  to  that  one  condition.  If  the  only  condition  which  can  be  supposed  to  be  unknown  is 
a negative  condition,  the  negative  condition  may  be  spoken  of  as  the  cause.  It  might  be  said 
that  a person  died  for  want  of  medical  advice:  though  this  would  not  be  likely  to  be  said,  un- 
less the  person  was  already  understood  to  be  ill,  and  in  order  to  indicate  that  this  negative  cir- 
cumstance was  what  made  the  illness  fatal,  and  not  the  weakness  of  his  constitution,  or  the 
original  virulence  of  the  disease.  It  might  be  said  that  a person  was  drowned  because  he 
could  not  swim  ; the  positive  condition,  namely,  that  he  fell  into  the  water,  being  already  im- 
plied in  the  word  drowned.  And  here  let  me  remark,  that  his  falling  into  the  water  is  in 
this  case  the  only  positive  condition  : all  the  conditions  not  expressly  or  virtually  included  in 
this  (as  that  he  could  not  swim,  that  nobody  helped  him,  and  so  forth)  are  negative.  Yet,  if 
it  were  simply  said  that  the  cause  of  a man’s  death  was  falling  into  the  water,  there  would  be 
quite  as  great  a sense  of  impropriety  in  the  expression,  as  there  would  be  if  it  were  said  that 
the  cause  was  his  inability  to  swim  ; because,  though  the  one  condition  is  positive  and  the  oth- 
er negative,  it  would  be  felt  that  neither  of  them  was  sufficient,  without  the  other,  to  produce 
death. 

With  regard  to  the  assertion  that  nothing  is  termed  the  cause,  except  the  element  which 
exerts  active  force ; I waive  the  question  as  to  the  meaning  of  active  force,  and  accepting  the 
phrase  in  its  popular  sense,  I revert  to  a former  example,  and  I ask,  would  it  be  more  agree- 
able to  custom  to  say  that  a man  fell  because  his  foot  slipped  in  climbing  a ladder,  or  that  he 
fell  because  of  his  weight?  for  his  weight,  and  not  the  motion  of  his  foot,  was  the  active  force 
which  determined  his  fall.  If  a person  walking  out  in  a frosty  day,  stumbled  and  fell,  it 
might  be  said  that  he  stumbled  because  the  ground  was  slippery,  or  because  he  was  not  suf- 
ficiently careful:  but  few  people,  I suppose,  would  say,  that  he  stumbled  because  he  walked, 
Yet  the  only  active  force  concerned  was  that  which  he  exerted  in  walking:  the  others  were 


LAW  OF  CAUSATION. 


241 


The  cause,  then,  philosophically  speaking,  is  the  sum  total  of  the  condi- 
tions, positive  and  negative  taken  together;  the  whole  of  the  contingencies 
of  every  description,  which  being  realized,  the  consequent  invariably  fol- 
lows. The  negative  conditions,  however,  of  any  phenomenon,  a special 
enumeration  of  which  would  generally  be  very  prolix,  may  be  all  summed 
up  under  one  head,  namely,  the  absence  of  preventing  or  counteracting 
causes.  The  convenience  of  this  mode  of  expression  is  mainly  grounded 
on  the  fact,  that  the  effects  of  any  cause  in  counteracting  another  cause 
may  in  most  cases  be,  with  strict  scientific  exactness,  regarded  as  a mere 
extension  of  its  own  proper  and  separate  effects.  If  gravity  retards  the 
upward  motion  of  a projectile,  and  deflects  it  into  a parabolic  trajectory, 
it  produces,  in  so  doing,  the  very  same  kind  of  effect,  and  even  (as  mathe- 
maticians know)  the  same  quantity  of  effect,  as  it  does  in  its  ordinary  op- 
eration of  causing  the  fall  of  bodies  when  simply  deprived  of  their  support. 
If  an  alkaline  solution  mixed  with  an  acid  destroys  its  sourness,  and  pre- 
vents it  from  reddening  vegetable  blues,  it  is  because  the  specific  effect  of 
the  alkali  is  to  combine  with  the  acid,  and  form  a compound  with  totally 
different  qualities.  This  property,  which  causes  of  all  descriptions  possess, 
of  preventing  the  effects  of  other  causes  by  virtue  (for  the  most  part)  of 
the  same  laws  according  to  which  they  produce  their  own,*  enables  us,  by 
establishing  the  general  axiom  that  all  causes  are  liable  to  be  counteracted 
in  their  effects  by  one  another,  to  dispense  with  the  consideration  of  nega- 
tive conditions  entirely,  and  limit  the  notion  of  cause  to  the  assemblage  of 
the  positive  conditions  of  the  phenomenon  : one  negative  condition  invaria- 
bly understood,  and  the  same  in  all  instances  (namely,  the  absence  of  coun- 
teracting causes)  being  sufficient,  along  with  the  sum  of  the  positive  condi- 
tions, to  make  up  the  whole  set  of  circumstances  on  which  the  phenomenon 
is  dependent. 

§ 4.  Among  the  positive  conditions,  as  we  have  seen  that  there  are  some 

mere  negative  conditions ; but  they  happened  to  be  the  only  ones  which  there  could  be  any 
necessity  to  state ; for  he  walked,  most  likely,  in  exactly  his  usual  manner,  and  the  nega- 
tive conditions  made  all  the  difference.  Again,  if  a person  were  asked  why  the  army  of 
Xerxes  defeated  that  of  Leonidas,  he  would  probably  say,  because  they  were  a thousand  times 
the  number;  but  I do  not  think  he  would  say,  it  was  because  they  fought,  though  that  was 
the  element  of  active  force.  To  borrow  another  example,  used  by  Mr.  Grove  and  by  Mr. 
Baden  Powell,  the  opening  of  flood-gates  is  said  to  be  the  cause  of  the  flow  of  water  ; yet  the 
active  force  is  exerted  by  the  water  itself,  and  opening  the  flood-gates  merely  supplies  a nega- 
tive condition.  The  reviewer  adds,  “There  are  some  conditions  absolutely  passive,  and  yet 
absolutely  necessary  to  physical  phenomena,  viz.,  the  relations  of  space  and  time;  and  to 
these  no  one  ever  applies  the  word  cause  without  being  immediately  arrested  by  those  who 
hear  him.”  Even  from  this  statement  I am  compelled  to  dissent.  Few  persons  would  feel  it 
incongruous  to  say  (for  example)  that  a secret  became  known  because  it  was  spoken  of  when 
A.  B.  was  within  hearing ; which  is  a condition  of  space  : or  that  the  cause  why  one  of  two 
particular  trees  is  taller  than  the  other,  is  that  it  has  been  longer  planted ; which  is  a condi- 
tion of  time. 

* There  are  a few  exceptions ; for  there  are  some  properties  of  objects  which  seem  to  be 
purely  preventive ; as  the  property  of  opaque  bodies,  by  which  they  intercept  the  passage  of 
iight.  This,  as  far  as  we  are  able  to  understand  it.  appears  an  instance  not  of  one  cause 
counteracting  another  by  the  same  law  whereby  it  produces  its  own  effects,  but  of  an  agencv 
which  manifests  itself  in  no  other  way  than  in  defeating  the  effects  of  another  agency.  If 
we  knerv  on  what  other  relations  to  light,  or  on  what  peculiarities  of  structure,  opacity  de- 
pends, we  might  find  that  this  is  only  an  apparent,  not  a real,  exception  to  the  general  propo- 
sition in  the  text.  In  any  case  it  needs  not  affect  the  practical  application.  The  formula 
which  includes  all  the  negative  conditions  of  an  effect  in  the  single  one  of  the  absence  of 
counteracting  causes,  is  not  violated  by  such  cases  as  this ; though,  if  all  counteracting  agen- 
cies were  of  this  description,  there  would  be  no  purnose  served  bv  emploving  the  formula. 

16 


242 


INDUCTION. 


to  which,  in  common  parlance,  the  term  cause  is  more  readily  and  frequent- 
ly awarded,  so  there  are  others  to  which  it  is,  in  ordinary  circumstances, 
refused.  In  most  cases  of  causation  a distinction  is  commonly  drawn  be- 
tween something  which  acts,  and  some  other  thing  which  is  acted  upon; 
between  an  agent  and  a •patient.  Both  of  these,  it  would  be  universally  al- 
lowed, are  conditions  of  the  phenomenon  ; but  it  would  be  thought  absurd 
to  call  the  latter  the  cause,  that  title  being  reserved  for  the  former.  The 
distinction,  however,  vanishes  on  examination,  or  rather  is  found  to  be  only 
verbal;  arising  from  an  incident  of  mere  expression,  namely,  that  the  ob- 
ject said  to  be  acted  upon,  and  which  is  considered  as  the  scene  in  which 
the  effect  takes  place,  is  commonly  included  in  the  phrase  by  which  the  ef- 
fect is  spoken  of,  so  that  if  it  were  also  reckoned  as  part  of  the  cause,  the 
seeming  incongruity  would  arise  of  its  being  supposed  to  cause  itself.  In 
the  instance  which  we  have  already  had,  of  falling  bodies,  the  question  was 
thus  put : What  is  the  cause  which  makes  a stoue  fall  ? and  if  the  answer 
had  been  “the  stone  itself,”  the  expression  would  have  been  in  apparent 
contradiction  to  the  meaning  of  the  word  cause.  The  stone,  therefore,  is 
conceived  as  the  patient,  and  the  earth  (or,  according  to  the  common  and 
most  unphilosophical  practice,  an  occult  quality  of  the  earth)  is  represented 
as  the  agent  or  cause.  But  that  there  is  nothing  fundamental  in  the  dis- 
tinction may.be  seen  from  this,  that  it  is  quite  possible  to  conceive  the 
stone  as  causing  its  own  fall,  provided  the  language  employed  be  such  as 
to  save  the  mere  verbal  incongruity.  We  might  say  that  the  stone  moves 
toward  the  earth  by  the  properties  of  the  matter  composing  it;  and  ac- 
cording to  this  mode  of  presenting  the  phenomenon,  the  stone  itself  might 
without  impropriety  be  called  the  agent;  though,  to  save  the  established 
doctrine  of  the  inactivity  of  matter,  men  usually  prefer  here  also  to  ascribe 
the  effect  to  an  occult  quality,  and  say  that  the  cause  is  not  the  stone  itself, 
but  the  weight  or  gravitation  of  the  stone. 

Those  who  have  contended  for  a radical  distinction  between  agent  and 
patient,  have  generally  conceived  the  agent  as  that  which  causes  some  state 
of,  or  some  change  in  the  state  of,  another  object  which  is  called  the  pa- 
tient. But  a little  reflection  will  show  that  the  license  we  assume  of  speak- 
ing of  phenomena  as  states  of  the  various  objects  which  take  part  in  them 
(an  artifice  of  which  so  much  use  has  been  made  by  some  philosophers, 
Brown  in  particular,  for  the  apparent  explanation  of  phenomena),  is  sim- 
ply a sort  of  logical  fiction,  useful  sometimes  as  one  among  several  modes 
of  expression,  but  which  should  never  be  supposed  to  be  the  enunciation 
of  a scientific  truth.  Even  those  attributes  of  an  object  which  might 
seem  with  greatest  propriety  to  be  called  states  of  the  object  itself,  its  sen- 
sible qualities,  its  color,  hardness,  shape,  and  the  like,  are  in  reality  (as  no 
one  has  pointed  out  more  clearly  than  Brown  himself)  phenomena  of  cau- 
sation, in  which  the  substance  is  distinctly  the  agent,  or  producing  cause, 
the  patient  being  our  own  organs,  and  those  of  other  sentient  beings. 
W hat  we  call  states  of  objects,  are  always  sequences  into  which  the  objects 
enter,  generally  as  antecedents  or  causes;  and  things  are  never  more  active 
than  in  the  production  of  those  phenomena  in  which  they  are  said  to  be 
acted  upon.  Thus,  in  the  example  of  a stone  falling  to  the  earth,  according 
to  the  theory  of  gravitation  the  stone  is  as  much  an  agent  as  the  earth, 
which  not  only  attracts,  but  is  itself  attracted  by,  the  stone.  In  the  case  of 
a sensation  produced  in  our  organs,  the  laws  of  our  organization,  and  even 
those  of  our  minds,  are  as  directly  operative  in  determining  the  effect  pro- 
duced, as  the  laws  of  the  outward  object.  Though  we  call  prussic  acid 


LAW  OF  CAUSATION. 


243 


the  agent  of  a person’s  death,  the  whole  of  the  vital  and  organic  properties 
of  the  patient  are  as  actively  instrumental  as  the  poison,  in  the  chain  of  ef- 
fects which  so  rapidly  terminates  his  sentient  existence.  In  the  process  of 
education,  we  may  call  the  teacher  the  agent,  and  the  scholar  only  the  ma- 
terial acted  upon  ; yet  in  truth  all  the  facts  which  pre-existed  in  the  schol- 
ar’s mind  exert  either  co-operating  or  counteracting  agencies  in  relation  to 
the  teacher’s  efforts.  It  is  not  light  alone  which  is  the  agent  in  vision,  but 
light  coupled  with  the  active  properties  of  the  eye  and  brain,  and  with 
those  of  the  visible  object.  The  distinction  between  agent  and  patient  is 
merely  verbal : patients  are  always  agents ; in  a great  proportion,  indeed, 
of  all  natural  phenomena,  they  are  so  to  such  a degree  as  to  react  forcibly 
on  the  causes  which  acted  upon  them  : and  even  when  this  is  not  the  case, 
they  contribute,  in  the  same  manner  as  any  of  the  other  conditions,  to  the 
production  of  the  effect  of  which  they  are  vulgarly  treated  as  the  mere  the- 
atre. All  the  positive  conditions  of  a phenomenon  are  alike  agents,  alike 
active ; and  in  any  expression  of  the  cause  which  professes  to  be  complete, 
none  of  them  can  with  reason  be  excluded,  except  such  as  have  already 
been  implied  in  the  words  used  for  describing  the  effect ; nor  by  including 
even  these  would  there  be  incurred  any  but  a merely  verbal  impropriety. 

§ 5.  There  is  a case  of  causation  which  calls  for  separate  notice,  as  it 
possesses  a peculiar  feature,  and  presents  a greater  degree  of  complexity 
than  the  common  case.  It  often  happens  that  the  effect,  or  one  of  the  ef- 
fects, of  a cause,  is,  not  to  produce  of  itself  a certain  phenomenon,  but  to 
fit  something  else  for  producing  it.  In  other  words,  there  is  a case  of  cau- 
sation in  which  the  effect  is  to  invest  an  object  with  a certain  property. 
When  sulphur,  charcoal,  and  nitre  are  put  together  in  certain  proportions 
and  in  a certain  manner,  the  effect  is,  not  an  explosion,  but  that  the  mixture 
acquires  a property  by  which,  in  given  circumstances,  it  will  explode.  The 
various  causes,  natural  and  artificial,  which  educate  the  human  body  or  the 
human  mind,  have  for  their  principal  effect,  not  to  make  the  body  or  mind 
immediately  do  any  thing,  but  to  endow  it  with  certain  properties — in  oth- 
er words,  to  give  assurance  that  in  given  circumstances  certain  results  will 
take  place  in  it,  or  as  consequences  of  it.  Physiological  agencies  often 
have  for  the  chief  part  of  their  operation  to  'predispose  the  constitution  to 
some  mode  of  action.  To  take  a simpler  instance  than  all  these:  putting 
a coat  of  white  paint  upon  a wall  does  not  merely  produce  in  those  who 
see  it  done,  the  sensation  of  white ; it  confers  on  the  wall  the  permanent 
property  of  giving  that  kind  of  sensation.  Regarded  in  reference  to  the 
sensation,  the  putting  on  of  the  paint  is  a condition  of  a condition ; it  is  a 
condition  of  the  wall’s  causing  that  particular  fact.  The  wall  may  have 
been  painted  years  ago,  but  it  has  acquired  a property  which  has  lasted  till 
now,  and  will  last  longer;  the  antecedent  condition  necessary  to  enable  the 
wall  to  become  in  its  turn  a condition,  has  been  fulfilled  once  for  all.  In  a 
case  like  this,  where  the  immediate  consequent  in  the  sequence  is  a proper- 
ty produced  in  an  object,  no  one  now  supposes  the  property  to  be  a sub- 
stantive entity  “ inherent  ” in  the  object.  What  has  been  produced  is  what, 
in  other  language,  may  be  called  a state  of  preparation  in  an  object  for  pro- 
ducing an  effect.  The  ingredients  of  the  gunpowder  have  been  brought  into 
a state  of  preparation  for  exploding  as  soon  as  the  other  conditions  of  an 
explosion  shall  have  occurred.  In  the  case  of  the  gunpowder,  this  state  of 
preparation  consists  in  a certain  collocation  of  its  particles  relatively  to  one 
another.  In  the  example  of  the  wall,  it  consists  in  a new  collocation  of  two 


244 


INDUCTION. 


things  relatively  to  each  other — the  wall  and  the  paint.  In  the  example  of 
the  molding  influences  on  the  human  mind,  its  being  a collocation  at  all  is 
only  conjectural;  for,  even  on  the  materialistic  hypothesis,  it  would  remain 
to  be  proved  that  the  increased  facility  with  which  the  brain  sums  up  a 
column  of  figures  when  it  has  been  long  trained  to  calculation,  is  the  result 
of  a permanent  new  arrangement  of  some  of  its  material  particles.  We 
must,  therefore,  content  ourselves  with  what  we  know,  and  must  include 
among  the  effects  of  causes,  the  capacities  given  to  objects  of  being  causes 
of  other  effects.  This  capacity  is  not  a real  thing  existing  in  the  objects; 
it  is  but  a name  for  our  conviction  that  they  will  act  in  a particular  man- 
ner when  certain  new  circumstances  arise.  We  may  invest  this  assurance 
of  future  events  with  a fictitious  objective  existence,  by  calling  it  a state  of 
the  object.  But  unless  the  state  consists,  as  in  the  case  of  the  gunpowder 
it  does,  in  a collocation  of  particles,  it  expresses  no  present  fact ; it  is  but 
the  contingent  future  fact  brought  back  under  another  name. 

It  may  be  thought  that  this  form  of  causation  requires  us  to  admit  an 
exception  to  the  doctrine  that  the  conditions  of  a phenomenon — the  ante- 
cedents required  for  calling  it  into  existence — must  all  be  found  among  the 
facts  immediately,  not  remotely,  preceding  its  commencement.  But  what 
we  have  arrived  at  is  not  a correction,  it  is  only  an  explanation,  of  that  doc- 
trine. In  the  enumeration  of  the  conditions  required  for  the  occurrence  of 
any  phenomenon,  it  always  has  to  be  included  that  objects  must  be  present, 
possessed  of  given  properties.  It  is  a condition  of  the  phenomenon  explo- 
sion that  an  object  should  be  present,  of  one  or  other  of  certain  kinds, 
which  for  that  reason  are  called  explosive.  The  presence  of  one  of  these 
objects  is  a condition  immediately  precedent  to  the  explosion.  The  condi- 
tion which  is  not  immediately  precedent  is  the  cause  which  produced,  not 
the  explosion,  but  the  explosive  property.  The  conditions  of  the  explosion 
itself  were  all  present  immediately  before  it  took  place,  and  the  general  law, 
therefore,  remains  intact. 

§ 6.  It  now  remains  to  advert  to  a distinction  which  is  of  first-rate  im- 
portance both  for  clearing  up  the  notion  of  cause,  and  for  obviating  a very 
specious  objection  often  made  against  the  view  which  we  have  taken  of  the 
subject. 

When  we  define  the  cause  of  any  thing  (in  the  only  sense  in  which  the 
present  inquiry  has  any  concern  with  causes)  to  be  “the  antecedent  which 
it  invariably  follows,”  we  do  not  use  this  phrase  as  exactly  synonymous 
with  “ the  antecedent  which  it  invariably  has  followed  in  our  past  expe- 
rience.” Such  a mode  of  conceiving  causation  would  be  liable  to  the  ob- 
jection very  plausibly  urged  by  Dr.  Reid,  namely,  that  according  to  this 
doctrine  night  must  be  the  cause  of  day,  and  day  the  cause  of  night;  since 
these  phenomena  have  invariably  succeeded  one  another  from  the  begin- 
ning of  the  world.  But  it  is  necessary  to  our  using  the  word  cause,  that 
we  should  believe  not  only  that  the  antecedent  always  has  been  followed  by 
the  consequent,  but  that,  as  long  as  the  present  constitution  of  things*  en- 
dures, it  always  will  be  so.  And  this  would  not  be  true  of  day  and  night. 
We  do  not  believe  that  night  will  be  followed  by  day  under  all  imaginable 
circumstances,  but  only  that  it  will  be  so  provided  the  sun  rises  above  the 

* I mean  by  this  expression,  the  ultimate  laws  of  nature  (whatever  they  may  be)  as  distin- 
guished from  the  derivative  laws  and  from  the  collocations.  The  diurnal  revolution  of  the 
earth  (for  example)  is  not  a part  of  the  constitution  of  things,  because  nothing  can  be  so  called 
which  might  possibly  be  terminated  or  altered  by  natural  causes. 


LAW  OF  CAUSATION. 


245 


horizon.  If  the  sun  ceased  to  rise,  which,  for  aught  we  know,  may  be  per- 
fectly compatible  with  the  general  laws  of  matter,  night  would  be,  or  might 
be,  eternal.  On  the  other  hand,  if  the  sun  is  above  the  horizon,  his  light 
not  extinct,  and  no  opaque  body  between  us  and  him,  we  believe  firmly  that 
unless  a change  takes  place  in  the  properties  of  matter,  this  combination  of 
antecedents  will  be  followed  by  the  consequent,  day;  that  if  the  combina- 
tion of  antecedents  could  be  indefinitely  prolonged,  it  would  be  always  day ; 
and  that  if  the  same  combination  had  always  existed,  it  would  always  have 
been  day,  quite  independently  of  night  as  a previous  condition.  Therefore 
is  it  that  we  do  not  call  night  the  cause,  nor  even  a condition,  of  day.  The 
existence  of  the  sun  (or  some  such  luminous  body),  and  there  being  no 
opaque  medium  in  a straight  line*  between  that  body  and  the  part  of  the 
earth  where  we  are  situated,  are  the  sole  conditions;  and  the  union  of 
these,  Avithout  the  addition  of  any  superfluous  circumstance,  constitutes  the 
cause.  This  is  what  Avriters  mean  when  they  say  that  the  notion  of  cause 
involves  the  idea  of  necessity.  If  there  be  any  meaning  which  confessedly 
belongs  to  the  term  necessity,  it  is  unconditionalness.  That  Avhieh  is  nec- 
essary, that  Avhieh  must  be,  means  that  Avhieh  Avill  be,  Avhatever  supposition 
Ave  may  make  in  regard  to  all  other  things.  The  succession  of  day  and 
night  evidently  is  not  necessary  in  this  sense.  It  is  conditional  on  the  oc- 
currence of  other  antecedents.  That  Avhieh  Avill  be  followed  by  a given 
consequent  when,  and  only  when,  some  third  circumstance  also  exists,  is  not 
the  cause,  even  though  no  case  should  ever  have  occurred  in  Avhieh  the  phe- 
nomenon took  place  without  it. 

Invariable  sequence,  therefore,  is  not  synonymous  with  causation,  unless 
the  sequence,  besides  being  invariable,  is  unconditional.  There  are  se- 
quences, as  uniform  in  past  experience  as  any  others  Avhatever,  which  yet 
Ave  do  not  regard  as  cases  of  causation,  but  as  conjunctions  in  some  sort 
accidental.  Such,  to  an  accurate  thinker,  is  that  of  day  and  night.  The  one 
might  have  existed  for  any  length  of  time,  and  the  other  not  have  followed 
the  sooner  for  its  existence ; it  folloAvs  only  if  certain  other  antecedents 
exist ; and  where  those  antecedents  existed,  it  Avould  follow  in  any  case. 
No  one,  probably,  ever  called  night  the  cause  of  day;  mankind  must  so 
soon  have  arrived  at  the  very  obvious  generalization,  that  the  state  of  gen- 
eral illumination  which  Ave  call  day  would  folloAV  from  the  presence  of  a 
sufficiently  luminous  body,  Avbether  darkness  had  preceded  or  not. 

We  may  define,  therefore,  the  cause  of  a phenomenon,  to  be  the  ante- 
cedent, or  the  concurrence  of  antecedents,  on  which  it  is  invariably  and 
unconditionally  consequent.  Or  if  Ave  adopt  the  convenient  modification 
of  the  meaning  of  the  word  cause,  which  confines  it  to  the  assemblage  of 
positive  conditions  Avithout  the  negative,  then  instead  of  “unconditional- 
ly,” Ave  must  say,  “ subject  to  no  other  than  negative  conditions.” 

To  some  it  may  appear,  that  the  sequence  between  night  and  day  being 
invariable  in  our  experience,  Ave  have  as  much  ground  in  this  case  as  ex- 
perience can  give  in  any  case,  for  recognizing  the  two  phenomena  as  cause 
and  effect;  and  that  to  say  that  more  is  necessary- — to  require  a belief  that 
the  succession  is  unconditional,  or,  in  other  words,  that  it  would  be  invari- 
able under  all  changes  of  circumstances,  is  to  acknowledge  in  causation  an 

* I use  the  words  “straight  line”  for  brevity  and  simplicity.  In  reality  the  line  in  question 
is  not  exactly  straight,  for,  from  the  effect  of  refraction,  we  actually  see  the  sun  for  a short 
interval  during  which  the  opaque  mass  of  the  earth  is  interposed  in  a direct  line  between  the 
sun  and  our  eyes ; thus  realizing,  though  but  to  a limited  extent,  the  coveted  desideratum  of 
seeing  round  a corner. 


240 


INDUCTION. 


clement  of  belief  not  derived  from  experience.  The  answer  to  this  is,  that 
it  is  experience  itself  which  teaches  us  that  one  uniformity  of  sequence  is 
conditional  and  another  unconditional.  When  we  judge  that  the  succes- 
sion of  night  and  day  is  a derivative  sequence,  depending  on  something 
else,  we  proceed  on  grounds  of  experience.  It  is  the  evidence  of  experi- 
ence which  convinces  us  that  day  could  equally  exist  without  being  fol- 
lowed by  night,  and  that  night  could  equally  exist  without  being  followed 
by  day.  To  say  that  these  beliefs  are  “ not  generated  by  our  mere  ob- 
servation of  sequence,”*  is  to  forget  that  twice  in  every  twenty-four  hours, 
when  the  sky  is  clear,  we  have  an  experimentum  crucis  that  the  cause  of 
day  is  the  sun.  We  have  an  experimental  knowledge  of  the  sun  which 
justifies  us  on  experimental  grounds  in  concluding,  that  if  the  sun  were 
always  above  the  horizon  there  would  be  day,  though  there  had  been  no 
night,  and  that  if  the  sun  were  always  below  the  horizon  there  would  be 
night,  though  there  had  been  no  day.  We  thus  know  from  experience 
that  the  succession  of  night  and  day  is  not  unconditional.  Let  me  add, 
that  the  antecedent  which  is  only  conditionally  invariable,  is  not  the  in- 
variable antecedent.  Though  a fact  may,  in  experience,  have  always  been 
followed  by  another  fact,  yet  if  the  remainder  of  our  experience  teaches 
us  that  it  might  not  always  be  so  followed,  or  if  the  experience  itself  is 
such  as  leaves  room  for  a possibility  that  the  known  cases  may  not  cor- 
rectly represent  all  possible  cases,  the  hitherto  invariable  antecedent  is  not 
accounted  the  cause ; but  why  ? Because  we  are  not  sure  that  it  is  the  in- 
variable antecedent. 

Such  cases  of  sequence  as  that  of  day  and  night  not  only  do  not  contra- 
dict the  doctrine  which  resolves  causation  into  invariable  sequence,  but  are 
necessarily  implied  in  that  doctrine.  It  is  evident,  that  from  a limited 
number  of  unconditional  sequences,  there  will  result  a much  greater  num- 
ber of  conditional  ones.  Certain  causes  being  given,  that  is,  certain  ante- 
cedents which  are  unconditionally  followed  by  certain  consequents ; the 
mere  co-existence  of  these  causes  will  give  rise  to  an  unlimited  number 
of  additional  uniformities.  If  two  causes  exist  together,  the  effects  of  both 
will  exist  together ; and  if  many  causes  co-exist,  these  causes  (by  what  wo 
shall  term  hereafter  the  intermixture  of  their  laws)  will  give  rise  to  new  ef- 
fects, accompanying  or  succeeding  one  another  in  some  particular  order, 
which  order  will  be  invariable  while  the  causes  continue  to  co-exist,  but  no 
longer.  The  motion  of  the  earth  in  a given  orbit  round  the  sun,  is  a series 
of  changes  which  follow  one  another  as  antecedents  and  consequents,  and 
will  continue  to  do  so  while  the  sun’s  attraction,  and  the  force  with  which 
the  earth  tends  to  advance  in  a direct  line  through  space,  continue  to  co- 
exist in  the  same  quantities  as  at  present.  But  vary  either  of  these  causes, 
and  this  particular  succession  of  motions  would  cease  to  take  place.  The 
series  of  the  earth’s  motions,  therefore,  though  a case  of  sequence  invari- 
able within  the  limits  of  human  experience,  is  not  a case  of  causation.  It 
is  not  unconditional. 

This  distinction  between  the  relations  of  succession  which,  so  far  as  we 
know,  are  unconditional,  and  those  relations,  whether  of  succession  or  of 
co-existence,  which,  like  the  earth’s  motions,  or  the  succession  of  day  and 
night,  depend  on  the  existence  or  on  the  co-existence  of  other  antecedent 
facts  — corresponds  to  the  great  division  which  Dr.  Whewell  and  other 
writers  have  made  of  the  field  of  science,  into  the  investigation  of  what 


Second  Burnett  Prize  Essay,  by  Principal  Tulloch,  p.  25. 


LAW  OF  CAUSATION. 


247 


they  term  the  Laws  of  Phenomena,  and  the  investigation  of  causes ; a 
phraseology,  as  I conceive,  not  philosophically  sustainable,  inasmuch  as  the 
ascertainment  of  causes,  such  causes  as  the  human  faculties  can  ascertain, 
namely,  causes  which  are  themselves  phenomena,  is,  therefore,  merely  the 
ascertainment  of  other  and  more  universal  Laws  of  Phenomena.  And  let 
me  here  observe,  that  Dr.  Whewell,  and  in  some  degree  even  Sir  John 
Herschel,  seem  to  have  misunderstood  the  meaning  of  those  writers  who, 
like  M.  Comte,  limit  the  sphere  of  scientific  investigation  to  Laws  of  Phe- 
nomena, and  speak  of  the  inquiry  into  causes  as  vain  and  futile.  The 
causes  which  M.  Comte  designates  as  inaccessible,  are  efficient  causes.  The 
investigation  of  physical,  as  opposed  to  efficient,  causes  (including  the  study 
of  all  the  active  forces  in  Nature,  considered  as  facts  of  observation)  is  as 
important  a part  of  M.  Comte’s  conception  of  science  as  of  Dr.  Whewell’s. 
His  objection  to  the  word  cause  is>  a mere  matter  of  nomenclature,  in  which, 
as  a matter  of  nomenclature,  I consider  him  to  be  entirely  wrong.  “ Those,” 
it  is  justly  remarked  by  Mr.  Bailey,*  “ who,  like  M.  Comte,  object  to  desig- 
nate events  as  causes,  are  objecting  without  any  real  ground  to  a mere  but 
extremely  convenient  generalization,  to  a very  useful  common  name,  the 
employment  of  which  involves,  or  needs  involve,  no  particular  theory.”  To 
which  it  may  be  added,  that  by  rejecting  this  form  of  expression,  M.  Comte 
leaves  himself  without  any  term  for  marking  a distinction  which,  however 
incorrectly  expressed,  is  not  only  real,  but  is  one  of  the  fundamental  dis- 
tinctions in  science;  indeed  it  is  on  this  alone,  as  we  shall  hereafter  find, 
that  the  possibility  rests  of  framing  a rigorous  Canon  of  Induction.  And 
as  things  left  without  a name  are  apt  to  be  forgotten,  a Canon  of  that  de- 
scription is  not  one  of  the  many  benefits  which  the  philosophy  of  Induction 
lias  received  from  M.  Comte’s  great  powers. 

§ 7.  Does  a cause  always  stand  with  its  effect  in  the  relation  of  anteced- 
ent and  consequent?  Do  we  not  often  say  of  two  simultaneous  facts  that 
they  are  cause  and  effect — as  when  we  say  that  fire  is  the  cause  of  warmth, 
the  sun  and  moisture  the  cause  of  vegetation,  and  the  like?  Since  a cause 
does  not  necessarily  perish  because  its  effect  has  been  produced,  the  two 
things  do  very  generally  co-exist;  and  there  are  some  appearances,  and 
some  common  expressions,  seeming  to  imply  not  only  that  causes  may,  but 
that  they  must,  be  contemporaneous  with  their  effects.  Cessante  causa 
cessat  et  effectus,  has  been  a dogma  of  the  schools:  the  necessity  for  the 
continued  existence  of  the  cause  in  order  to  the  continuance  of  the  effect, 
seems  to  have  been  once  a generally  received  doctrine.  Kepler’s  numerous 
attempts  to  account  for  the  motions  of  the  heavenly  bodies  on  mechanical 
principles,  were  rendered  abortive  by  his  always  supposing  that  the  agency 
which  set  those  bodies  in  motion  must  continue  to  operate  in  order  to  keep 
up  the  motion  which  it  at  first  produced.  Yet  there  were  at  all  times 
many  familiar  instances  of  the  continuance  of  effects,  long  after  their  causes 
had  ceased.  A coup  de  soleil  gives  a person  brain- fever  : will  the  fever  go 
off  as  soon  as  he  is  moved  out  of  the  sunshine  ? A sword  is  run  through 
his  body:  must  the  sword  remain  in  his  body  in  order  that  he  may  con- 
tinue dead?  A plowshare  once  made,  remains  a plowshare,  without  any 
continuance  of  heating  and  hammering,  and  even  after  the  man  who  heat- 
ed and  hammered  it  has  been  gathered  to  his  fathers.  On  the  other  hand, 
the  pressure  which  forces  up  the  mercury  in  an  exhausted  tube  must  be 


* Letters  on  the  Philosophy  of  the  Human  Mind , First  Series,  p.  219. 


24S 


INDUCTION. 


continued  in  order  to  sustain  it  in  the  tube.  This  (it  may  be  replied)  is 
because  another  force  is  acting  without  intermission,  the  force  of  gravity, 
which  would  restore  it  to  its  level,  unless  counterpoised  by  a force  equally 
constant.  But  again : a tight  bandage  causes  pain,  which  pain  will  some- 
times go  off  as  soon  as  the  bandage  is  removed.  The  illumination  which 
the  sun  diffuses  over  the  earth  ceases  when  the  sun  goes  down. 

There  is,  therefore,  a distinction  to  be  drawn.  The  conditions  which  are 
necessary  for  the  first  production  of  a phenomenon,  are  occasionally  also 
necessary  for  its  continuance;  though  more  commonly  its  continuance  re- 
quires no  condition  except  negative  ones.  Most  things,  once  produced,  con- 
tinue as  they  are,  until  something  changes  or  destroys  them ; but  some  re- 
quire the  permanent  presence  of  the  agencies  which  produced  them  at  first. 
These  may,  if  we  please,  be  considered  as  instantaneous  phenomena,  re- 
quiring to  be  renewed  at  each  instant  by  the  cause  by  which  they  were  at 
first  generated.  Accordingly,  the  illumination  of  any  given  point  of  space 
has  always  been  looked  upon  as  an  instantaneous  fact,  which  perishes  and 
is  perpetually  renewed  as  long  as  the  necessary  conditions  subsist.  If  we 
adopt  this  language  we  avoid  the  necessity  of  admitting  that  the  continu- 
ance of  the  cause  is  ever  required  to  maintain  the  effect.  We  may  say,  it 
is  not  required  to  maintain,  but  to  reproduce,  the  effect,  or  else  to  coun- 
teract some  force  tending  to  destroy  it.  And  this  may  be  a convenient 
phraseology.  But  it  is  only  a phraseology.  The  fact  remains,  that  in 
some  cases  (though  those  are  a minority)  the  continuance  of  the  conditions 
which  produced  an  effect  is  necessary  to  the  continuance  of  the  effect. 

As  to  the  ulterior  question,  whether  it  is  strictly  necessary  that  the 
cause,  or  assemblage  of  conditions,  should  precede,  by  ever  so  short  an  in- 
stant, the  production  of  the  effect  (a  question  raised  and  argued  with  much 
ingenuity  by  Sir  John  Herschel  in  an  Essay  already  quoted),*  the  inquiry 
is  of  no  consequence  for  our  present  purpose.  There  certainly  are  cases 
in  which  the  effect  follows  without  any  interval  perceptible  by  our  faculties  ; 
and  when  there  is  an  interval,  we  can  not  tell  by  how  many  intermediate 
links  imperceptible  to  us  that  inverval  may  really  be  filled  up.  But  even 
granting  that  an  effect  may  commence  simultaneously  with  its  cause,  the 
view  I have  taken  of  causation  is  in  no  way  practically  affected.  Wheth- 
er the  cause  and  its  effect  be  necessarily  successive  or  not,  the  begin- 
ning of  a phenomenon  is  what  implies  a cause,  and  causation  is  the  law  of 
the  succession  of  phenomena.  If  these  axioms  be  granted,  we  can  afford, 
though  I see  no  necessity  for  doing  so,  to  drop  the  words  antecedent  and 
consequent  as  applied  to  cause  and  effect.  I have  no  objection  to  define  a 
cause,  the  assemblage  of  phenomena,  which  occurring,  some  other  phenom- 
enon invariably  commences,  or  has  its  origin.  Whether  the  effect  coin- 
cides in  point  of  time  with,  or  immediately  follows,  the  hindmost  of  its 
conditions,  is  immaterial.  At  all  events,  it  does  not  precede  it;  and  when 
we  are  in  doubt,  between  two  co-existent  phenomena,  which  is  cause  and 
which  effect,  we  rightly  deem  the  question  solved  if  we  can  ascertain  which 
of  them  preceded  the  other. 

§ 8.  It  continually  happens  that  several  different  phenomena,  which  are 
not  in  the  slightest  degree  dependent  or  conditional  on  one  another,  are 
found  all  to  depend,  as  the  phrase  is,  on  one  and  the  same  agent ; in  other 
words,  one  and  the  same  phenomenon  is  seen  to  be  followed  by  several 


Essays,  pp.  20G-208. 


LAW  OF  CAUSATION. 


249 


sorts  of  effects  quite  heterogeneous,  but  which  go  on  simultaneously  one 
with  another ; provided,  of  course,  that  all  other  conditions  requisite  for 
each  of  them  also  exist.  Thus,  the  sun  produces  the  celestial  motions ; it 
produces  daylight,  and  it  produces  heat.  The  earth  causes  the  fall  of  heavy 
bodies,  and  it  also,  in  its  capacity  of  a great  magnet,  causes  the  phenomena 
of  the  magnetic  needle.  A crystal  of  galena  causes  the  sensations  of  hard- 
ness, of  weight,  of  cubical  form,  of  gray  color,  and  many  others  between 
which  we  can  trace  no  interdependence.  The  purpose  to  which  the  phrase- 
ology of  Properties  and  Powers  is  specially  adapted,  is  the  expression  of 
this  sort  of  cases.  When  the  same  phenomenon  is  followed  (either  sub- 
ject or  not  to  the  presence  of  other  conditions)  by  effects  of  different  and 
dissimilar  orders,  it  is  usual  to  say  that  each  different  sort  of  effect  is  pro- 
duced by  a different  property  of  the  cause.  Thus  we  distinguish  the  at- 
tractive or  gravitative  property  of  the  earth,  and  its  magnetic  property : 
the  gravitative,  luminiferous,  and  calorific  properties  of  the  sun:  the  color, 
shape,  weight,  and  hardness  of  a crystal.  These  are  mere  phrases,  which 
explain  nothing,  and  add  nothing  to  our  knowledge  of  the  subject;  but, 
considered  as  abstract  names  denoting  the  connection  between  the  differ- 
ent effects  produced  and  the  object  which  produces  them,  they  are  a very 
powerful  instrument  of  abridgment,  and  of  that  acceleration  of  the  proc- 
ess of  thought  which  abridgment  accomplishes. 

This  class  of  considerations  leads  to  a conception  which  we  shall  find  to 
be  of  great  importance,  that  of  a Permanent  Cause,  or  original  natural 
agent.  There  exist  in  nature  a number  of  permanent  causes,  which  have 
subsisted  ever  since  the  human  race  has  been  in  existence,  and  for  an  in- 
definite and  probably  an  enormous  length  of  time  previous.  The  sun,  the 
earth,  and  planets,  with  their  various  constituents,  air,  water,  and  other  dis- 
tinguishable substances,  whether  simple  or  compound,  of  which  nature  is 
made  up,  are  such  Permanent  Causes.  These  have  existed,  and  the  effects 
or  consequences  which  they  were  fitted  to  produce  have  taken  place  (as 
often  as  the  other  conditions  of  the  production  met),  from  the  very  begin- 
ning of  our  experience.  But  we  can  give  no  account  of  the  origin  of  the 
Permanent  Causes  themselves.  Why  these  particular  natural  agents  ex- 
isted originally  and  no  others,  or  why  they  are  commingled  in  such  and 
such  proportions,  and  distributed  in  such  and  such  a manner  throughout 
space,  is  a question  we  can  not  answer.  More  than  this : we  can  discover 
nothing  regular  in  the  distribution  itself;  we  can  reduce  it  to  no  uniformi- 
ty, to  no  law.  There  are  no  means  by  which,  from  the  distribution  of  these 
causes  or  agents  in  one  part  of  space,  we  could  conjecture  whether  a simi- 
lar distribution  prevails  in  another.  The  co-existence,  therefore,  of  Prime- 
val Causes  ranks,  to  us,  among  merely  casual  concurrences:  and  all  those 
sequences  or  co-existences  among  the  effects  of  several  such  causes,  which, 
though  invariable  while  those  causes  co-exist,  would,  if  the  co-existence  ter- 
minated, terminate  along  with  it,  we  do  not  class  as  cases  of  causation,  or 
laws  of  nature : we  can  only  calculate  on  finding  these  sequences  or  co-ex- 
istences  where  we  know  by  direct  evidence,  that  the  natural  agents  on  the 
properties  of  which  they  ultimately  depend,  are  distributed  in  the  requisite 
manner.  These  Permanent  Causes  are  not  always  objects ; they  are  some- 
times events,  that  is  to  say,  periodical  cycles  of  events,  that  being  the  only 
mode  in  which  events  can  possess  the  property  of  permanence.  Not  only, 
for  instance,  is  the  earth  itself  a permanent  cause,  or  primitive  natural 
agent,  but  the  earth’s  rotation  is  so  too:  it  is  a cause  which  has  produced, 
from  the  earliest  period  (by  the  aid  of  other  necessary  conditions),  the  sue- 


250 


INDUCTION. 


cession  of  day  and  night,  the  ebb  and  flow  of  the  sea,  and  many  other  ef- 
fects, while,  as  we  can  assign  no  cause  (except  conjecturally)  for  the  rota- 
tion itself,  it  is  entitled  to  be  ranked  as  a primeval  cause.  It  is,  however, 
only  the  origin  of  the  rotation  which  is  mysterious  to  us:  once  begun,  its 
continuance  is  accounted  for  by  the  first  law  of  motion  (that  of  the  perma- 
nence of  rectilinear  motion  once  impressed)  combined  with  the  gravitation 
of  the  parts  of  the  earth  toward  one  another. 

All  phenomena  without  exception  which  begin  to  exist,  that  is,  all  except 
the  primeval  causes,  are  effects  either  immediate  or  remote  of  those  primi- 
tive facts,  or  of  some  combination  of  them.  There  is  no  Thing  produced, 
no  event  happening,  in  the  known  universe,  which  is  not  connected  by  a 
uniformity,  or  invariable  sequence,  with  some  one  or  more  of  the  phenom- 
ena which  preceded  it;  insomuch  that  it  will  happen  again  as  often  as 
those  phenomena  occur  again,  and  as  no  other  phenomenon  having  the 
character  of  a counteracting  cause  shall  co-exist.  These  antecedent  phe- 
nomena, again,  were  connected  in  a similar  manner  with  some  that  pre- 
ceded them;  and  so  on,  until  we  reach,  as  the  ultimate  step  attainable  by 
us,  either  the  properties  of  some  one  primeval  cause,  or  the  conjunction  of 
several.  The  whole  of  the  phenomena  of  nature  were  therefore  the  neces- 
sary, or,  in  other  words,  the  unconditional,  consequences  of  some  former  col- 
location of  the  Permanent  Causes. 

The  state  of  the  whole  universe  at  any  instant,  we  believe  to  be  the  con- 
sequence of  its  state  at  the  previous  instant;  insomuch  that  one  who  knew 
all  the  agents  which  exist  at  the  present  moment,  their  collocation  in  space, 
and  all  their  properties,  in  other  words,  the  laws  of  their  agency,  could  pre- 
dict the  whole  subsequent  history  of  the  universe,  at  least  unless  some  new 
volition  of  a power  capable  of  controlling  the  universe  should  supervene.* 
And  if  any  particular  state  of  the  entire  universe  could  ever  recur  a second 
time,  all  subsequent  states  would  return  too,  and  history  would,  like  a cir- 
culating decimal  of  many  figures,  periodically  repeat  itself: 

Jam  redit  et  virgo,  redeunt  Saturnia  regna 

Alter  erit  turn  Tiphys,  et  altera  quos  vehnt  Argo 

Delectos  heroas ; erunt  qiioque  altera  bella, 

Atque  iteram  ad  Trojam  magnus  mittetur  Achilles. 

And  though  things  do  not  really  revolve  in  this  eternal  round,  the  whole 
series  of  events  in  the  history  of  the  universe,  past  and  future,  is  not  the 
less  capable,  in  its  own  nature,  of  being  constructed  a priori  by  any  one 

* To  the  universality  which  mankind  are  agreed  in  ascribing  to  the  Law  of  Causation,  there 
is  one  claim  of  exception,  one  disputed  case,  that  of  the  Human  Will ; the  determinations  of 
which,  a large  class  of  metaphysicians  are  not  willing  to  regard  as  following  the  causes  called 
motives,  according  to  as  strict  laws  as  those  which  they  suppose  to  exist  in  the  world  of  mere 
matter.  This  controverted  point  will  undergo  a special  examination  when  we  come  to  treat 
particularly  of  the  Logic  of  the  Moral  Sciences  (Book  vi. , chap.  2).  In  the  mean  time,  I may 
remark  that  these  metaphysicians,  who,  it  must  be  observed,  ground  the  main  part  of  their  ob- 
jection on  the  supposed  repugnance  of  the  doctrine  in  question  to  our  consciousness,  seem  to 
me  to  mistake  the  fact  which  consciousness  testifies  against.  What  is  really  in  contradiction 
to  consciousness,  they  would,  I think,  on  strict  self-examination,  find  to  be,  the  application  to 
human  actions  and  volitions  of  the  ideas  involved  in  the  common  use  of  the  term  Necessity; 
which  I agree  with  them  in  objecting  to.  But  if  they  would  consider  that  bv  saying  that  a 
person’s  actions  necessarily  follow  from  his  character,  all  that  is  really  meant  (for  no  more  is 
meant  in  any  case  whatever  of  causation)  is  that  he  invariably  does  act  in  conformity  to  his 
character,  and  that  any  one  who  thoroughly  knew  his  character  could  certainly  predict  how  he 
would  act  in  any  supposable  case  ; they  probably  would  not  find  this  doctrine  either  contrary 
to  their  experience  or  revolting  to  their  feelings.  And  no  more  than  this  is  contended  for  by 
auy  one  but  an  Asiatic  fatalist. 


LAW  OF  CAUSATION. 


251 


whom  we  can  suppose  acquainted  with  the  original  distribution  of  all  nat- 
ural agents,  and  with  the  whole  of  their  properties,  that  is,  the  laws  of  suc- 
cession existing  between  them  and  their  effects  : saving  the  far  more  than 
human  powers  of  combination  and  calculation  which  would  be  required, 
even  in  one  possessing  the  data,  for  the  actual  performance  of  the  task. 

§ 9.  Since  every  thing  which  occurs  is  determined  by  laws  of  causation 
and  collocations  of  the  original  causes,  it  follows  that  the  co-existences 
which  are  observable  among  effects  can  not  be  themselves  the  subject  of 
any  similar  set  of  laws,  distinct  from  laws  of  causation.  Uniformities 
there  are,  as  well  of  co-existence  as  of  succession,  among  effects ; but  these 
must  in  all  cases  be  a mere  result  either  of  the  identity  or  of  th,e  co-exist- 
ence  of  their  causes : if  the  causes  did  not  co-exist,  neither  could  the  ef- 
fects. And  these  causes  being  also  effects  of  prior  causes,  and  these  of 
others,  until  we  reach  the  primeval  causes,  it  follows  that  (except  in  the 
case  of  effects  which  can  be  traced  immediately  or  remotely  to  one  and 
the  same  cause)  the  co-existences  of  phenomena  can  in  no  case  be  univers- 
al, unless  the  co-existences  of  the  primeval  causes  to  which  the  effects  are 
ultimately  traceable  can  be  reduced  to  a universal  law : but  we  have  seen 
that  they  can  not.  There  are,  accordingly,  no  original  and  independent,  in 
other  words  no  unconditional,  uniformities  of  co-existence,  between  effects 
of  different  causes ; if  they  co-exist,  it  is  only  because  the  causes  have  cas- 
ually co-existed.  The  only  independent  and  unconditional  co  - existences 
which  are  sufficiently  invariable  to  have  any  claim  to  the  character  of 
laws,  are  between  different  and  mutually  independent  effects  of  the  same 
cause ; in  other  words,  between  different  properties  of  the  same  natural 
agent.  This  portion  of  the  Laws  of  Nature  will  be  treated  of  in  the  lat- 
ter part  of  the  present  Book,  under  the  name  of  the  Specific  Properties  of 
Kinds. 

§ 10.  Since  the  first  publication  of  the  present  treatise,  the  sciences  of 
physical  nature  have  made  a great  advance  in  generalization,  through  the 
doctrine  known  as  the  Conservation  or  Persistence  of  Force.  This  impo- 
sing edifice  of  theory,  the  building  and  laying  out  of  which  has  for  some 
time  been  the  principal  occupation  of  the  most  systematic  minds  among 
physical  inquirers,  consists  of  two  stages : one,  of  ascertained  fact,  the  oth- 
er containing  a large  element  of  hypothesis. 

To  begin  with  the  first.  It  is  proved  by  numerous  facts,  both  natural 
and  of  artificial  production,  that  agencies  which  had  been  regarded  as  dis- 
tinct and  independent  sources  of  force — heat,  electricity,  chemical  action, 
nervous  and  muscular  action,  momentum  of  moving  bodies  — are  inter- 
changeable, in  definite  and  fixed  quantities,  with  one  another.  It  had  long 
been  known  that  these  dissimilar  phenomena  had  the  power,  under  certain 
conditions,  of  producing  one  another:  what  is  new  in  the  theory  is  a more 
accurate  estimation  of  what  this  production  consists  in.  What  happens  is, 
that  the  whole  or  part  of  the  one  kind  of  phenomena  disappears,  and  is  re- 
placed by  phenomena  of  one  of  the  other  descriptions,  and  that  there  is  an 
equivalence  in  quantity  between  the  phenomena  that  have  disappeared  and 
those  which  have  been  produced,  insomuch  that  if  the  process  be  reversed, 
the  very  same  quantity  which  had  disappeared  will  re-appear,  without  in- 
crease or  diminution.  Thus  the  amount  of  heat  which  will  raise  the  tem- 
perature of  a pound  of  water  one  degree  of  the  thermometer,  will,  if  ex- 
pended, say  in  the  expansion  of  steam,  lift  a weight  of  '772  pounds  one 


252 


INDUCTION. 


foot,  or  a weight  of  one  pound  '772  feet:  and  the  same  exact  quantity  of 
heat  can,  by  certain  means,  be  recovered,  through  the  expenditure  of  exact- 
ly that  amount  of  mechanical  motion. 

The  establishment  of  this  comprehensive  law  has  led  to  a change  in  the 
language  in  which  the  scientific  world  had  been  accustomed  to  speak  of 
what  are  called  the  Forces  of  nature.  Before  this  correlation  between  phe- 
nomena most  unlike  one  another  had  been  ascertained,  their  unlikeness  had 
caused  them  to  be  referred  to  so  many  distinct  forces.  Now  that  they  are 
known  to  be  convertible  into  one  another  without  loss,  they  are  spoken  of 
as  all  of  them  results  of  one  and  the  same  force,  manifesting  itself  in  dif- 
ferent modes.  This  force  (it  is  said)  can  only  produce  a limited  and  defi- 
nite quantity  of  effect,  but  always  does  produce  that  definite  quantity;  and 
produces  it,  according  to  circumstances,  in  one  or  another  of  the  forms,  or 
divides  it  among  several,  but  so  as  (according  to  a scale  of  numerical 
equivalents  established  by  experiment)  always  to  make  up  the  same  sum; 
and  no  one  of  the  manifestations  can  be  produced,  save  by  the  disappear- 
ance of  the  equivalent  quantity  of  another,  which  in  its  turn,  in  appropriate 
circumstances,  will  re-appear  undiminished.  This  mutual  interchangeabil- 
ity of  the  forces  of  nature,  according  to  fixed  numerical  equivalents,  is  the 
part  of  the  new  doctrine  which  rests  on  irrefragable  fact. 

To  make  the  statement  true,  however,  it  is  necessary  to  add,  that  an  in- 
definite and  perhaps  immense  interval  of  time  may  elapse  between  the  dis- 
appearance of  the  force  in  one  form  and  its  re-appearance  in  another.  A 
stone  thrown  up  into  the  air  with  a given  force,  and  falling  back  immedi- 
ately, will,  by  the  time  it  reaches  the  earth,  recover  the  exact  amount  of  me- 
chanical momentum  which  was  expended  in  throwing  it  up,  deduction  be- 
ing made  of  a small  portion  of  motion  which  has  been  communicated  to 
the  air.  But  if  the  stone  has  lodged  on  a height,  it  may  not  fall  back  for 
years,  or  perhaps  ages,  and  until  it  does,  the  force  expended  in  raising  it  is 
temporarily  lost,  being  represented  only  by  what,  in  the  language  of  the 
new  theory,  is  called  potential  energy.  The  coal  imbedded  in  the  earth  is 
considered  by  the  theory  as  a vast  reservoir  of  force,  which  has  remained 
dormant  for  many  geological  periods,  and  will  so  remain  until,  by  being 
burned,  it  gives  out  the  stored-up  force  in  the  form  of  heat.  Yet  it  is 
not  supposed  that  this  force  is  a material  thing  which  can  be  confined  by 
bounds,  as  used  to  be  thought  of  latent  heat  when  that  important  phenom- 
enon was  first  discovered.  What  is  meant  is  that  when  the  coal  does  at 
last,  by  combustion,  generate  a quantity  of  heat  (transformable  like  all  oth- 
er heat  into  mechanical  momentum,  and  the  other  forms  of  force),  this  ex- 
trication of  heat  is  the  re-appearance  of  a force  derived  from  the  sun’s  rays, 
expended  myriads  of  ages  ago  in  the  vegetation  of  the  organic  substances 
which  were  the  material  of  the  coal. 

Let  us  now  pass  to  the  higher  stage  of  the  theory  of  Conservation  of 
Force;  the  part  which  is  no  longer  a generalization  of  proved  fact,  but  a 
combination  of  fact  and  hypothesis.  Stated  in  few  words,  it  is  as  follows: 
That  the  Conservation  of  Force  is  really  the  Conservation  of  Motion  ; that 
in  the  various  interchanges  between  the  forms  of  force,  it  is  always  motion 
that  is  transformed  into  motion.  To  establish  this,  it  is  necessary  to  as- 
sume motions  which  are  hypothetical.  The  supposition  is,  that  there  are 
motions  which  manifest  themselves  to  our  senses  only  as  heat,  electricity, 
etc.,  being  molecular  motions;  oscillations,  invisible  to  us,  among  the  mi- 
nute particles  of  bodies ; and  that  these  molecular  motions  are  transmutable 
into  molar  motions  (motions  of  masses),  and  molar  motions  into  molecular. 


LAW  OF  CAUSATION. 


253 


Now  there  is  a real  basis  of  fact  for  this  supposition : we  have  positive  evi- 
dence of  the  existence  of  molecular  motion  in  these  manifestations  of  force. 
In  the  case  of  chemical  action,  for  instance,  the  particles  separate  and  form 
new  combinations,  often  with  a great  visible  disturbance  of  the  mass.  In 
the  case  of  heat,  the  evidence  is  equally  conclusive,  since  heat  expands  bod- 
ies (that  is,  causes  their  particles  to  move  from  one  another) ; and  if  of 
sufficient  amount,  changes  their  mode  of  aggregation  from  solid  to  liquid, 
or  from  liquid  to  gaseous.  Again,  the  mechanical  actions  which  produce 
heat — friction,  and  the  collision  of  bodies — must  from  the  nature  of  the 
case  produce  a shock,  that  is,  an  internal  motion  of  particles,  which  indeed, 
we  find,  is  often  so  violent  as  to  break  them  permanently  asunder.  Such 
facts  are  thought  to  warrant  the  inference,  that  it  is  not,  as  was  supposed, 
heat  that  causes  the  motion  of  particles,  but  the  motion  of  particles  that 
causes  heat;  the  original  cause  of  both  being  the  previous  motion  (whether 
molar  or  molecular — collision  of  bodies  or  combustion  of  fuel)  which  form- 
ed the  heating  agency.  This  inference  already  contains  hypothesis ; but  at 
least  the  supposed  cause,  the  intestine  motion  of  molecules,  is  a vera  causa. 
But  in  order  to  reduce  the  Conservation  of  Force  to  Conservation  of  Mo- 
tion, it  was  necessary  to  attribute  to  motion  the  heat  propagated,  through 
apparently  empty  space,  from  the  sun.  This  required  the  supposition 
(already  made  for  the  explanation  of  the  laws  of  light)  of  a subtle  ether 
pervading  space,  which,  though  impalpable  to  us,  must  have  the  property 
which  constitutes  matter,  that  of  resistance,  since  waves  are  propagated 
through  it  by  an  impulse  from  a given  point.  The  ether  must  be  supposed 
(a  supjDOsition  not  required  by  the  theory  of  light)  to  penetrate  into  the 
minute  interstices  of  all  bodies.  The  vibratory  motion  supposed  to  be  tak- 
ing place  in  the  heated  mass  of  the  sun,  is  considered  as  imparted  from 
that  mass  to  the  particles  of  the  surrounding  ether,  and  through  them  to 
the  particles  of  the  same  ether  in  the  interstices  of  terrestrial  bodies ; and 
this,  too,  with  a sufficient  mechanical  force  to  throw  the  particles  of  those 
bodies  into  a state  of  similar  vibration,  producing  the  expansion  of  their 
mass,  and  the  sensation  of  heat  in  sentient  creatures.  All  this  is  hypothe- 
sis, though,  of  its  legitimacy  as  hypothesis,  I do  not  mean  to  express  any 
doubt.  It  -would  seem  to  follow  as  a consequence  from  this  theory,  that 
Force  may  and  should  be  defined,  matter  in  motion.  This  definition,  how- 
ever, will  not  stand,  for,  as  has  already  been  seen,  the  matter  needs  not  be 
in  actual  motion.  It  is  not  necessary  to  suppose  that  the  motion  after- 
ward manifested,  is  actually  taking  place  among  the  molecules  of  the  coal 
during  its  sojourn  in  the  earth  ;*  certainly  not  in  the  stone  which  is  at  rest 
on  the  eminence  to  which  it  has  been  raised.  The  true  definition  of  Force 
must  be,  not  motion,  but  Potentiality  of  Motion ; and  what  the  doctrine, 
if  established,  amounts  to,  is,  not  that  there  is  at  all  times  the  same  quan- 
tity of  actual  motion  in  the  universe ; but  that  the  possibilities  of  motion 
are  limited  to  a definite  quantity,  -which  can  not  be  added  to,  but  which 
can  not  be  exhausted;  and  that  ail  actual  motion  which  takes  place  in  Na- 
ture is  a draft  upon  this  limited  stock.  It  needs  not  all  of  it  have  ever  ex- 
isted as  actual  motion.  There  is  a vast  amount  of  potential  motion  in  the 
universe  in  the  form  of  gravitation,  which  it  would  be  a great  abuse  of 

* I believe,  however,  the  accredited  authorities  do  suppose  that  molecular  motion,  equiva- 
lent in  amount  to  that. which  will  be  manifested  in  the  combustion  of  the  coal,  is  actually  tak- 
ing place  during  the  whole  of  the  long  interval,  if  not  in  the  coal,  yet  in  the  oxygen  which 
will  then  combine  with  it.  But  how  purely  hypothetical  this  supposition  is,  need  hardly  be 
remarked  ; I venture  to  say,  unnecessarily  and  extravagantly  hypothetical. 


254 


INDUCTION. 


hypothesis  to  suppose  to  have  been  stored  up  by  the  expenditure  of  an 
equal  amount  of  actual  motion  in  some  former  state  of  the  universe.  Nor 
does  the  motion  produced  by  gravity  take  place,  so  far  as  we  know,  at  the 
expense  of  any  other  motion,  either  molar  or  molecular. 

It  is  proper  to  consider  whether  the  adoption  of  this  theory  as  a scien- 
tifie  truth,  involving  as  it  does  a change  in  the  conception  hitherto  enter- 
tained of  the  most  general  physical  agencies,  requires  any  modification  in 
the  view  I have  taken  of  Causation  as  a law  of  nature.  As  it  appears  to 
me,  none  whatever.  The  manifestations  which  the  theory  regards  as 
modes  of  motion,  are  as  much  distinct  and  separate  phenomena  when  re- 
ferred to  a single  force,  as  when  attributed  to  several.  Whether  the  phe- 
nomenon is  called  a transformation  of  force  or  the  generation  of  one,  it  has 
its  own  set  or  sets  of  antecedents,  with  which  it  is  connected  by  invariable 
and  unconditional  sequence;  and  that  set,  or  those  sets,  of  antecedents  are 
its  cause.  The  relation  of  the  Conservation  theory  to  the  principle  of 
Causation  is  discussed  in  much  detail,  and  very  instructively,  by  Professor 
Bain,  in  the  second  volume  of  his  Logic.  The  chief  practical  conclusion 
drawn  by  him,  bearing  on  Causation,  is,  that  we  must  distinguish  in  the 
assemblage  of  conditions  which  constitutes  the  Cause  of  a phenomenon, 
two  elements:  one,  the  presence  of  a force;  the  other,  the  collocation  or 
position  of  objects  which  is  required  in  order  that  the  force  may  undergo 
the  particular  transmutation  which  constitutes  the  phenomenon.  Now,  it 
might  always  have  been  said  with  acknowledged  correctness,  that  a force 
and  a collocation  were  both  of  them  necessary  to  produce  any  phenomenon. 
The  law  of  causation  is,  that  change  can  ordy  be  produced  by  change. 
Along  with  any  number  of  stationary  antecedents,  which  are  collocations, 
there  must  be  at  least  one  changing  antecedent,  which  is  a force.  To  pro- 
duce a bonfire,  there  must  not  only  be  fuel,  and  air,  and  a spark,  which  are 
collocations,  but  chemical  action  between  the  air  and  the  materials,  which 
is  a force.  To  grind  corn,  there  must  bo  a certain  collocation  of  the  parts 
composing  a mill,  relatively  to  one  another  and  to  the  corn ; but  there  must 
also  be  the  gravitation  of  water,  or  the  motion  of  wind,  to  supply  a force. 
But  as  the  force  in  these  cases  was  regarded  as  a property  of  the  objects 
in  which  it  is  embodied,  it  seemed  tautology  to  say  that  there  must  be  the 
collocation  and  the  force.  As  the  collocation  must  be  a collocation  of  ob- 
jects possessing  the  force-giving  property,  the  collocation,  so  understood, 
included  the  force. 

How,  then,  shall  we  have  to  express  these  facts,  if  the  theory  be  finally 
substantiated  that  all  Force  is  reducible  to  a previous  Motion?  We  shall 
have  to  say,  that  one  of  the  conditions  of  every  phenomenon  is  an  ante- 
cedent Motion.  But  it  will  have  to  be  explained  that  this  needs  not  be 
actual  motion.  The  coal  which  supplies  the  force  exerted  in  combustion 
is  not  shown  to  have  been  exerting  that  force  in  the  form  of  molecular 
motion  in  the  pit;  it  was  not  even  exerting  pressure.  The  stone  on  the 
eminence  is  exerting  a pressure,  but  only  equivalent  to  its  weight,  not  to 
the  additional  momentum  it  would  acquire  by  falling.  The  antecedent, 
therefore,  is  not  a force  in  action ; and  we  can  still  only  call  it  a property 
of  the  objects,  by  which  they  would  exert  a force  on  the  occurrence  of  a 
fresh  collocation.  The  collocation,  therefore,  still  includes  the  force.  The 
force  said  to  be  stored  up,  is  simply  a particular  property  which  the  object 
has  acquired.  The  cause  we  are  in  search  of,  is  a collocation  of  objects 
possessing  that  particular  property.  When,  indeed,  we  inquire  further  into 
the  cause  from  which  they  derive  that  property,  the  new  conception  intro- 


LAW  OF  CAUSATION. 


255 


dnced  by  the  Conservation  theory  comes  in : the  property  is  itself  an  ef- 
fect, and  its  cause,  according  to  the  theory,  is  a former  motion  of  exactly 
equivalent  amount,  which  has  been  impressed  on  the  particles  of  the  body, 
perhaps  at  some  very  distant  period.  But  the  case  is  simply  one  of  those 
we  have  already  considered,  in  which  the  efficacy  of  a cause  consists  in  its 
investing  an  object  with  a property.  The  force  said  to  be  laid  up,  and 
merely  potential,  is  no  more  a really  existing  thing  than  any  other  proper- 
ties of  objects  are  really  existing  things.  The  expression  is  a mere  arti- 
fice of  language,  convenient  for  describing  the  phenomena:  it  is  unneces- 
sary to  suppose  that  any  thing  has  been  in  continuous  existence  except  an 
abstract  potentiality.  A force  suspended  in  its  operation,  neither  mani- 
festing itself  by  motion  nor  by  pressure,  is  not  an  existing  fact,  but  a name 
for  our  conviction  that  in  appropriate  circumstances  a fact  would  take 
place.  We  know  that  a pound  weight,  were  it  to  fall  from  the  earth  into 
the  sun,  would  acquire  in  falling  a momentum  equal  to  millions  of  pounds; 
but  we  do  not  credit  the  pound  weight  with  more  of  actually  existing  force 
than  is  equal  to  the  pressure  it  is  now  exerting  on  the  earth,  and  that  is 
exactly  a pound.  We  might  as  well  say  that  a force  of  millions  of  pounds 
exists  in  a pound,  as  that  the  force  which  will  manifest  itself  when  the 
coal  is  burned  is  a real  thing  existing  in  the  coal.  What  is  fixed  in  the  coal 
is  only  a certain  property:  it  has  become  fit  to  be  the  antecedent  of  an  ef- 
fect called  combustion,  which  partly  consists  in  giving  out,  under  certain 
conditions,  a given  definite  quantity  of  heat. 

We  thus  see  that  no  new  general  conception  of  Causation  is  introduced 
by  the  Conservation  theory.  The  indestructibility  of  Force  no  more  in- 
terferes with  the  theory  of  Causation  than  the  indestructibility  of  Matter, 
meaning  by  matter  the  element  of  resistance  in  the  sensible  world.  It 
only  enables  us  to  understand  better  than  before  the  nature  and  laws  of 
some  of  the  sequences. 

This  better  understanding,  however,  enables  us,  with  Mr.  Bain,  to  admit, 
as  one.  of  the  tests  for  distinguishing  causation  from  mere  concomitance, 
the  expenditure  or  transfer  of  energy.  If  the  effect,  or  any  part  of  the 
effect,  to  be  accounted  for,  consists  in  putting  matter  in  motion,  then  any 
of  the  objects  present  which  has  lost  motion  has  contributed  to  the  effect; 
and  this  is  the  true  meaning  of  the  proposition  that  the  cause  is  that  one 
of  the  antecedents  which  exerts  active  force. 

§ 11.  It  is  proper  in  this  place  to  advert  to  a rather  ancient  doctrine  re- 
specting causation,  which  has  been  revived  during  the  last  few  years  in 
many  quarters,  and  at  present  gives  more  signs  of  life  than  any  other  the- 
ory of  causation  at  variance  with  that  set  forth  in  the  preceding  pages. 

According  to  the  theory  in  question,  Mind,  or  to  speak  more  precisely, 
Will,  is  the  only  cause  of  phenomena.  The  type  of  Causation,  as  well  as 
the  exclusive  source  from  which  we  derive  the  idea,  is  our  own  voluntary 
agency.  Here,  and  here  only  (it  is  said),  we  have  direct  evidence  of  causa- 
tion. We  know  that  we  can  move  our  bodies.  Respecting  the  phenom- 
ena of  inanimate  nature,  we  have  no  other  direct  knowledge  than  that  of 
antecedence  and  sequence.  But  in  the  case  of  our  voluntary  actions,  it  is 
affirmed  that  we  are  conscious  of  power  before  we  have  experience  of  re- 
sults. An  act  of  volition,  whether  followed  by  an  effect  or  not,  is  ac- 
companied by  a consciousness  of  effort,  “of  force  exerted,  of  power  in  ac- 
tion, which  is  necessarily  causal,  or  causative.”  This  feeling  of  energy  or 
force,  inherent  in  an  act  of  will,  is  knowledge  a J priori  • assurance,  prior  to 


25G 


INDUCTION. 


experience,  that  we  have  the  power  of  causing  effects.  Volition,  therefore, 
it  is  asserted,  is  something  more  than  an  unconditional  antecedent;  it  is  a 
cause,  in  a different  sense  from  that  in  which  physical  phenomena  are  said 
to  cause  one  another : it  is  an  Efficient  Cause.  From  this  the  transition  is 
easy  to  the  further  doctrine,  that  Volition  is  the  sole  Efficient  Cause  of  all 
phenomena.  “ It  is  inconceivable  that  dead  force  could  continue  unsup- 
ported for  a moment  beyond  its  creation.  We  can  not  even  conceive  of 
change  or  phenomena  without  the  energy  of  a mind.”  “The  word  action  ” 
itself,  says  another  writer  of  the  same  school,  “ has  no  real  significance  ex- 
cept when  applied  to  the  doings  of  an  intelligent  agent.  Let  any  one  con- 
'ceive,  if  he  can,  of  any  power,  energy, or  force  inherent  in  a lump  of  mat- 
ter.” Phenomena  may  have  the  semblance  of  being  produced  by  phys- 
ical causes,  but  they  are  in  reality  produced,  say  these  writers,  by  the  im- 
mediate agency  of  mind.  All  things  which  do  not  proceed  from  a human 
(or,  I suppose,  an  animal)  will  proceed,  they  say,  directly  from  divine  will. 
The  earth  is  not  moved  by  the  combination  of  a centripetal  and  a pro- 
jectile force;  this  is  but  a mode  of  speaking,  which  serves  to  facilitate  our 
conceptions.  It  is  moved  by  the  direct  volition  of  an  omnipotent  Being,  in 
a path  coinciding  with  that  which  we  deduce  from  the  hypothesis  of  these 
two  forces. 

As  I have  so  often  observed,  the  general  question  of  the  existence  of  Ef- 
ficient Causes  does  not  fall  within  the  limits  of  our  subject;  but  a theory 
which  represents  them  as  capable  of  being  subjects  of  human  knowledge, 
and  which  passes  off  as  efficient  causes  what  are  only  physical  or  phenom- 
enal causes,  belongs  as  much  to  Logic  as  to  metaphysics,  and  is  a fit  sub- 
ject for  discussion  here. 

To  my  apprehension,  a volition  is  not  an  efficient,  but  simply  a physical 
cause.  Our  will  causes  our  bodily  actions  in  the  same  sense,  aud  in  no 
other,  in  which  cold  causes  ice,  or  a spark  causes  an  explosion  of  gunpow- 
der. The  volition,  a state  of  our  mind,  is  the  antecedent;  the  motion  of 
our  limbs  in  conformity  to  the  volition,  is  the  consequent.  This  sequence 
I conceive  to  be  not  a subject  of  direct  consciousness,  in  the  sense  intend- 
ed by  the  theory.  The  antecedent,  indeed,  and  the  consequent,  are  sub- 
jects of  consciousness.  But  the  connection  between’ them  is  a subject  of 
experience.  I can  not  admit  that  our  consciousness  of  the  volition  con- 
tains in  itself  any  a priori  knowledge  that  the  muscular  motion  will  fol- 
low. If  our  nerves  of  motion  were  paralyzed,  or  our  muscles  stiff  and  in- 
flexible, and  had  been  so  all  our  lives,  I do  not  see  the  slightest  ground  for 
supposing  that  we  should  ever  (unless  by  information  from  other  people) 
have  known  any  thing  of  volition  as  a physical  power,  or  been  conscious  of 
any  tendency  in  feelings  of  our  mind  to  produce  motions  of  our  body,  or  of 
other  bodies.  I will  not  undertake  to  say  whether  we  should  in  that  case 
have  had  the  physical  feeling  which  I suppose  is  meant  when  these  writers 
speak  of  “ consciousness  of  effort:”  I see  no  reason  why  we  should  not; 
since  that  physical  feeling  is  probably  a state  of  nervous  sensation  begin- 
ning and  ending  in  the  brain,  without  involving  the  motory  apparatus: 
but  we  certainly  should  not  have  designated  it  by  any  term  equivalent  to 
effort,  since  effort  implies  consciously  aiming  at  an  end,  which  we  should 
not  only  in  that  case  have  had  no  reason  to  do,  but  could  not  even  have 
had  the  idea  of  doing.  If  conscious  at  all  of  this  peculiar  sensation,  we 
should  have  been  conscious  of  it,  I conceive,  only  as  a kind  of  uneasiness, 
accompanying  our  feelings  of  desire. 

It  is  well  argued  by  Sir  William  Hamilton  against  the  theory  in  question, 


LAW  OF  CAUSATION. 


257 


that  it  “ is  refuted  by  the  consideration  that  between  the  overt  fact  of  cor- 
poreal movement  of  which  we  are  cognizant,  and  the  internal  act  of  mental 
determination  of  which  we  are  also  cognizant,  there  intervenes  a numerous 
series  of  intermediate  agencies  of  which  we  have  no  knowledge ; and,  con- 
sequently, that  we  can  have  no  consciousness  of  any  causal  connection  be- 
tween the  extreme  links  of  this  chain,  the  volition  to  move  and  the  limb 
moving,  as  this  hypothesis  asserts.  No  one  is  immediately  conscious,  for 
example,  of  moving  his  arm  through  his  volition.  Previously  to  this  ulti- 
mate movement,  muscles,  nerves,  a multitude  of  solid  and  fluid  parts,  must 
be  set  in  motion  by  the  will,  but  of  this  motion  we  know,  from  conscious- 
ness, absolutely  nothing.  A person  struck  with  paralysis  is  conscious  of 
no  inability  in  his  limb  to  fulfill  the  determinations  of  his  will;  and  it  is 
only  after  having  willed,  and  finding  that  his  limbs  do  not  obey  his  volition, 
that  he  learns  by  this  experience,  that  the  external  movement  does  not  fol- 
low the  internal  act.  But  as  the  paralytic  learns  after  the  volition  that  his 
limbs  do  not  obey  his  mind ; so  it  is  only  after  volition  that  the  man  in 
health  learns,  that  his  limbs  do  obey  the  mandates  of  his  will.”* 

Those  against  whom  I am  contending  have  never  produced,  and  do  not 
pretend  to  produce,  any  positive  evidencef  that  the  power  of  our  will  to 
move  our  bodies  would  be  known  to  us  independently  of  experience.  What 
they  have  to  say  on  the  subject  is,  that  the  production  of  physical  events 
by  a will  seems  to  carry  its  own  explanation  with  it,  while  the  action  of 
matter  upon  matter  seems  to  require  something  else  to  explain  it;  and  is 
even,  according  to  them,  “ inconceivable”  on  any  other  supposition  than 
that  some  will  intervenes  between  the  apparent  cause  and  its  apparent 
effect.  They  thus  rest  their  case  on  an  appeal  to  the  inherent  laws  of  our  con- 
ceptive  faculty ; mistaking,  as  I apprehend,  for  the  laws  of  that  faculty  its 
acquired  habits,  grounded  on  the  spontaneous  tendencies  of  its  uncultured 
state.  The  succession  between  the  will  to  move  a limb  and  the  actual  mo- 
tion is  one  of  the  most  direct  and  instantaneous  of  all  sequences  which 
come  under  our  observation,  and  is  familiar  to  every  moment’s  experience 
from  our  earliest  infancy;  more  familiar  than  any  succession  of  events  ex- 

* Lectures  on  Metaphysics,  vol.  ii. , Lect.  xxxix.,  pp.  391-2. 

I regret  that  I can  not  invoke  the  authority  of  Sir  William  Hamilton  in  favor  of  my  own 
opinions  on  Causation,  as  I can  against  the  particular  theory  which  I am  now  combating. 
But  that  acute  thinker  has  a theory  of  Causation  peculiar  to  himself,  which  has  never  yet,  as 
far  as  I know,  been  analytically  examined,  but  which,  I venture  to  think,  admits  of  as  com- 
plete refutation  as  any  one  of  the  false  or  insufficient  psychological  theories  which  strew  the 
ground  in  such  numbers  under  his  potent  metaphysical  scythe.  (Since  examined  and  contro- 
verted in  the  sixteenth  chapter  of  An  Examination  of  Sir  William  Hamilton  s Philosophy.') 

t Unless  we  are  to  consider  as  such  the  following  statement,  by  one  of  the  writers  quoted 
in  the  text : “In  the  case  of  mental  exertion,  the  result  to  be  accomplished  is  preconsidered 
or  meditated,  and  is  therefore  known  a priori,  or  before  experience.” — (Bowen's  Lowell  Lec- 
tures on  the  Application  of  Metaphysical  and  Ethical  Science  to  the  Evidence  of  Religion. 
Boston,  1849.)  This  is  merely  saying  that  when  we  will  a thing  we  have  an  idea  of  it.  But 
to  have  an  idea  of  what  we  wish  to  happen,  does  not  imply  a prophetic  knowledge  that  it  will 
happen.  Perhaps  it  will  be  said  that  the  first  time  we  exerted  our  will,  when  we  had  of 
course  no  experience  of  any  of  the  powers  residing  in  us,  we  nevertheless  must  already  have 
known  that  we  possessed  them,  since  we  can  not  will  that  which  we  do  not  believe  to  be  in 
our  power.  But  the  impossibility  is  perhaps  in  the  words  only,  and  not  in  the  facts ; for  we 
may  desire  what  we  do  not  know  to  be  in  our  power ; and  finding  by  experience  that  our 
bodies  move  according  to  our  desire,  we  may  then,  and  only  then,  pass  into  the  more  compli- 
cated mental  state  which  is  termed  will. 

After  all,  even  if  we  had  an  instinctive  knowledge  that  our  actions  would  follow  our  will, 
this,  as  Brown  remarks,  would  prove  nothing  as  to  the  nature  of  Causation.  Our  knowing, 
previous  to  experience,  that  an  antecedent  will  be  followed  by  a certain  consequent,  would 
not  prove  the  relation  between  them  to  be  anv  thing  more  than  antecedence  and  consequence. 

17 


25S 


INDUCTION. 


terior  to  our  bodies,  and  especially  more  so  than  any  other  case  of  the  ap- 
parent origination  (as  distinguished  from  the  mere  communication)  of  mo- 
tion. Now,  it  is  the  natural  tendency  of  the  mind  to  be  always  attempting 
to  facilitate  its  conception  of  unfamiliar  facts  by  assimilating  them  to  oth- 
ers which  are  familiar.  Accordingly,  our  voluntary  acts,  being  the  most 
familiar  to  us  of  all  cases  of  causation,  are,  in  the  infancy  and  early  youth 
of  the  human  race,  spontaneously  taken  as  the  type  of  causation  in  general, 
and  all  phenomena  are  supposed  to  be  directly  produced  by  the  will  of 
some  sentient  being.  This  original  Fetichism  I shall  not  characterize  in 
the  words  of  Hume,  or  of  any  follower  of  Hume,  but  in  those  of  a religious 
metaphysician,  Dr.  Reid,  in  order  more  effectually  to  show  the  unanimity 
which  exists  on  the  subject  among  all  competent  thinkers. 

“When  we  turn  our  attention  to  external  objects,  and  begin  to  exercise 
our  rational  faculties  about  them,  we  find  that  there  are  some  motions  and 
changes  in  them  which  we  have  power  to  produce,  and  that  there  are  many 
which  must  have  some  other  cause.  Either  the  objects  must  have  life  and 
active  power,  as  we  have,  or  they  must  be  moved  or  changed  by  something 
that  has  life  and  active  power,  as  external  objects  are  moved  by  us. 

“Our  first  thoughts  seem  to  be,  that  the  objects  in  which  we  perceive 
such  motion  have  understanding  and  active  power  as  we  have.  ‘ Savages,’ 
says  the  Abbe  Raynal, £ wherever  they  see  motion  which  they  can  not  ac- 
count for,  there  they  suppose  a soul.’  All  men  may  be  considered  as  sav- 
ages in  this  respect, until  they  are  capable  of  instruction,  and  of  using  their 
faculties  in  a more  perfect  manner  than  savages  do. 

“The  Abbe  Raynal’s  observation  is  sufficiently  confirmed,  both  from 
fact,  and  from  the  structure  of  all  languages. 

“ Rude  nations  do  really  believe  sun,  moon,  and  stars,  earth,  sea,  and  air, 
fountains,  and  lakes,  to  have  understanding  and  active  power.  To  pay 
homage  to  them,  and  implore  their  favor,  is  a kind  of  idolatry  natural  to 
savages. 

“All  languages  carry  in  their  structure  the  marks  of  their  being  formed 
when  this  belief  prevailed.  The  distinction  of  verbs  and  participles  into 
active  and  passive,  which  is  found  in  all  languages,  must  have  been  origi- 
nally intended  to  distinguish  what  is  really  active  from  what  is  merely  pas- 
sive ; and  in  all  languages,  we  find  active  verbs  applied  to  those  objects,  in 
which,  according  to  the  Abbe  Raynal’s  observation,  savages  suppose  a soul. 

“ Thus  we  say  the  sun  rises  and  sets,  and  comes  to  the  meridian,  the 
moon  changes,  the  sea  ebbs  and  flows,  the  winds  blow.  Languages  were 
formed  by  men  who  believed  these  objects  to  have  life  and  active  power 
in  themselves.  It  was  therefore  proper  and  natural  to  expi-ess  their  mo- 
tions and  changes  by  active  verbs. 

“ There  is  no  surer  way  of  tracing  the  sentiments  of  nations  before  they 
have  records,  than  by  the  structure  of  their  language,  which,  notwithstanding 
the  changes  produced  in  it  by  time,  will  always  retain  some  signatures  of 
the  thoughts  of  those  by  whom  it  was  invented.  When  we  find  the  same 
sentiments  indicated  in  the  structure  of  all  languages,  those  sentiments  must 
have  been  common  to  the  human  species  when  languages  were  invented. 

“ When  a few,  of  superior  intellectual  abilities,  find  leisure  for  specula- 
tion, they  begin  to  philosophize,  and  soon  discover,  that  many  of  those  ob- 
jects which  at  first  they  believed  to  be  intelligent  and  active  are  really 
lifeless  and  passive.  This  is  a very  important  discovery.  It  elevates  the 
mind,  emancipates  from  many  vulgar  superstitions,  and  invites  to  further 
discoveries  of  the  same  kind. 


LAW  OF  CAUSATION. 


259 


“As  philosophy  advances,  life  and  activity  in  natural  objects  retires,  and 
leaves  them  dead  and  inactive.  Instead  of  moving  voluntarily,  we  find 
them  to  be  moved  necessarily;  instead  of  acting,  we  find  them  to  be  acted 
upon ; and  Nature  appears  as  one  great  machine,  where  one  wheel  is  turn- 
ed by  another, that  by  a third;  and  how  far  this  necessary  succession  may 
reach,  the  philosopher  does  not  know.”* 

There  is,  then,  a spontaneous  tendency  of  the  intellect  to  account  to  it- 
self for  all  cases  of  causation  by  assimilating  them  to  the  intentional  acts 
of  voluntary  agents  like  itself.  This  is  the  instinctive  philosophy  of  the 
human  mind  in  its  earliest  stage,  before  it  has  become  familiar  with  any 
other  invariable  sequences  than  those  between  its  own  volitions  or  those 
of  other  human  beings  and  their  voluntary  acts.  As  the  notion  of  fixed 
laws  of  succession  among  external  phenomena  gradually  establishes  itself, 
the  propensity  to  refer  all  phenomena  to  voluntary  agency  slowly  gives 
way  before  it.  The  suggestions,  however,  of  daily  life  continuing  to  be 
more  powerful  than  those  of  scientific  thought,  the  original  instinctive  phi- 
losophy maintains  its  ground  in  the  mind,  underneath  the  growths  obtain- 
ed by  cultivation,  and  keeps  up  a constant  resistance  to  their  throwing 
their  roots  deep  into  the  soil.  The  theory  against  which  I am  contend- 
ing derives  its  nourishment  from  that  substratum.  Its  strength  does  not 
lie  in  argument,  but  in  its  affinity  to  an  obstinate  tendency  of  the  infancy 
of  the  human  mind. 

That  this  tendency,  however,  is  not  the  result  of  an  inherent  mental  law, 
is  proved  by  superabundant  evidence.  The  history  of  science,  from  its 
eai’liest  dawn,  shows  that  mankind  have  not  been  unanimous  in  thinking 
either  that  the  action  of  matter  upon  matter  was  not  conceivable,  or  that 
the  action  of  mind  upon  matter  was.  To  some  thinkers,  and  some  schools 
of  thinkers,  both  in  ancient  and  in  modern  times,  this  last  has  appeared 
much  more  inconceivable  than  the  former.  Sequences  entirely  physical 
and  material,  as  soon  as  they  had  become  sufficiently  familiar  to  the  human 
mind,  came  to  be  thought  perfectly  natural,  and  were  regarded  not  only  as 
needing  no  explanation  themselves,  but  as  being  capable  of  affording  it  to 
others,  and  even  of  serving  as  the  ultimate  explanation  of  things  in  gen- 
eral. 

One  of  the  ablest  recent  supporters  of  the  Volitional  theory  has  furnish- 
ed an  explanation,  at  once  historically  true  and  philosophically  acute,  of 
the  failure  of  the  Greek  philosophers  in  physical  inquiry,  in  which,  as  I 
conceive,  he  unconsciously  depicts  his  own  state  of  mind.  “ Their  stum- 
bling-block was  one  as  to  the  nature  of  the  evidence  they  had  to  expect 

for  their  conviction They  had  not  seized  the  idea  that  they  must  not 

expect  to  understand  the  processes  of  outward  causes,  but  only  their  re- 
sults ; and  consequently,  the  whole  physical  philosophy  of  the  Greeks  was 
an  attempt  to  identify  mentally  the  effect  with  its  cause,  to  feel  after  some 
not  only  necessary  but  natural  connection,  where  they  meant  by  natural 
that  which  would  per  se  carry  some  presumption  to  their  own  mind. 
....  They  wanted  to  see  some  reason  why  the  physical  antecedent  should 
produce  this  particular  consequent,  and  their  only  attempts  were  in  direc- 
tions where  they  could  find  such  reasons.”f  In  other  words,  they  were 
not  content  merely  to  know  that  one  phenomenon  was  always  followed  by 
another ; they  thought  that  they  had  not  attained  the  true  aim  of  science, 
unless  they  could  perceive  something  in  the  nature  of  the  one  phenomenon 

* Reid’s  Essays  on  the  Active  Powers,  Essay  iv. , chap.  3. 

t Prospective  Review  for  February,  1850. 


260 


INDUCTION. 


from  which  it  might  have  been  known  or  presumed  previous  to  trial  that 
it  would  be  followed  by  the  other:  just  what  the  writer,  who  has  so  clear- 
ly pointed  out  their  error,  thinks  that  he  perceives  in  the  nature  of  the 
phenomenon  Volition.  And  to  complete  the  statement  of  the  case,  he 
should  have  added  that  these  early  speculators  not  only  made  this  their 
aim,  but  were  quite  satisfied  with  their  success  in  it;  not  only  sought  for 
causes  which  should  carry  in  their  mere  statement  evidence  of  their  effi- 
ciency, but  fully  believed  that  they  had  found  such  causes.  The  reviewer 
can  see  plainly  that  this  was  an  error,  because  he  does  not  believe  that 
there  exist  any  relations  between  material  phenomena  which  can  account 
for  their  producing  one  another ; but  the  very  fact  of  the  persistency  of 
the  Greeks  in  this  error,  shows  that  their  minds  were  in  a very  different 
state : they  were  able  to  derive  from  the  assimilation  of  physical  facts  to 
other  physical  facts,  the  kind  of  mental  satisfaction  which  we  connect  with 
the  word  explanation,  and  which  the  reviewer  would  have  us  think  can 
only  be  found  in  referring  phenomena  to  a will.  When  Thales  and  Hippo 
held  that  moisture  was  the  universal  cause,  and  external  element,  of  which 
all  other  things  were  but  the  infinitely  various  sensible  manifestations ; 
when  Anaximenes  predicated  the  same  thing  of  air,  Pythagoras  of  numbers, 
and  the  like,  they  all  thought  that  they  had  found  a real  explanation;  and 
were  content  to  rest  in  this  explanation  as  ultimate.  The  ordinary  se- 
quences of  the  external  universe  appeared  to  them,  no  less  than  to  their 
critic,  to  be  inconceivable  without  the  supposition  of  some  universal  agen- 
cy to  connect  the  antecedents  with  the  consequents;  but  they  did  not 
think  that  Volition,  exerted  by  minds,  was  the  only  agency  which  fulfilled 
this  requirement.  Moisture,  or  air,  or  numbers,  carried  to  their  minds  a 
precisely  similar  impression  of  making  intelligible  what  was  otherwise  in- 
conceivable, and  gave  the  same  full  satisfaction  to  the  demands  of  their 
conceptive  faculty. 

It  was  not  the  Greeks  alone,  who  “ wanted  to  see  some  reason  why  the 
physical  antecedent  should  produce  this  particular  consequent,”  some  con- 
nection “ which  would  per  se  carry  some  presumption  to  their  own  mind.” 
Among  modern  philosophers,  Leibnitz  laid  it  down  as  a self-evident  prin- 
ciple that  all  physical  causes  without  exception  must  contain  in  their  own 
nature  something  which  makes  it  intelligible  that  they  should  be  able  to 
produce  the  effects  which  they  do  produce.  Far  from  admitting  Volition 
as  the  only  kind  of  cause  which  carried  internal  evidence  of  its  own  pow- 
er, and  as  the  real  bond  of  connection  between  physical  antecedents  and 
their  consequents,  he  demanded  some  naturally  and  per  se  efficient  physic- 
al antecedent  as  the  bond  of  connection  between  Volition  itself  and  its  ef- 
fects. He  distinctly  refused  to  admit  the  will  of  God  as  a sufficient  ex- 
planation of  any  thing  except  miracles ; and  insisted  upon  finding  some- 
thing that  would  account  better  for  the  phenomena  of  nature  than  a mere 
reference  to  divine  volition.* 

Again,  and  conversely,  the  action  of  mind  upon  matter  (which,  we  are 
now  told,  not  only  needs  no  explanation  itself,  but  is  the  explanation  of  all 
other  effects),  has  appeared  to  some  thinkers  to  be  itself  the  grand  incon- 
ceivability. It  was  to  get  over  this  very  difficulty  that  the  Cartesians  in- 
vented the  system  of  Occasional  Causes.  They  could  not  conceive  that 
thoughts  in  a mind  could  produce  movements  in  a body,  or  that  bodily 
movements  could  produce  thoughts.  They  could  see  no  necessary  connee- 


* Vide  supra,  p.  178,  note. 


LAW  OF  CAUSATION. 


261 


tion,  no  relation  a priori , between  a motion  and  a thought.  And  as  the 
Cartesians,  more  than  any  other  school  of  philosophical  speculation  before 
or  since,  made  their  own  minds  the  measure  of  all  things,  and  refused,  on 
principle,  to  believe  that  Nature  had  done  what  they  were  unable  to  see 
any  reason  why  she  must  do,  they  affirmed  it  to  be  impossible  that  a ma- 
terial and  a mental  fact  could  be  causes  one  of  another.  They  regarded 
them  as  mere  Occasions  on  which  the  real  agent,  God,  thought  fit  to  exert 
his  power  as  a Cause.  When  a man  wills  to  move  his  foot,  it  is  not  his 
will  that  moves  it,  but  God  (they  said)  moves  it  on  the  occasion  of  his 
will.  God,  according  to  this  system,  is  the  only  efficient  cause,  not  qua 
mind,  or  qua  endowed  with  volition,  but  qua  omnipotent.  This  hypoth- 
esis was,  as  I said,  originally  suggested  by  the  supposed  inconceivability 
of  any  real  mutual  action  between  Mind  and  Matter;  but  it  was  afterward 
extended  to  the  action  of  Matter  upon  Matter,  for  on  a nicer  examination 
they  found  this  inconceivable  too,  and  therefore,  according  to  their  logic, 
impossible.  The  deus  ex  maehind  was  ultimately  called  in  to  produce  a 
spark  on  the  occasion  of  a dint  and  steel  coming  together,  or  to  break  an 
egg  on  the  occasion  of  its  falling  on  the  ground. 

All  this,  undoubtedly,  shows  that  it  is  the  disposition  of  mankind  in  gen- 
eral, not  to  be  satisfied  with  knowing  that  one  fact  is  invariably  anteced- 
ent and  another  consequent,  but  to  look  out  for  something  which  may  seem 
to  explain  their  being  so.  But  we  also  see  that  this  demand  may  be  com- 
pletely satisfied  by  an  agency  purely  physical,  provided  it  be  much  more 
familiar  than  that  which  it  is  invoked  to  explain.  To  Thales  and  Anaxim- 
enes, it  appeared  inconceivable  that  the  antecedents  which  we  see  in  nature 
should  produce  the  consequents ; but  perfectly  natural  that  water,  or  air, 
should  produce  them.  The  writers  whom  I oppose  declare  this  inconceiv- 
able, but  can  conceive  that  mind,  or  volition,  is  per  se  an  efficient  cause: 
while  the  Cartesians  could  not  conceive  even  that,  but  peremptorily  de- 
clared that  no  mode  of  production  of  any  fact  whatever  was  conceivable, 
except  the  direct  agency  of  an  omnipotent  being;  thus  giving  additional 
proof  of  what  finds  new  confirmation  in  every  stage  of  the  history  of  sci- 
ence: that  both  what  persons  can,  and  what  they  can  not,  conceive,  is  very 
much  an  affair  of  accident,  and  depends  altogether  on  their  experience,  and 
their  habits  of  thought ; that  by  cultivating  the  requisite  associations  of 
ideas,  people  may  make  themselves  unable  to  conceive  any  given  thing; 
and  may  make  themselves  able  to  conceive  most  things,  however  inconceiv- 
able these  may  at  first  appear ; and  the  same  facts  in  each  person’s  mental 
history  which  determine  what  is  or  is  not  conceivable  to  him,  determine 
also  which  among  the  various  sequences  in  nature  will  appear  to  him  so 
natural  and  plausible,  as  to  need  no  other  proof  of  their  existence ; to  be 
evident  by  their  own  light,  independent  equally  of  experience  and  of  ex- 
planation. 

By  what  rule  is  any  one  to  decide  between  one  theory  of  this  descrip- 
tion and  another  ? The  theorists  do  not  direct  us  to  any  external  evidence ; 
they  appeal  each  to  his  own  subjective  feelings.  One  says,  the  succession 
C B appears  to  me  more  natural,  conceivable,  and  credible  per  se,  than  the 
succession  A B ; you  are  therefore  mistaken  in  thinking  that  B depends 
upon  A;  I am  certain,  though  I can  give  no  other  evidence  of  it,  that  C 
comes  in  between  A and  B,  and  is  the  real  and  only  cause  of  B.  The  oth- 
er answers,  the  successions  C B and  A B appear  to  me  equally  natural  and 
conceivable,  or  the  latter  more  so  than  the  former:  A is  quite  capable  of 
producing  B without  any  other  intervention.  A third  agrees  with  the  first 


262 


INDUCTION. 


in  being  unable  to  conceive  that  A can  produce  B,  but  finds  the  sequence 
D B still  more  natural  than  C B,  or  of  nearer  kin  to  the  subject-matter,  and 
prefers  his  D theory  to  the  C theory.  It  is  plain  that  there  is  no  universal 
law  operating  here,  except  the  law  that  each  person’s  conceptions  are  gov- 
erned and  limited  by  his  individual  experiences  and  habits  of  thought. 
We  are  warranted  in  saying  of  all  three,  what  each  of  them  already  be- 
lieves of  the  other  two,  namely,  that  they  exalt  into  an  original  law  of  the 
human  intellect  and  of  outward  nature  one  particular  sequence  of  phe- 
nomena, which  appears  to  them  more  natural  and  more  conceivable  than 
other  sequences,  only  because  it  is  more  familiar.  And  from  this  judg- 
ment I am  unable  to  except  the  theory,  that  Volition  is  an  Efficient  Cause. 

I am  unwilling  to  leave  the  subject  without  adverting  to  the  additional 
fallacy  contained  in  the  corollary  from  this  theory;  in  the  inference  that 
because  Volition  is  an  efficient  cause,  therefore  it  is  the  only  cause,  and  the 
direct  agent  in  producing  even  what  is  apparently  produced  by  something 
else.  Volitions  are  not  known  to  produce  any  thing  directly  except  nerv- 
ous ac'tion,  for  the  will  influences  even  the  muscles  only  through  the  nerves. 
Though  it  were  granted,  then,  that  every  phenomenon  has  an  efficient,  and 
not  merely  a phenomenal  cause,  and  that  volition,  in  the  case  of  the  pe- 
culiar phenomena  which  are  known  to  be  produced  by  it,  is  that  efficient 
cause ; are  we  therefore  to  say,  with  these  writers,  that  since  we  know  of 
no  other  efficient  cause,  and  ought  not  to  assume  one  without  evidence, 
there  is  no  other,  and  volition  is  the  direct  cause  of  all  phenomena?  A 
more  outrageous  stretch  of  inference  could  hardly  be  made.  Because 
among  the  infinite  variety  of  the  phenomena  of  nature  there  is  one,  namely, 
a particular  mode  of  action  of  certain  nerves,  which  has  for  its  cause,  and 
as  we  are  now  supposing  for  its  efficient  cause,  a state  of  our  mind ; and 
because  this  is  the  only  efficient  cause  of  which  we  are  conscious,  being  the 
only  one  of  which  in  the  nature  of  the  case  we  can  be  conscious,  since  it  is 
the  only  one  which  exists  within  ourselves;  does  this  justify  us  in  conclud- 
ing that  all  other  phenomena  must  have  the  same  kind  of  efficient  cause 
with  that  one  eminently  special,  narrow,  and  peculiarly  human  or  animal, 
phenomenon  ? The  nearest  parallel  to  this  specimen  of  generalization  is 
suggested  by  the  recently  revived  controversy  on  the  old  subject  of  Plural- 
ity of  Worlds,  in  which  the  contending  parties  have  been  so  conspicuously 
successful  in  overthrowing  one  another.  Here  also  we  have  experience 
only  of  a single  case,  that  of  the  world  in  which  we  live,  but  that  this  is  in- 
habited we  know  absolutely,  and  without  possibility  of  doubt.  Now  if  on 
this  evidence  any  one  were  to  infer  that  every  heavenly  body  without  ex- 
ception, sun,  planet,  satellite,  comet,  fixed  star  or  nebula,  is  inhabited,  and 
must  be  so  from  the  inherent  constitution  of  things,  his  inference  would 
exactly  resemble  that  of  the  writers  who  conclude  that  because  volition  is 
the  efficient  cause  of  our  own  bodily  motions,  it  must  be  the  efficient  cause 
of  every  thing  else  in  the  universe.  It  is  true  there  are  cases  in  which, 
with  acknowledged  propriety,  we  generalize  from  a single  instance  to  a 
multitude  of  instances.  But  they  must  be  instances  which  resemble  the 
one  known  instance,  and  not  such  as  have  no  circumstance  in  common  with 
it  except  that  of  being  instances.  I have,  for  example,  no  direct  evidence 
that  any  creature  is  alive  except  myself,  yet  I attribute,  with  full  assur- 
ance, life  and  sensation  to  other  human  beings  and  animals.  But  I do  not 
conclude  that  all  other  things  are  alive  merely  because  I am.  I ascribe  to 
certain  other  creatures  a life  like  my  own,  because  they  manifest  it  by  the 
same  sort  of  indications  by  which  mine  is  manifested.  I find  that  their 


LAW  OF  CAUSATION. 


263 


phenomena  and  mine  conform  to  the  same  laws,  and  it  is  for  this  reason 
that  I believe  both  to  arise  from  a similar  cause.  Accordingly  I do  not 
extend  the  conclusion  beyond  the  grounds  for  it.  Earth,  fire,  mountains, 
trees,  are  remarkable  agencies,  but  their  phenomena  do  not  conform  to  the 
same  laws  as  my  actions  do,  and  I therefore  do  not  believe  earth  or  fire, 
mountains  or  trees,  to  possess  animal  life.  But  the  supporters  of  the  Voli- 
tion Theory  ask  us  to  infer  that  volition  causes  every  thing,  for  no  reason 
except  that  it  causes  one  particular  thing ; although  that  one  phenomenon, 
far  from  being  a type  of  all  natural  phenomena,  is  eminently  peculiar;  its 
laws  bearing  scarcely  any  resemblance  to  those  of  any  other  phenomenon, 
whether  of  inorganic  or  of  organic  nature. 

NOTE  SUPPLEMENTARY  TO  THE  PRECEDING  CHAPTER. 

The  author  of  the  Second  Burnett  Prize  Essay  (Dr.  Tulloch),  -who  has  employed  a consid- 
erable number  of  pages  in  controverting  the  doctrines  of  the  preceding  chapter,  has  somewhat 
surprised  me  by  denying  a fact,  which  I imagined  too  well  known  to  require  proof — that  there 
have  been  philosophers  who  found  in  physical  explanations  of  phenomena  the  same  complete 
mental  satisfaction  which  we  are  told  is  only  given  by  volitional  explanation,  and  others  who 
denied  the  Volitional  Theory  on  the  same  ground  of  inconceivability  on  which  it  is  defended. 
The  assertion  of  the  Essayist  is  countersigned  still  more  positively  by  an  able  reviewer  of  the 
Essay:*  “Two  illustrations,”  says  the  reviewer,  “are  advanced  by  Mr.  Mill:  the  case  of 
Thales  and  Anaximenes,  stated  by  him  to  have  maintained,  the  one  Moisture  and  the  other 
Air  to  be  the  origin  of  all  things ; and  that  of  Descartes  and  Leibnitz,  whom  he  asserts  to 
have  found  the  action  of  Mind  upon  Matter  the  grand  inconceivability.  In  counter-statement 
as  to  the  first  of  these  cases  the  author  shows — what  we  believe  now  hardly  admits  of  doubt 
— that  the  Greek  philosophers  distinctly  recognized  as  beyond  and  above  their  primal  material 
source,  the  vov g,  or  Divine  Intelligence,  as  the  efficient  and  originating  Source  of  all ; and  as 
to  the  second,  by  proof  that  it  was  the  mode,  not  the  fact,  of  that  action  on  matter,  which  was 
represented  as  inconceivable.” 

A greater  quantity  of  historical  error  has  seldom  been  comprised  in  a single  sentence. 
With  regard  to  Thales,  the  assertion  that  he  considered  water  as  a mere  material  in  the  hands 
of  voi/g  rests  on  a passage  of  Cicero  de  Natura  Deorum ; and  whoever  will  refer  to  any  of 
the  accurate  historians  of  philosophy,  will  find  that  they  treat  this  as  a mere  fancy  of  Cicero, 
resting  on  no  authority,  opposed  to  all  the  evidence;  and  make  surmises  as  to  the  manner  in 
which  Cicero  may  have  been  led  into  the  error.  (See  Ritter,  vol.  i.,  p.  211,  2d  ed. ; Brandis, 
vol.  i.,  pp.  118-9,  1st  ed.  ; Preller,  Historia  Philosophice  Grceco-Romance,  p.  10.  “Schiefe 
Ansicht,  durchaus  zu  verwerfen;”  “ augenscheinlich  folgernd  statt  zu  berichten;”  “ quibus 
vera  sententia  Thaletis  plane  detorquetur,”  are  the  expressions  of  these  writers.)  As  for  An- 
aximenes, he  even  according  to  Cicero,  maintained,  not  that  air  was  the  material  out  of  which 
God  made  the  world,  but  that  the  air  was  a god  : “ Anaximenes  aera  deum  statuit or,  ac- 
cording to  St.  Augustine,  that  it  was  the  material  out  of  which  the  gods  were  made:  “ non 
tamen  ab  ipsis  [Diis]  aerem  factum,  sed  ipsos  ex  aere  ortos  credidit.”  Those  who  are  not  fa- 
miliar with  the  metaphysical  terminology  of  antiquity,  must  not  be  misled  by  finding  it  stated 
that  Anaximenes  attributed  i pvxv  (translated  soul , or  life ) to  his  universal  element,  the  air. 
The  Greek  philosophers  acknowledged  several  kinds  of  i/nyty),  the  nutritive,  the  sensitive,  and 
the  intellective.!  Even  the  moderns,  with  admitted  correctness,  attribute  life  to  plants.  As 
far  as  we  can  make  out  the  meaning  of  Anaximenes,  he  made  choice  of  Air  as  the  universal 
agent,  on  the  ground  that  it  is  perpetually  in  motion,  without  any  apparent  cause  external  to 
itself : so  that  he  conceived  it  as  exercising  spontaneous  force,  and  as  the  principle  of  life  and 
activity  in  all  things,  men  and  gods  inclusive.  If  this  be  not  representing  it  as  the  Efficient 
Cause  the  dispute  altogether  has  no  meaning. 

If  either  Anaximenes,  or  Thales,  or  any  of  their  contemporaries,  had  held  the  doctrine  that 
vovg  was  the  Efficient  Cause,  that  doctrine  could  not  have  been  reputed,  as  it  was  throughout 
antiquity,  to  have  originated  with  Anaxagoras.  The  testimony  of  Aristotle,  in  the  first  book 
of  his  Metaphysics,  is  perfectly  decisive  with  respect  to  these  early  speculations.  After  enu- 
merating four  kinds  of  causes,  or  rather  four  different  meanings  of  the  word  Cause,  viz.,  the 
Essence  of  a thing,  the  Matter  of  it,  the  Origin  of  Motion  (Efficient  Cause),  and  the  End  or 


* Westminster  Review  for  October,  1855. 

f See  the  whole  doctrine  in  Aristotle  de  Anima,  where  the  dpexTiK?)  ifrvxv  is  treated  as 
exactly  equivalent  to  dpe-XTUir]  dvva/ug. 


264 


INDUCTION. 


Final  Cause,  he  proceeds  to  say,  that  most  of  the  early  philosophers  recognized  only  the  sec- 
ond kind  of  Cause,  the  Matter  of  a thing,  rdf  kv  iiAyg  e'tdci  pova g ur/Or/oav  apxug  slvai  ttuvtuv. 
As  his  first  example  lie  specifies  Thales,  whom  he  describes  as  taking  the  lead  in  this  view  of 
the  subject,  6 ryg  ruiavn/g  upxr/ybg  (pi’Aoaoip'iag,  and  goes  on  to  Hippon,  Anaximenes,  Dioge- 
nes (of  Apollonia),  Hippasus  of  Metapontum,  Heraclitus,  and  Empedocles.  Anaxagoras, 
however  (lie  proceeds  to  say),  taught  a different  doctrine,  as  we  know,  and  it  is  alleged  that 
Hermotimus  of  Clazomento  taught  it  before  him.  Anaxagoras  represented,  that  even  if  these 
various  theories  of  the  universal  material  were  true,  there  would  be  need  of  some  other  cause 
to  account  for  the  transformations  of  the  materials,  since  the  material  can  not  originate  its 
own  changes:  ou  ydp  6ij  to  ye  VTcoKelpevov  avru  ttolci  peTafitlAAeiv  kavro • Akyu  (S’  oiov  ovre 
to  $v?i ov  oire  6 ynA/cof  aiTtog  tov  peTa/jdAAeiv  enuTepov  ovtuv,  ovdi  tx oiel  to  piv  tjvAov  kMvj) o 
o 6k  xaAicbg  avdpiuvTa,  aAX  krepov  tl  rr/g  peTafloAyg  uitiov,  viz.,  the  other  kind  of  cause,  bdev 
V <1  PX*1  Kivrjaeug — an  Efficient.  Cause.  Aristotle  expresses  great  approbation  of  this  doc- 
trine (which  he  says  made  its  author  appear  the  only  sober  man  among  persons  raving,  olov 
i >jj(puv  k<j>dvr/  nap’  eii<f/  Akyovrag  Tovg  it purepov)  ; but  while  describing  the  influence  which  it  ex- 
ercised over  subsequent  speculation,  he  remarks  that  the  philosophers  against  whom  this,  as  he 
thinks,  insuperable  difficulty  was  urged,  had  not  felt  it  to  be  any  difficulty  : owYev  kdvoxepbvav 
tv  kavTolg.  It  is  surely  unnecessary  to  say  more  in  proof  of  the  matter  of  fact  which  Dr.  Tul- 
locli  and  his  reviewer  disbelieve. 

Having  pointed  out  what  he  thinks  the  error  of  these  early  speculators  in  not  recognizing 
the  need  of  an  efficient  cause,  Aristotle  goes  on  to  mention  two  other  efficient  causes  to  which 
they  might  have  had  recourse,  instead  of  intelligence:  tvxv,  chance,  and  to  avropuTov,  spon- 
taneity. He  indeed  puts  these  aside  as  not  sufficiently  worthy  causes  for  the  order  in  the  uni- 
verse, ov6’  av  to  avTopuTip  kui  r;/  rvxy  roaovTov  eKirpeipat  Txpuypa  naAug  elx ev ; but  he  does 
not  reject  them  as  incapable  of  producing  any  effect,  but  only  as  incapable  of  producing  that 
effect.  He  himself  recognizes  tvxv  and  to  avTopuTov  as  co-ordinate  agents  with  Mind  in  pro- 
ducing the  phenomena  of  the  universe;  the  department  allotted  to  them  being  composed  of 
all  the  classes  of  phenomena  which  are  not  supposed  to  follow  any  uniform  law.  By  thus  in- 
cluding Chance  among  efficient  causes,  Aristotle  fell  into  an  error  which  philosophy  has  now 
outgrown,  but  which  is  by  no  means  so  alien  to  the  spirit  even  of  modern  speculation  as  it 
may  at  first  sight  appear.  Up  to  quite  a recent  period  philosophers  went  on  ascribing,  and 
many  of  them  have  not  yet  ceased  to  ascribe,  a real  existence  to  the  results  of  abstraction. 
Chance  could  make  out  as  good  a title  to  that  dignity  as  many  other  of  the  mind’s  abstract 
creations  : it  had  had  a name  given  to  it,  and  why  should  it  not  be  a reality?  As  for  to  av- 
TopuTov,  it  is  recognized  even  yet  as  one  of  the  modes  of  origination  of  phenomena  by  all 
those  thinkers  who  maintain  what  is  called  the  Freedom  of  the  Will.  The  same  self-deter- 
mining power  which  that  doctrine  attributes  to  volitions,  was  supposed  by  the  ancients  to  be 
possessed  also  by  some  other  natural  phenomena:  a circumstance  which  throws  considerable 
light  on  more  than  one  of  the  supposed  invincible  necessities  of  belief.  I have  introduced  it 
here,  because  this  belief  of  Aristotle,  or  rather  of  the  Greek  philosophers  generally,  is  as  fatal 
as  the  doctrines  of  Thales  and  the  Ionic  school  to  the  theory  that  the  human  mind  is  com- 
pelled by  its  constitution  to  conceive  volition  as  the  origin  of  all  force,  and  the  efficient  cause 
of  all  phenomena.* 


* It  deserves  notice  that  the  parts  of  nature  which  Aristotle  regards  as  representing  evi- 
dence of  design,  are  the  Uniformities:  the  phenomena  in  so  far  as  reducible  to  law.  Tvxy 
and  rb  avTopuTov  satisfy  him  as  explanations  of  the  variable  element  in  phenomena,  but  their 
occurring  according  to  a fixed  rule  can  only,  to  his  conceptions,  be  accounted  for  by  an  In- 
telligent Will.  The  common,  or  what  may  be  called  the  instinctive,  religious  interpretation 
of  nature,  is  the  reverse  of  this.  The  events  in  which  men  spontaneously  see  the  hand  of  a 
supernatural  being,  are  those  which  can  not,  as  they  think,  be  reduced  to  a physical  law. 
What  they  can  distinctly  connect  with  physical  causes,  and  especially  what  they  can  predict, 
though  of  course  ascribed  to  an  Author  of  Nature,  if  they  already  recognize  such  an  author, 
might  be  conceived,  they  think,  to  arise  from  a blind  fatality,  and  in  any  case  do  not  appear 
to  them  to  bear  so  obviously  the  mark  of  a divine  will.  And  this  distinction  has  been  counte- 
nanced by  eminent  writers  on  Natural  Theology,  in  particular  by  Dr.  Chalmers,  who  thinks 
that  though  design  is  present  everywhere,  the  irresistible  evidence  of  it  is  to  be  found  not  in 
the  laws  of  nature  but  in  the  collocations,  i.  e .,  in  the  part  of  nature  in  which  it  is  impossible 
to  trace  any  law.  A few  properties  of  dead  matter  might,  he  thinks,  conceivably  account  for 
the  regular  and  invariable  succession  of  effects  and  causes  ; but  that  the  different  kinds  of 
matter  have  been  so  placed  as  to  promote  beneficent  ends,  is  what  he  regards  at  the  proof  of 
a Divine  Providence.  Mr.  Baden  Powell,  in  his  Essay  entitled  “Philosophy  of  Creation,” 
has  returned  to  the  point  of  view  of  Aristotle  and  the  ancients,  and  vigorously  re-asserts  the 
doctrine  that  the  indication  of  design  in  the  universe  is  not  special  adaptations,  but  Uniformi- 
ty and  Law,  these  being  the  evidences  of  mind,  and  not  what  appears  to  us  to  be  a provision 


LAW  OF  CAUSATION. 


265 


With  regard  to  the  modern  philosophers  (Leibnitz  and  the  Cartesians)  whom  I had  cited  as 
having  maintained  that  the  action  of  mind  upon  matter,  so  far  from  being  the  only  conceiva- 
ble origin  of  material  phenomena,  is  itself  inconceivable;  the  attempt  to  rebut  this  argument 
by  asserting  that  the  mode,  not  the  fact,  of  the  action  of  mind  on  matter  was  represented  as 
inconceivable,  is  an  abuse  of  the  privilege  of  writing  confidently  about  authors  without  read- 
ing them  ; for  any  knowledge  whatever  of  Leibnitz  would  have  taught  those  who  thus  speak 
of  him,  that  the  inconceivability  of  the  mode,  and  the  impossibility  of  the  thing,  were  in  his 
mind  convertible  expressions.  What  was  his  famous  Principle  of  the  Sufficient  Reason,  the 
very  corner-stone  of  his  Philosophy,  from  which  the  Pre-established  Harmony,  the  doctrine 
of  Monads,  and  all  the  opinions  most  characteristic  of  Leibnitz,  were  corollaries  ? It  was, 
that  nothing  exists,  the  existence  of  which  is  not  capable  of  being  proved  and  explained  a 
priori;  the  proof  and  explanation  in  the  case  of  contingent  facts  being  derived  from  the  na- 
ture of  their  causes ; which  could  not  be  the  causes  unless  there  was  something  in  their  nature 
showing  them  to  be  capable  of  producing  those  particular  effects.  And  this  “something” 
which  accounts  for  the  production  of  physical  effects,  he  was  able  to  find  in  many  physical 
causes,  but  could  not  find  it  in  any  finite  minds,  which  therefore  he  unhesitatingly  asserted  to 
be  incapable  of  producing  any  physical  effects  whatever.  “ On  ne  saurait  concevoir,”  he  says, 
“ une  action  reciproque  de  la  matiere  et  de  l'intelligence  l'une  sur  l’autre,”  and  there  is  there- 
fore (he  contends)  no  choice  but  between  the  Occasional  Causes  of  the  Cartesians  and  his 
own  Pre-established  Harmony,  according  to  which  there  is  no  more  connection  between  our 
volitions  and  our  muscular  actions  than  there  is  between  two  clocks  which  are  wound  up 
to  strike  at  the  same  instant.  But  he  felt  no  similar  difficulty  as  to  physical  causes;  and 
throughout  his  speculations,  as  in  the  passage  I have  already  cited  respecting  gravitation,  he 
distinctly  refuses  to  consider  as  part  of  the  order  of  nature  any  fact  which  is  not  explicable 
from  the  nature  of  its  physical  cause. 

With  regard  to  the  Cartesians  (not  Descartes ; I did  not  make  that  mistake,  though  the  re- 
viewer of  Dr.  Tulloch's  Essay  attributes  it  to  me)  I take  a passage  almost  at  random  from 
Malebranche,  who  is  the  best  known  of  the  Cartesians,  and,  though  not  the  inventor  of  the  sys- 
tem of  Occasional  Causes,  is  its  principal  expositor.  In  Part  II.,  chap.  iii. , of  his  Sixth  Book, 
having  first  said  that  matter  can  not  have  the  power  of  moving  itself,  he  proceeds  to  argue 
that  neither  can  mind  have  the  power  of  moving  it,  “ Quand  on  examine  l idee  que  1'on  a de 
tous  les  esprits  finis,  on  ne  voit  point  de  liaison  necessaire  entre  leur  volonte  et  le  mouvement 
de  quelque  corps  que  ce  soit,  on  voit  an  contraire  qu’il  n’y  en  a point,  et  qu’il  n’y  en  peut  avoir  ” 
(there  is  nothing  in  the  idea  of  finite  mind  which  can  account  for  its  causing  the  motion  of  a 
body)  ; “ on  doit  aussi  conelure,  si  on  vent  raisonner  selon  ses  lumieres,  qu’il  n’y  a aucun  esprit 
cree  qui  puisse  remuer  quelque  corps  que  ce  soit  comme  cause  veritable  on  principale,  de 
meme  que  Ton  a dit  qu’aucun  corps  ne  se  pouvait  remuer  soi-meme  thus  the  idea  of  Mind 
is  according  to  him  as  incompatible  as  the  idea  of  Matter  with  the  exercise  of  active  force. 
But  when,  he  continues,  we  consider  not  a created  but  a Divine  Mind,  the  case  is  altered; 
for  the  idea  of  a Divine  Mind  includes  omnipotence ; and  the  idea  of  omnipotence  does  con- 
tain the  idea  of  being  able  to  move  bodies.  Thus  it  is  the  nature  of  omnipotence  which  ren- 
ders the  motion  of  bodies  even  by  the  Divine  Mind  credible  or  conceivable,  while,  so  far  as 
depended  on  the  mere  nature  of  mind,  it  would  have  been  inconceivable  and  incredible.  If 
Malebranche  had  not  believed  in  an  omnipotent  Being,  he  would  have  held  all  action  of  mind 
on  body  to  be  a demonstrated  impossibility.* * 

A doctrine  more  precisely  the  reverse  of  the  Volitional  theory  of  causation  can  not  well  be 
imagined.  The  Volitional  theory  is,  that  we  know  by  intuition  or  by  direct  experience  the 
action  of  our  own  mental  volitions  on  matter ; that  we  may  hence  infer  all  other  action  upon 
matter  to  be  that  of  volition,  and  might  thus  know,  without  any  other  evidence,  that  matter 
is  under  the  government  of  a Divine  Mind.  Leibnitz  and  the  Cartesians,  on  the  contrary, 
maintain  that  our  volitions  do  not  and  can  not  act  upon  matter,  and  that  it  is  only  the  ex- 
istence of  an  all-governing  Being,  and  that  Being  omnipotent,  which  can  account  for  the  se- 
quence between  our  volitions  and  our  bodily  actions.  When  we  consider  that  each  of  these  two 
theories,  which,  as  theories  of  causation,  stand  at  the  opposite  extremes  of  possible  divergence 


for  our  uses.  While  I decline  to  express  any  opinion  here  on  this  vexata  queestio,  I ought 
not  to  mention  Mr.  Powell’s  volume  without  the  acknowledgment  due  to  the  philosophic 
spirit  which  pervades  generally  the  three  Essays  composing  it,  forming  in  the  case  of  one  of 
them  (the  “Unity  of  Worlds”)  an  honorable  contrast  with  the  other  dissertations,  so  far  as 
they  have  come  under  my  notice,  which  have  appeared  on  either  side  of  that  controversy. 

* In  the  words  of  Fontenelle,  another  celebrated  Cartesian,  “les  philosophes  aussi  bien  que 
le  people  avaient  cm  que  lame  et  le  corps  agissaient  re'ellement  et  physiquement  Fun  sur 
l’autre.  Descartes  vinf,  qui  prouva  que  leur  nature  ne  permettait  point  cette  sorte  de  com- 
munication veritable,  et  qu’ils  n’en  pouvaient  avoir  qu’une  apparente,  dont  Dieu  etait  le  Medi- 
ateur.” — CCEuvres  de  Fontenelle,  ed.  17(37,  tom.  v.,  p.  531.) 


266 


INDUCTION. 


from  one  another,  invokes  not  only  as  its  evidence,  but  as  its  sole  evidence,  the  absolute  in- 
conceivability of  any  theory  but  itself,  we  are  enabled  to  measure  the  worth  of  this  kind  of 
evidence:  and  when  we  find  the  Volitional  theory  entirely  built  upon  the  assertion  that  bv 
our  mental  constitution  we  are  compelled  to  recognize  our  volitions  as  efficient  causes,  and 
then  find  other  thinkers  maintaining  that  we  know  that  they  are  not  and  can  not  be  such 
causes,  and  can  not  conceive  them  to  be  so,  I think  we  have  a right  to  say  that  this  supposed 
law  of  our  mental  constitution  does  not  exist. 

Dr.  Tulloch  (pp.  45-47)  thinks  it  a sufficient  answer  to  this,  that  Leibnitz  and  the  Cartesians 
were  Theists,  and  believed  the  will  of  God  to  be  an  efficient  cause.  Doubtless  they  did,  and 
the  Cartesians  even  believed  (though  Leibnitz  did  not)  that  it  is  the  only  such  cause.  Dr. 
Tulloch  mistakes  the  nature  of  the  question.  I was  not  writing  on  Theism,  as  Dr.  Tulloch 
is,  but  against  a particular  theory  of  causation,  which,  if  it  be  unfounded,  can  give  no  effect- 
ive support  to  Theism  or  to  any  thing  else.  I found  it  asserted  that  volition  is  the  only  ef- 
ficient cause,  on  the  ground  that  no  other  efficient  cause  is  conceivable.  To  this  assertion  I 
oppose  the  instances  of  Leibnitz  and  of  the  Cartesians,  who  affirmed  with  equal  positiveness 
that  volition  as  an  efficient  cause  is  itself  not  conceivable,  and  that  omnipotence,  which  ren- 
ders all  things  conceivable,  can  alone  take  away  the  impossibility.  This  I thought,  and  think, 
a conclusive  answer  to  the  argument  on  which  this  theory  of  causation  avowedly  depends. 
But  I certainly  did  not  imagine  that  Theism  was  bound  up  with  that  theory;  nor  expected 
to  be  charged  with  denying  Leibnitz  and  the  Cartesians  to  be  Theists  because  I denied  that 
they  held  the  theory. 


CHAPTER  YI. 

OX  THE  COMPOSITION  OF  CAUSES. 

§ 1.  To  complete  the  general  notion  of  causation  on  which  the  rules  of 
experimental  inquiry  into  the  laws  of  nature  must  be  founded,  one  dis- 
tinction still  remains  to  be  pointed  out:  a distinction  so  radical,  and  of  so 
much  importance,  as  to  require  a chapter  to  itself. 

The  preceding  discussions  have  rendered  us  familiar  with  the  case  in 
which  several  agents,  or  causes,  concur  as  conditions  to  the  production  of 
an  effect;  a case,  in  truth,  almost  universal,  there  being  very  few  effects  to 
the  production  of  which  no  more  than  one  agent  contributes.  Suppose, 
then,  that  two  different  agents,  operating  jointly,  are  followed,  under  a 
certain  set  of  collateral  conditions,  by  a given  effect.  If  either  of  these 
agents,  instead  of  being  joined  with  the  other,  had  operated  alone,  under 
the  same  set  of  conditions  in  all  other  respects,  some  effect  would  probably 
have  followed,  which  would  have  been  different  from  the  joint  effect  of 
the  two,  and  more  or  less  dissimilar  to  it.  How,  if  we  happen  to  know 
what  would  be  the  effect  of  each  cause  when  acting  separately  from  the 
other,  we  are  often  able  to  arrive  deductively,  or  a priori,  at  a correct  pre- 
diction of  what  will  arise  from  their  conjunct  agency.  To  render  this  pos- 
sible, it  is  only  necessary  that  the  same  law  which  expresses  the  effect  of 
each  cause  acting  by  itself,  shall  also  correctly  express  the  part  due  to  that 
cause  of  the  effect  which  follows  from  the  two  together.  This  condition  is 
realized  in  the  extensive  and  important  class  of  phenomena  commonly  call- 
ed mechanical,  namely  the  phenomena  of  the  communication  of  motion  (or 
of  pressure,  which  is  tendency  to  motion)  from  one  body  to  another.  In 
this  important  class  of  cases  of  causation,  one  cause  never,  properly  speak- 
ing, defeats  or  frustrates  another;  both  have  their  full  effect.  If  a body  is 
propelled  in  two  directions  by  two  forces,  one  tending  to  drive  it  to  the 
north  and  the  other  to  the  east,  it  is  caused  to  move  in  a given  time  exact- 
ly as  far  in  both  directions  as  the  two  forces  would  separately  have  carried 
it ; and  is  left  precisely  where  it  would  have  arrived  if  it  had  been  acted 


COMPOSITION  OF  CAUSES. 


267 


upon  first  by  one  of  the  two  forces,  and  afterward  by  the  other.  This  law 
of  nature  is  called,  in  dynamics,  the  principle  of  the  Composition  of  Forces  ; 
and  in  imitation  of  that  well-chosen  expression,  I shall  give  the  name  of  the 
Composition  of  Causes  to  the  principle  which  is  exemplified  in  all  cases  in 
which  the  joint  effect  of  several  causes  is  identical  with  the  sum  of  their 
separate  effects. 

This  principle,  however,  by  no  means  prevails  in  all  departments  of  the 
field  of  nature.  The  chemical  combination  of  two  substances  produces,  as 
is  well  known,  a third  substance,  with  properties  different  from  those  of 
either  of  the  two  substances  separately,  or  of  both  of  them  taken  together. 
Not  a trace  of  the  properties  of  hydrogen  or  of  oxygen  is  observable  in 
those  of  their  compound,  water.  The  taste  of  sugar  of  lead  is  not  the 
sum  of  the  tastes  of  its  component  elements,  acetic  acid  and  lead  or  its 
oxide;  nor  is  the  color  of  blue  vitriol  a mixture  of  the  colors  of  sulphuric 
acid  and  copper.  This  explains  why  mechanics  is  a deductive  or  demon- 
strative science,  and  chemistry  not.  In  the  one,  we  can  compute  the  ef- 
fects of  combinations  of  causes,  whether  real  or  hypothetical,  from  the 
laws  which  we  know  to  govern  those  causes  when  acting  separately,  be- 
cause they  continue  to  observe  the  same  laws  when  in  combination  which 
they  observe  when  separate : whatever  would  have  happened  in  conse- 
quence of  each  cause  taken  by  itself,  happens  when  they  are  together, 
and  we  have  only  to  cast  up  the  results.  Not  so  in  the  phenomena  which 
are  the  peculiar  subject  of  the  science  of  chemistry.  There  most  of  the 
uniformities  to  which  the  causes  conform  when  separate,  cease  altogether 
when  they  are  conjoined;  and  we  are  not,  at  least  in  the  present  state  of 
our  knowledge,  able  to  foresee  what  result  will  follow  from  any  new  com- 
bination until  we  have  tried  the  specific  experiment. 

If  this  be  true  of  chemical  combinations,  it  is  still  more  true  of  those  far 
more  complex  combinations  of  elements  which  constitute  organized  bodies ; 
and  in  which  those  extraordinary  new  uniformities  arise  which  are  called 
the  laws  of  life.  All  organized  bodies  are  composed  of  parts  similar  to 
those  composing  inorganic  nature,  and  which  have  even  themselves  existed 
in  an  inorganic  state;  but  the  phenomena  of  life,  which  result  from  the 
juxtaposition  of  those  parts  in  a certain  manner,  bear  no  analogy  to  any 
of  the  effects  which  would  be  produced  by  the  action  of  the  component 
substances  considered  as  mere  physical  agents.  To  whatever  degree  we 
might  imagine  our  knowledge  of  the  properties  of  the  several  ingredients 
of  a living  body  to  be  extended  and  perfected,  it  is  certain  that  no  mere 
summing  up  of  the  separate  actions  of  those  elements  will  ever  amount  to 
the  action  of  the  living  body  itself.  The  tongue,  for  instance,  is,  like  all 
other  parts  of  the  animal  frame,  composed  of  gelatine,  fibrine,  and  other 
products  of  the  chemistry  of  digestion ; but  from  no  knowledge  of  the 
properties  of  those  substances  could  we  ever  predict  that  it  could  taste,  un- 
less gelatine  or  fibrine  could  themselves  taste;  for  no  elementary  fact  can 
be  in  the  conclusion  which  was  not  in  the  premises. 

There  are  thus  two  different  modes  of  the  conjunct  action  of  causes; 
from  which  arise  two  modes  of  conflict,  or  mutual  interference,  between 
laws  of  nature.  Suppose,  at  a given  point  of  time  and  space,  two  or  more 
causes,  which,  if  they  acted  separately,  would  produce  effects  contrary,  or 
at  least  conflicting  with  each  other ; one  of  them  tending  to  undo,  wholly 
or  partially,  what  the  other  tends  to  do.  Thus  the  expansive  force  of  the 
gases  generated  by  the  ignition  of  gunpowder  tends  to  project  a bullet 
toward  the  sky,  while  its  gravity  tends  to  make  it  fall  to  the  ground.  A 


268 


INDUCTION. 


stream  running  into  a reservoir  at  one  end  tends  to  fill  it  higher  and  high- 
er, while  a drain  at  the  other  extremity  tends  to  empty  it.  Now,  in  such 
cases  as  these,  even  if  the  two  causes  which  are  in  joint  action  exactly  an- 
nul one  another,  still  the  laws  of  both  are  fulfilled;  the  effect  is  the  same 
as  if  the  drain  had  been  open  for  half  an  hour  first,*  and  the  stream  had 
flowed  in  for  as  long  afterward.  Each  agent  produces  the  same  amount  of 
effect  as  if  it  had  acted  separately,  though  the  contrary  effect  which  was 
taking  place  during  the  same  time  obliterated  it  as  fast  as  it  was  produced. 
Here,  then,  are  two  causes,  producing  by  their  joint  operations  an  effect 
which  at  first  seems  quite  dissimilar  to  those  which  they  produce  separate- 
ly, but  which  on  examination  proves  to  be  really  the  sum  of  those  separate 
effects.  It  will  be  noticed  that  we  here  enlarge  the  idea  of  the  sum  of  two 
effects,  so  as  to  include  what  is  commonly  called  their  difference,  but  which 
is  in  reality  the  result  of  the  addition  of  opposites;  a conception  to  which 
mankind  are  indebted  for  that  admirable  extension  of  the  algebraical  cal- 
culus, which  has  so  vastly  increased  its  powers  as  an  instrument  of  discov- 
ery, by  introducing  into  its  reasonings  (with  the  sign  of  subtraction  pre- 
fixed, and  under  the  name  of  Negative  Quantities)  every  description  what- 
ever of  positive  phenomena,  provided  they  are  of  such  a quality  in  reference 
to  those  previously  introduced,  that  to  add  the  one  is  equivalent  to  sub- 
tracting an  equal  quantity  of  the  other. 

There  is,  then,  one  mode  of  the  mutual  interference  of  laws  of  nature,  in 
which,  even  when  the  concurrent  causes  annihilate  each  other’s  effects,  each 
exerts  its  full  efficacy  according  to  its  own  law — its  law  as  a separate  agent. 
But  in  the  other  description  of  cases,  the  agencies  which  are  brought  to- 
gether cease  entirely,  and  a totally  different  set  of  phenomena  arise : as  in 
the  experiment  of  two  liquids  which,  when  mixed  in  certain  proportions, 
instantly  become,  not  a larger  amount  of  liquid,  but  a solid  mass. 

§ 2.  This  difference  between  the  case  in  which  the  joint  effect  of  causes 
is  the  sum  of  their  separate  effects,  and  the  case  in  which  it  is  heteroge- 
neous to  them — between  laws  which  work  together  without  alteration,  and 
laws  which,  when  called  upon  to  work  together,  cease  and  give  place  to  oth- 
ers— is  one  of  the  fundamental  distinctions  in  nature.  The  former  case, 
that  of  the  Composition  of  Causes,  is  the  general  one ; the  other  is  always 
special  and  exceptional.  There  are  no  objects  which  do  not,  as  to  some  of 
their  phenomena,  obey  the  principle  of  the  Composition  of  Causes;  none 
that  have  not  some  laws  which  are  rigidly  fulfilled  in  every  combination 
into  which  the  objects  euter.  The  weight  of  a body,  for  instance,  is  a 
property  which  it  retains  in  all  the  combinations  in  which  it  is  placed. 
The  weight  of  a chemical  compound,  or  of  an  organized  body,  is  equal  to 
the  sum  of  the  weights  of  the  elements  which  compose  it.  The  weight 
either  of  the  elements  or  of  the  compound  will  vary,  if  they  be  carried  far- 
ther from  their  centre  of  attraction,  or  brought  nearer  to  it;  but  whatever 
effects  the  one  effects  the  other.  They  always  remain  precisely  equal.  So, 
again,  the  component  parts  of  a vegetable  or  animal  substance  do  not  lose 
their  mechanical  and  chemical  properties  as  separate  agents,  when,  by  a 
peculiar  mode  of  juxtaposition,  they,  as  an  aggregate  whole,  acquire  physi- 
ological or  vital  properties  in  addition.  Those  bodies  continue,  as  before, 

* I omit,  for  simplicity,  to  take  into  account  the  effect,  in  this  latter  case,  of  the  diminution 
of  pressure,  in  diminishing  the  flow  of  water  through  the  drain ; which  evidently  in  no  way 
affects  the  truth  or  applicability  of  the  principle,  since  when  the  two  causes  act  simultaneously 
the  conditions  of  that  diminution  of  pressure  do  not  arise. 


COMPOSITION  OF  CAUSES. 


269 


to  obey  mechanical  and  chemical  laws,  in  so  fai-  as  the  operation  of  those 
laws  is  not  counteracted  by  the  new  laws  which  govern  them  as  organized 
beings ; when,  in  short,  a concurrence  of  causes  takes  place  which  calls  into 
action  new  laws  bearing  no  analogy  to  any  that  we  can  trace  in  the  sepa- 
rate operation  of  the  causes,  the  new  laws,  while  they  supersede  one  portion 
of  the  previous  laws,  may  co-exist  with  another  portion,  and  may  even  com- 
pound the  effect  of  those  previous  laws  with  their  own. 

Again,  laws  which  were  themselves  generated  in  the  second  mode,  may 
generate  others  in  the  first.  Though  there  are  laws  which,  like  those  of 
chemistry  and  physiology,  owe  their  existence  to  a breach  of  the  principle 
of  Composition  of  Causes,  it  does  not  follow  that  these  peculiar,  or,  as  they 
might  be  termed,  heteropathic  laws,  are  not  capable  of  composition  with 
one  another.  The  causes  which  by  one  combination  have  had  their  laws 
altered,  may  carry  their  new  laws  with  them  unaltered  into  their  ulterior 
combinations.  And  hence  there  is  no  reason  to  despair  of  ultimately  raising 
chemistry  and  physiology  to  the  condition  of  deductive  sciences  ; for  though 
it  is  impossible  to  deduce  all  chemical  and  physiological  truths  from  the 
laws  or  properties  of  simple  substances  or  elementary  agents,  they  may 
possibly  be  deducible  from  laws  which  commence  when  these  elementary 
agents  are  brought  together  into  some  moderate  number  of  not  very  com- 
plex combinations.  The  Laws  of  Life  will  never  be  deducible  from  the 
mere  laws  of  the  ingredients,  but  the  prodigiously  complex  Facts  of  Life 
may  all  be  deducible  from  comparatively  simple  laws  of  life ; which  laws 
(depending  indeed  on  combinations,  but  on  comparatively  simple  combi- 
nations, of  antecedents)  may,  in  more  complex  circumstances,  be  strictly 
compounded  with  one  another,  and  with  the  physical  and  chemical  laws  of 
the  ingredients.  The  details  of  the  vital  phenomena,  even  now,  afford  innu- 
merable exemplifications  of  the  Composition  of  Causes  ; and  in  proportion 
as  these  phenomena  are  more  accurately  studied,  there  appears  more  reason 
to  believe  that  the  same  laws  which  operate  in  the  simpler  combinations 
of  circumstances  do,  in  fact,  continue  to  be  observed  in  the  more  complex. 
This  will  be  found  equally  true  in  the  phenomena  of  mind;  and  even  in 
social  and  political  phenomena,  the  results  of  the  laws  of  mind.  It  is  in 
the  case  of  chemical  phenomena  that  the  least  progress  has  yet  been  made 
in  bringing  the  special  laws  under  general  ones  from  which  they  may  be 
deduced  ; but  there  are  even  in  chemistry  many  circumstances  to  encourage 
the  hope  that  such  general  laws  will  hereafter  be  discovered.  The  differ- 
ent actions  of  a chemical  compound  will  never,  undoubtedly,  be  found  to 
be  the  sums  of  the  actions  of  its  separate  elements ; but  there  may  exist, 
between  the  properties  of  the  compound  and  those  of  its  elements,  some 
constant  relation,  which,  if  discoverable  by  a sufficient  induction,  would  en- 
able us  to  foresee  the  sort  of  compound  which  will  result  from  a new  com- 
bination before  we  have  actually  tried  it,  and  to  judge  of  what  sort  of  el- 
ements some  new  substance  is  compounded  before  we  have  analyzed  it. 
The  law  of  definite  proportions,  first  discovered  in  its  full  generality  by 
Dalton,  is  a complete  solution  of  this  problem  in  one,  though  but  a second- 
ary aspect,  that  of  quantity ; and  in  respect  to  quality,  we  have  already 
some  partial  generalizations,  sufficient  to  indicate  the  possibility  of  ulti- 
mately proceeding  farther.  We  can  predicate  some  common  properties 
of  the  kind  of  compounds  which  result  from  the  combination,  in  each  of  the 
small  number  of  possible  proportions,  of  any  acid  whatever  with  any  base. 
We  hqtve  also  the  curious  law,  discovered  by  Berthollet,  that  two  soluble 
salts  mutually  decompose  one  another  whenever  the  new  combinations 


270 


INDUCTION. 


which  result  produce  au  insoluble  compound,  or  one  less  soluble  than  the 
two  former.  Another  uniformity  is  that  called  the  law  of  isomorphism; 
the  identity  of  the  crystalline  forms  of  substances  which  possess  in  common 
certain  peculiarities  of  chemical  composition.*  Thus  it  appears  that  even 
heteropathic  laws,  such  laws  of  combined  agency  as  are  not  compounded 
of  the  laws  of  the  separate  agencies,  are  j et,  at  least  in  some  cases,  derived 
from  them  according  to  a fixed  principle.  There  may,  therefore,  be  laws 
of  the  generation  of  laws  from  others  dissimilar  to  them ; and  in  chemis- 
try, these  undiscovered  laws  of  the  dependence  of  the  properties  of  the 
compound  on  the  properties  of  its  elements,  may,  together  with  the  laws  of 
the  elements  themselves,  furnish  the  premises  by  which  the  science  is  per- 
haps destined  one  day  to  be  rendered  deductive. 

It  would  seem,  therefore,  that  there  is  no  class  of  phenomena  in  which 
the  Composition  of  Causes  does  not  obtain:  that  ns  a general  rule, causes 
in  combination  produce  exactly  the  same  effects  as  when  acting  singly:  but 
that  this  rule, though  general,  is  not  universal:  that  in  some  instances,  at 
some  particular  points  in  the  transition  from  separate  to  united  action,  the 
laws  change,  and  an  entirely  new  set  of  effects  are  either  added  to,  or  take 
the  place  of,  those  which  arise  from  the  separate  agency  of  the  same  causes: 
the  laws  of  these  new  effects  being  again  susceptible  of  composition,  to  an 
indefinite  extent,  like  the  laws  which  they  superseded. 

§ 3.  That  effects  are  proportional  to  their  causes  is  laid  down  by  some 
writers  as  an  axiom  in  the  theory  of  causation ; and  great  use  is  sometimes 
made  of  this  principle  in  reasonings  respecting  the  laws  of  nature,  though  it 
is  encumbered  with  many  difficulties  and  apparent  exceptions,  which  much 
ingenuity  has  been  expended  in  showing  not  to  be  real  ones.  This  propo- 
sition, in  so  far  as  it  is  true,  enters  as  a particular  case  into  the  general 
principle  of  the  Composition  of  Causes ; the  causes  compounded  being,  in 
this  instance,  homogeneous ; in  which  case,  if  in  any,  their  joint  effect  might 
be  expected  to  be  identical  with  the  sum  of  their  separate  effects.  If  a 
force  equal  to  one  hundred  weight  will  raise  a certain  body  along  an  in- 
clined plane,  a force  equal  to  two  hundred  weight  will  raise  two  bodies  ex- 
actly similar,  and  thus  the  effect  is  proportional  to  the  cause.  But  does 
not  a force  equal  to  two  hundred  weight  actually  contain  in  itself  two  forces 
each  equal  to  one  hundred  weight,  which,  if  employed  apart,  would  sepa- 
rately raise  the  two  bodies  in  question?  The  fact, therefore, that  when  ex- 
erted jointly  they  raise  both  bodies  at  once,  results  from  the  Composition 
of  Causes,  and  is  a mere  instance  of  the  general  fact  that  mechanical  forces 
are  subject  to  the  law  of  Composition.  And  so  in  every  other  case  which 
can  be  supposed.  For  the  doctrine  of  the  proportionality  of  effects  to  their 
causes  can  not  of  course  be  applicable  to  cases  in  which  the  augmentation 
of  the  cause  alters  the  kind  of  effect;  that  is,  in  which  the  surplus  quanti- 
ty superadded  to  the  cause  does  not  become  compounded  with  it,  but  the 
two  together  generate  an  altogether  new  phenomenon.  Suppose  that  the 
application  of  a certain  quantity  of  heat  to  a body  merely  increases  its 
bulk,  that  a double  quantity  melts  it,  and  a triple  quantity  decomposes  it: 
these  three  effects  being  heterogeneous,  no  ratio,  whether  corresponding 

* Professor  Bain  adds  several  other  well-established  chemical  generalizations:  “The  laws 
that  simple  substances  exhibit  the  strongest  affinities ; that  compounds  are  more  fusible  than 
their  elements;  that  combination  tends  to  a lower  state  of  matter  from  gas  down  to  solid;” 
and  some  general  propositions  concerning  the  circumstances  which  facilitate  or  resist  chem- 
ical combination.  (Logic,  ii. , 254.) 


COMPOSITION  OF  CAUSES. 


271 


or  not  to  that  of  the  quantities  of  heat  applied,  can  be  established  between 
them.  Thus  the  supposed  axiom  of  the  proportionality  of  effects  to  their 
causes  fails  at  the  precise  point  where  the  principle  of  the  Composition  of 
Causes  also  fails;  viz.,  where  the  concurrence  of  causes  is  such  as  to  deter- 
mine a change  in  the  properties  of  the  body  generally,  and  render  it  sub- 
ject to  new  laws,  more  or  less  dissimilar  to  those  to  which  it  conformed  in 
its  previous  state.  The  recognition,  therefore,  of  any  such  law  of  propor- 
tionality is  superseded  by  the  more  comprehensive  principle,  in  which  as 
much  of  it  as  is  true  is  implicitly  asserted.* 

The  general  remarks  on  causation,  which  seemed  necessary  as  an  intro- 
duction to  the  theory  of  the  inductive  process,  may  here  terminate.  That 
process  is  essentially  an  inquiry  into  cases  of  causation.  All  the  uniformi- 
ties which  exist  in  the  succession  of  phenomena,  and  most  of  the  uniformi- 
ties in  their  co-existence,  are  either,  as  we  have  seen,  themselves  laws  of 
causation,  or  consequences  resulting  from,  and  corollaries  capable  of  being 
deduced  from,  such  laws.  If  we  could  determine  what  causes  are  correct- 
ly assigned  to  what  effects,  and  what  effects  to  what  causes,  we  should  be 
virtually  acquainted  with  the  whole  course  of  nature.  All  those  uniformi- 
ties which  are  mere  results  of  causation  might  then  be  explained  and  ac- 
counted for ; and  every  individual  fact  or  event  might  be  predicted,  pro- 
vided we  had  the  requisite  data,  that  is,  the  requisite  knowledge  of  the  cir- 
cumstances which,  in  the  particular  instance,  preceded  it. 

To  ascertain,  therefore,  what  are  the  laws  of  causation  -which  exist  in  na- 
ture; to  determine  the  effect  of  every  cause,  and  the  causes  of  all  effects, 
is  the  main  business  of  Induction ; and  to  point  out  hojv  this  is  done  is  the 
chief  object  of  Inductive  Logic. 

* Professor  Bain  (Logie,  ii. , 39)  points  out  a class  of  cases,  other  than  that  spoken  of  in 
the  text,  which  he  thinks  must  be  regarded  as  an  exception  to  the  Composition  of  Causes. 
“Causes  that  merely  make  good  the  collocation  for  bringing  a prime  mover  into  action,  or 
that  release  a potential  force,  do  not  follow  any  such  rule.  One  man  may  direct  a gun  upon 
a fort  as  well  as  three  : two  sparks  are  not  more  effectual  than  one  in  exploding  a barrel  of 
gunpowder.  In  medicine  there  is  a certain  dose  that  answers  the  end  ; and  adding  to  it  does 
no  more  good.” 

I am  not  sure  that  these  cases  are  really  exceptions.  The  law  of  Composition  of  Causes,  I 
think,  is  really  fulfilled,  and  the  appearance  to  the  contrary  is  produced  by  attending  to  the 
remote  instead  of  the  immediate  effect  of  the  causes.  In  the  cases  mentioned,  the  immedi- 
ate effect  of  the  causes  in  action  is  a collocation,  and  the  duplication  of  the  cause  does  double 
the  quantity  of  collocation.  Two  men  could  raise  the  gun  to  the  required  angle  twice  as 
quickly  as  one,  though  one  is  enough.  Two  sparks  put  two  sets  of  particles  of  the  gunpow- 
der into  the  state  of  intestine  motion  which  makes  them  explode,  though  one  is  sufficient.  It 
is  the  collocation  itself  that  does  not,  by  being  doubled,  always  double  the  effect ; because  in 
many  cases  a certain  collocation,  once  obtained,  is  all  that  is  required  for  the  production  of 
the  whole  amount  of  effect  which  can  be  produced  at  all  at  the  given  time  and  place.  Dou- 
bling the  collocation  with  difference  of  time  and  place,  as  by  pointing  two  guns,  or  exploding 
a second  barrel  after  the  first,  does  double  the  effect.  This  remark  applies  still  more  to  Mr. 
Bain’s  third  example,  that  of  a double  dose  of  medicine ; for  a double  dose  of  an  aperient 
does  purge  more  violently,  and  a double  dose  of  laudanum  does  produce  longer  and  sounder 
sleep.  But  a double  purging,  or  a double  amount  of  narcotism,  may  have  remote  effects  dif- 
ferent in  kind  from  the  effect  of  the  smaller  amount,  reducing  the  case  to  that  of  heteropathic 
laws,  discussed  in  the  text. 


272 


INDUCTION. 


CHAPTER  VII. 

OF  OBSERVATION  AND  EXPERIMENT. 

§ 1.  It  results  from  the  preceding  exposition,  that  the  process  of  ascer- 
taining what  consequents,  in  nature,  are  invariably  connected  with  what 
antecedents,  or  in  other  words  what  phenomena  are  related  to  each  other 
as  causes  and  effects,  is  in  some  sort  a process  of  analysis.  That  every 
fact  which  begins  to  exist  has  a cause,  and  that  this  cause  must  be  found 
in  some  fact  or  concourse  of  facts  which  immediately  preceded  the  occur- 
rence, may  be  taken  for  certain.  The  whole  of  the  present  facts  are  the 
infallible  result  of  all  past  facts,  and  more  immediately  of  all  the  facts 
which  existed  at  the  moment  previous.  Here,  then,  is  a great  sequence, 
which  we  know  to  be  uniform.  If  the  whole  prior  state  of  the  entire  uni- 
verse could  again  recur,  it  would  again  be  followed  by  the  present  state. 
The  question  is,  how  to  resolve  this  complex  uniformity  into  the  simpler 
uniformities  which  compose  it,  and  assign  to  each  portion  of  the  vast  an- 
tecedent the  portion  of  the  consequent  which  is  attendant  on  it. 

This  operation,  which  we  have  called  analytical,  inasmuch  as  it  is  the 
resolution  of  a complex  whole  into  the  component  elements,  is  more  than 
a merely  mental  analysis.  No  mere  contemplation  of  the  phenomena,  and 
partition  of  them  by  the  intellect  alone,  will  of  itself  accomplish  the  end  we 
have  now  in  view.  Nevertheless,  such  a mental  partition  is  an  indispensa- 
ble first  step.  The  order  of  nature,  as  perceived  at  a first  glance,  presents 
at  every  instant  a chaos  followed  by  another  chaos.  We  must  decompose 
each  choas  into  single  facts.  We  must  learn  to  see  in  the  chaotic  ante- 
cedent a multitude  of  distinct  antecedents,  in  the  chaotic  consequent  a mul- 
titude of  distinct  consequents.  This,  supposing  it  done,  will  not  of  itself 
tell  us  on  which  of  the  antecedents  each  consequent  is  invariably  attendant. 
To  determine  that  point,  we  must  endeavor  to  effect  a separation  of  the 
facts  from  one  another,  not  in  our  minds  only,  but  in  nature.  The  mental 
analysis,  however,  must  take  place  first.  And  every  one  knows  that  in  the 
mode  of  performing  it,  one  intellect  differs  immensely  from  another.  It  is 
the  essence  of  the  act  of  observing;  for  the  observer  is  not  he  who  merely 
sees  the  thing  which  is  before  his  eyes,  but  he  who  sees  what  parts  that 
thing  is  composed  of.  To  do  this  well  is  a rare  talent.  One  person,  from 
inattention,  or  attending  only  in  the  wrong  place,  overlooks  half  of  what  he 
sees;  another  sets  down  much  more  than  he  sees,  confounding  it  with  what 
he  imagines,  or  with  what  he  infers;  another  takes  note  of  the  kind  of  all 
the  circumstances,  but  being  inexpert  in  estimating  their  degree,  leaves  the 
quantity  of  each  vague  and  uncertain  ; another  sees  indeed  the  whole,  but 
makes  such  an  awkward  division  of  it  into  parts,  throwing  things  into  one 
mass  which  require  to  be  separated,  and  separating  others  which  might 
more  conveniently  be  considered  as  one,  that  the  result  is  much  the  same, 
sometimes  even  worse,  than  if  no  analysis  had  been  attempted  at  all.  It 
would  be  possible  to  point  out  what  qualities  of  mind,  and  modes  of  men- 
tal culture,  fit  a person  for  being  a good  observer:  that,  however,  is  a 
question  not  of  Logic,  but  of  the  Theory  of  Education,  in  the  most  en- 
larged sense  of  the  term.  There  is  not  properly  an  Art  of  Observing. 


OBSERVATION  AND  EXPERIMENT. 


273 


There  may  be  rules  for  observing.  But  these,  like  rules  for  inventing,  are 
properly  instructions  for  the  preparation  of  one’s  own  mind ; for  putting 
it  into  the  state  in  which  it  will  be  most  fitted  to  observe,  or  most  likely 
to  invent.  They  are,  therefore,  essentially  rules  of  self-education,  which  is 
a different  thing  from  Logic.  They  do  not  teach  how  to  do  the  thing,  but 
how  to  make  ourselves  capable  of  doing  it.  They  are  an  art  of  strength- 
ening the  limbs,  not  an  art  of  using  them. 

The  extent  and  minuteness  of  observation  which  may  be  requisite,  and 
the  degree  of  decomposition  to  which  it  may  be  necessary  to  carry  the 
mental  analysis,  depend  on  the  particular  purpose  in  view.  To  ascertain 
the  state  of  the  whole  universe  at  any  particular  moment  is  impossible,  but 
would  also  be  useless.  In  making  chemical  experiments,  we  do  not  think 
it  necessary  to  note  the  position  of  the  planets;  because  experience  has 
shown,  as  a very  superficial  experience  is  sufficient  to  show,  that  in  such 
cases  that  circumstance  is  not  material  to  the  result:  and  accordingly,  in 
the  ages  when  men  believed  in  the  occult  influences  of  the  heavenly  bodies, 
it  might  have  been  unphilosophical  to  omit  ascertaining  the  precise  condi- 
tion of  those  bodies  at  the  moment  of  the  experiment.  As  to  the  degree 
of  minuteness  of  the  mental  subdivision,  if  we  were  obliged  to  break  down 
what  we  observe  into  its  very  simplest  elements,  that  is,  literally  into  sin- 
gle facts,  it  would  be  difficult  to  say  where  we  should  find  them ; we  can 
hardly  ever  affirm  that  our  divisions  of  any  kind  have  reached  the  ultimate 
unit.  But  this,  too,  is  fortunately  unnecessary.  The  only  object  of  the 
mental  separation  is  to  suggest  the  requisite  physical  separation,  so  that 
we  may  either  accomplish  it  ourselves,  or  seek  for  it  in  nature;  and  we 
have  done  enough  when  we  have  carried  the  subdivision  as  far  as  the  point 
at  which  we  are  able  to  see  what  observations  or  experiments  we  require. 
It  is  only  essential,  at  whatever  point  our  mental  decomposition  of  facts 
may  for  the  present  have  stopped,  that  we  should  hold  ourselves  ready  and 
able  to  carry  it  further  as  occasion  requires,  and  should  not  allow  the  free- 
dom of  our  discriminating  facility  to  be  imprisoned  bv  the  swathes  and 
bands  of  ordinary  classification ; as  was  the  case  with  all  early  speculative 
inquirers,  not  excepting  the  Greeks,  to  whom  it  seldom  occurred  that  what 
was  called  by  one  abstract  name  might,  in  reality,  be  several  phenomena, 
or  that  there  was  a possibility  of  decomposing  the  facts  of  the  universe  into 
any  elements  but  those  which  ordinary  language  already  recognized. 

§ 2.  The  different  antecedents  and  consequents  being,  then,  supposed  to 
be,  so  far  as  the  case  requires,  ascertained  and  discriminated  from  one  an- 
other, we  are  to  inquire  which  is  connected  with  which.  In  every  instance 
which  comes  under  our  observation,  there  are  many  antecedents  and  many 
consequents.  If  those  antecedents  could  not  be  severed  from  one  another 
except  in  thought,  or  if  those  consequents  never  were  found  apart,  it  would 
be  impossible  for  us  to  distinguish  (a  posteriori  at  least)  the  real  laws,  or 
to  assign  to  any  cause  its  effect,  or  to  any  effect  its  cause.  To  do  so,  we 
must  be  able  to  meet  with  some  of  the  antecedents  apart  from  the  rest,  and 
observe  what  follows  from  them  ; or  some  of  the  consequents,  and  observe 
by  what  they  are  preceded.  We  must,  in  short,  follow  the  Baconian  rule 
of  varying  the  circumstances.  This  is,  indeed,  only  the  first  rule  of  phys- 
ical inquiry,  and  not,  as  some  have  thought,  the  sole  rule;  but  it  is  the 
foundation  of  all  the  rest. 

For  the  purpose  of  varying  the  circumstances,  we  may  have  recourse 
(according  to  a distinction  commonly  made)  either  to  observation  or  to  ex- 

18 


274 


INDUCTION. 


perimcnt;  we  may  either  Jind-sxi  instance  in  nature  suited  to  our  purposes, 
or,  by  an  artificial  arrangement  of  circumstances,  make  one.  The  value  of 
the  instance  depends  on  what  it  is  in  itself,  not  on  the  mode  in  which  it  is 
obtained : its  employment  for  the  purposes  of  induction  depends  on  the 
same  principles  in  the  one  case  and  in  the  other;  as  the  uses  of  money  are 
the  same  whether  it  is  inherited  or  acquired.  There  is,  in  short,  no  differ- 
ence in  kind,  no  real  logical  distinction,  between  the  two  processes  of  in- 
vestigation. There  are,  however,  practical  distinctions  to  which  it  is  of 
considerable  importance  to  advert. 

§ 3.  The  first  and  most  obvious  distinction  between  Observation  and 
Experiment  is,  that  the  latter  is  an  immense  extension  of  the  former.  It 
not  only  enables  us  to  produce  a much  greater  number  of  variations  in  the 
circumstances  than  nature  spontaneously  offers,  but  also,  in  thousands  of 
cases,  to  produce  the  precise  sort  of  variation  which  we  are  in  want  of  for 
discovering  the  law  of  the  phenomenon ; a service  which  nature,  being  con- 
structed on  a quite  different  scheme  from  that  of  facilitating  our  studies, 
is  seldom  so  friendly  as  to  bestow  upon  us.  For  example,  in  order  to  as- 
certain what  principle  in  the  atmosphere  enables  it  to  sustain  life,  the 
variation  we  require  is  that  a living  animal  should  be  immersed  in  each 
component  element  of  the  atmosphere  separately.  But  nature  does  not 
supply  either  oxygen  or  azote  in  a separate  state.  We  are  indebted  to  ar- 
tificial experiment  for  our  knowledge  that  it  is  the  former,  and  not  the  lat- 
ter, which  supports  respiration ; and  for  our  knowledge  of  the  very  exist- 
ence of  the  two  ingredients. 

Thus  far  the  advantage  of  experimentation  over  simple  observation  is 
universally  recognized : all  are  aware  that  it  enables  us  to  obtain  innumer- 
able combinations  of  circumstances  which  are  not  to  be  found  in  nature, 
and  so  add  to  nature’s  experiments  a multitude  of  experiments  of  our  own. 
But  there  is  another  superiority  (or,  as  Bacon  would  have  expressed  it,  an- 
other prerogative)  of  instances  artificially  obtained  over  spontaneous  in- 
stances— of  our  own  experiments  over  even  the  same  experiments  when 
made  by  nature — which  is  not  of  less  importance,  and  which  is  far  from 
being  felt  and  acknowledged  in  the  same  degree. 

When  we  can  produce  a phenomenon  artificially,  we  can  take  it,  as  it 
were,  home  with  us,  and  observe  it  in  the  midst  of  circumstances  with 
which  in  all  other  respects  we  are  accurately  acquainted.  If  we  desire  to 
know  what  are  the  effects  of  the  cause  A,  and  are  able  to  produce  A by 
means  at  our  disposal,  we  can  generally  determine  at  our  own  discretion,  so 
far  as  is  compatible  with  the  nature  of  the  phenomenon  A,  the  whole  of 
the  circumstances  which  shall  be  present  along  with  it:  and  thus,  knowing 
exactly  the  simultaneous  state  of  every  thing  else  which  is  within  the  reach 
of  A’s  influence,  we  have  only  to  observe  what  alteration  is  made  in  that 
state  by  the  presence  of  A. 

For  example,  by  the  electric  machine  we  can  produce,  in  the  midst  of 
known  circumstances,  the  phenomena  which  nature  exhibits  on  a grander 
scale  in  the  form  of  lightning  and  thunder.  Now  let  any  one  consider 
what  amount  of  knowledge  of  the  effects  and  laws  of  electric  agency  man- 
kind could  have  obtained  from  the  mere  observation  of  thunder-storms,  and 
compare  it  with  that  which  they  have  gained,  and  may  expect  to  gain,  from 
electrical  and  galvanic  experiments.  This  example  is  the  more  striking, 
now  that  we  have  reason  to  believe  that  electric  action  is  of  all  natural 
phenomena  (except  heat)  the  most  pervading  and  universal,  which,  there 


OBSERVATION  AND  EXPERIMENT. 


275 


fore,  it  might  antecedently  have  been  supposed  could  stand  least  in  need  of 
artificial  means  of  production  to  enable  it  to  be  studied ; while  the  fact  is 
so  much  the  contrary,  that  without  the  electric  machine,  the  Leyden  jar, 
and  the  voltaic  battery,  we  probably  should  never  have  suspected  the  ex- 
istence of  electricity  as  one  of  the  great  agents  in  nature ; the  few  electric 
phenomena  we  should  have  known  of  would  have  continued  to  be  regard- 
ed either  as  supernatural,  or  as  a sort  of  anomalies  and  eccentricities  in  the 
order  of  the  universe. 

When  we  have  succeeded  in  insulating  the  phenomenon  which  is  the 
subject  of  inquiry,  by  placing  it  among  known  circumstances,  we  may  pro- 
duce further  variations  of  circumstances  to  any  extent,  and  of  such  kinds 
as  we  think  best  calculated  to  bring  the  laws  of  the  phenomenon  into  a 
clear  light.  By  introducing  one  well-defined  circumstance  after  another 
into  the  experiment,  we  obtain  assurance  of  the  manner  in  which  the  phe- 
nomenon behaves  under  an  indefinite  variety  of  possible  circumstances. 
Thus,  chemists,  after  having  obtained  some  newly-discovered  substance  in 
a pure  state  (that  is,  having  made  sure  that  there  is  nothing  present  which 
can  interfere  with  and  modify  its  agency),  introduce  various  other  sub- 
stances, one  by  one,  to  ascertain  whether  it  will  combine  with  them,  or  de- 
compose them,  and  with  what  result ; and  also  apply  heat,  or  electricity,  or 
pressure,  to  discover  what  will  happen  to  the  substance  under  each  of  these 
circumstances. 

But  if,  on  the  other  hand,  it  is  out  of  our  power  to  produce  the  phenom- 
enon, and  we  have  to  seek  for  instances  in  which  nature  produces  it,  the 
task  before  us  is  very  different. 

Instead  of  being  able  to  choose  what  the  concomitant  circumstances 
shall  be,  we  now  have  to  discover  what  they  are;  which,  when  we  go  be- 
yond the  simplest  and  most  accessible  cases,  it  is  next  to  impossible  to  do 
with  any  precision  and  completeness.  Let  us  take,  as  an  exemplification  of 
a phenomenon  which  we  have  no  means  of  fabricating  artificially,  a human 
mind.  Nature  produces  many;  but  the  consequence  of  our  not  being  able 
to  produce  them  by  art  is,  that  in  every  instance  in  which  we  see  a human 
mind  developing  itself,  or  acting  upon  other  things,  we  see  it  surrounded 
and  obscured  by  an  indefinite  multitude  of  unascertainable  circumstances, 
rendering  the  use  of  the  common  experimental  methods  almost  delusive. 
We  may  conceive  to  what  extent  this  is  true,  if  we  consider,  among 
other  things,  that  whenever  Nature  produces  a human  mind,  she  produces, 
in  close  connection  with  it,  a body ; that  is,  a vast  complication  of  physical 
facts,  in  no  two  cases  perhaps  exactly  similar,  and  most  of  which  (except 
the  mere  structure,  which  we  can  examine  in  a sort  of  coarse  way  after  it 
has  ceased  to  act),  are  radically  out  of  the  reach  of  our  means  of  explora- 
tion. If,  instead  of  a human  mind,  we  suppose  the  subject  of  investiga- 
tion to  be  a human  society  or  State,  all  the  same  difficulties  recur  in  a great- 
ly augmented  degree. 

We  have  thus  already  come  within  sight  of  a conclusion,  which  the  prog- 
ress of  the  inquiry  will,  I think,  bring  before  us  with  the  clearest  evi- 
dence : namely,  that  in  the  sciences  which  deal  with  phenomena  in  which 
artificial  experiments  are  impossible  (as  in  the  case  of  astronomy),  or  in 
which  they  have  a very  limited  range  (as  in  mental  philosophy,  social 
science,  and  even  physiology),  induction  from  direct  experience  is  practiced 
at  a disadvantage  inmost  cases  equivalent  to  impracticability;  from  which 
it  follows  that  the  methods  of  those  sciences,  in  order  to  accomplish  any 
thing  worthy  of  attainment,  must  be  to  a great  extent,  if  not  principally, 


276 


INDUCTION. 


deductive.  This  is  already  known  to  be  the  case  with  the  first  of  the  sci- 
ences we  have  mentioned,  astronomy ; that  it  is  not  generally  recognized 
as  true  of  the  others,  is  probably  one  of  the  reasons  why  they  are  not  in  a 
more  advanced  state. 

§ 4.  If  what  is  called  pure  observation  is  at  so  great  a disadvantage, 
compared  with  artificial  experimentation,  in  one  department  of  the  direct 
exploration  of  phenomena,  there  is  another  branch  in  which  the  advantage 
is  all  on  the  side  of  the  former. 

Inductive  inquiry  having  for  its  object  to  ascertain  what  causes  arc  con- 
nected with  what  effects,  we  may  begin  this  search  at  either  end  of  the  road 
which  leads  from  the  one  point  to  the  other:  we  may  either  inquire  into 
the  effects  of  a given  cause  or  into  the  causes  of  a given  effect.  The  fact 
that  light  blackens  chloride  of  silver  might  have  been  discovered  either  by 
experiments  on  light,  trying  what  effect  it  would  produce  on  various  sub- 
stances, or  by  observing  that  portions  of  the  chloride  had  repeatedly  be- 
come black,  and  inquiring  into  the  circumstances.  The  effect  of  the  urali 
poison  might  have  become  known  either  by  administering  it  to  animals, 
or  by  examining  how  it  happened  that  the  wounds  which  the  Indians  of 
Guiana  inliict  with  their  arrows  prove  so  uniformly  mortal.  Now  it  is 
manifest  from  the  mere  statement  of  the  examples,  without  any  theoretical 
discussion,  that  artificial  experimentation  is  applicable  only  to  the  former  of 
these  modes  of  investigation.  We  can  take  a cause,  and  try  what  it  will 
produce ; but  we  can  not  take  an  effect,  and  try  wThat  it  will  be  produced 
by.  We  can  only  watch  till  we  see  it  produced,  or  arc  enabled  to  produce 
it  by  accident. 

This  would  be  of  little  importance,  if  it  always  depended  on  our  choice 
from  which  of  the  two  ends  of  the  sequence  we  would  undertake  our  in- 
quiries. But  we  have  seldom  any  option.  As  we  can  only  travel  from 
the  known  to  the  unknown,  we  are  obliged  to  commence  at  whichever  end 
we  are  best  acquainted  with.  If  the  agent  is  more  familiar  to  us  than  its 
effects,  we  watch  for,  or  contrive,  instances  of  the  agent,  under  such  vari- 
eties of  circumstances  as  are  open  to  us,  and  observe  the  result.  If,  on  the 
contrary,  the  conditions  on  which  a phenomenon  depends  are  obscure,  but 
the  phenomenon  itself  familiar,  we  must  commence  our  inquiry  from  the 
effect.  If  we  are  struck  with  the  fact  that  chloride  of  silver  has  been 
blackened,  and  have  no  suspicion  of  the  cause,  we  have  no  resource  but  to 
compare  instances  in  which  the  fact  has  chanced  to  occur,  until  by  that 
comparison  we  discover  that  in  all  those  instances  the  substances  had  been 
exposed  to  light.  If  we  knew  nothing  of  the  Indian  arrows  but  their  fa- 
tal effect,  accident  alone  could  turn  our  attention  to  experiments  on  the 
urali;  in  the  regular  course  of  investigation,  we  could  only  inquire,  or  try 
to  observe,  what  had  been  done  to  the  arrows  in  particular  instances. 

Wherever,  having  nothing  to  guide  us  to  the  cause,  we  are  obliged  to 
set  out  from  the  effect,  and  to  apply  the  rule  of  varying  the  circumstances 
to  the  consequents,  not  the  antecedents,  we  are  necessarily  destitute  of  the 
resource  of  artificial  experimentation.  We  can  not,  at  our  choice,  obtain 
consequents,  as  we  can  antecedents,  under  any  set  of  circumstances  com- 
patible with  their  nature.  There  are  no  means  of  producing  effects  but 
through  their  causes,  and  by  the  supposition  the  causes  of  the  effect  in  ques- 
tion are  not  known  to  us.  We  have,  therefore,  no  expedient  but  to  study  it 
where  it  offers  itself  spontaneously.  If  nature  happens  to  present  us  with 
instances  sufficiently  varied  in  their  circumstances,  and  if  we  are  able  to  dis- 


OBSERVATION  AND  EXPERIMENT. 


277 


cover,  either  among  the  proximate  antecedents  or  among  some  other  order 
of  antecedents,  something  which  is  always  found  when  the  effect  is  found, 
however  various  the  circumstances,  and  never  found  when  it  is  not,  we 
may  discover,  by  mere  observation  without  experiment,  a real  uniformity 
in  nature. 

But  though  this  is  certainly  the  most  favorable  case  for  sciences  of  pure 
observation,  as  contrasted  with  those  in  which  artificial  experiments  are 
possible,  there  is  in  reality  no  case  which  more  strikingly  illustrates  the 
inherent  imperfection  of  direct  induction  when  not  founded  on  experimen- 
tation. Suppose  that,  by  a comparison  of  cases  of  the  effect,  we  have  found 
an  antecedent  which  appears  to  be,  and  perhaps  is,  invariably  connected 
with  it:  we  have  not  yet  proved  that  antecedent  to  be  the  cause  until  we 
have  reversed  the  process,  and  produced  the  effect  by  means  of  that  ante- 
cedent. If  we  can  produce  the  antecedent  artificially,  and  if,  when  we  do 
so,  the  effect  follows,  the  induction  is  complete;  that  antecedent  is  the 
cause  of  that  consequent.*  But  we  have  then  added  the  evidence  of  ex- 
periment to  that  of  simple  observation.  Until  we  had  done  so,  we  had 
only  proved  invariable  antecedence  within  the  limits  of  experience,  but 
not  unconditional  antecedence,  or  causation.  Until  it  had  been  shown  by 
the  actual  production  of  the  antecedent  under  known  circumstances,  and 
the  occurrence  thereupon  of  the  consequent,  that  the  antecedent  was  really 
the  condition  on  which  it  depended ; the  uniformity  of  succession  which 
was  proved  to  exist  between  them  might,  for  aught  we  knew,  be  (like  the 
succession  of  day  and  night)  not  a case  of  causation  at  all ; both  antecedent 
and  consequent  might  be  successive  stages  of  the  effect  of  an  ulterior  cause. 
Observation,  in  short,  without  experiment  (supposing  no  aid  from  deduction) 
can  ascertain  sequences  and  co-existences,  but  can  not  prove  causation. 

In  order  to  see  these  remarks  verified  by  the  actual  state  of  the  sciences, 
we  have  only  to  think  of  the  condition  of  natural  history.  In  zoology,  for 
example,  there  is  an  immense  number  of  uniformities  ascertained,  some  of 
co-existence,  others  of  succession,  to  many  of  which,  notwithstanding  con- 
siderable variations  of  the  attendant  circumstances,  we  know  not  any  ex- 
ception : but  the  antecedents,  for  the  most  part,  are  such  as  we  can  not 
artificially  produce;  or  if  we  can,  it  is  only  by  setting  in  motion  the  ex- 
act process  by  which  nature  produces  them  ; and  this  being  to  us  a myste- 
rious process,  of  which  the  main  circumstances  are  not  only  unknown  but 
unobservable,  we  do  not  succeed  in  obtaining  the  antecedents  under  known 
circumstances.  What  is  the  result?  That  on  this  vast  subject,  which  af- 
fords so  much  and  such  varied  scope  for  observation,  we  have  made  most 
scanty  progress  in  ascertaining  any  laws  of  causation.  We  know  not  with 
certainty,  in  the  case  of  most  of  the  phenomena  that  we  find  conjoined, 
which  is  the  condition  of  the  other ; which  is  cause,  and  which  effect,  or 
whether  either  of  them  is  so,  or  they  are  not  rather  conjunct  effects  of 
causes  yet  to  be  discovered,  complex  results  of  laws  hitherto  unknown. 

Although  some  of  the  foregoing  observations  may  be,  in  technical  strict- 
ness of  arrangement,  premature  in  this  place,  it  seemed  that  a few  general 
remarks  on  the  difference  between  sciences  of  mere  observation  and  sciences 
of  experimentation,  and  the  extreme  disadvantage  under  which  directly  in- 
ductive inquiry  is  necessarily  carried  on  in  the  former,  were  the  best  prep- 

* Unless,  indeed,  the  consequent  was  generated,  not  by  the  antecedent,  but  by  the  means 
employed  to  produce  the  antecedent.  As,  however,  these  means  are  under  our  power,  there 
is  so  far  a probability  that  they  are  also  sufficiently  within  our  knowledge  to  enable  us  to 
judge  whether  that  could  be  the  case  or  not. 


278 


INDUCTION. 


aration  for  discussing  the  methods  of  direct  induction  ; a preparation  ren- 
dering superfluous  much  that  must  otherwise  have  been  introduced,  with 
some  inconvenience,  into  the  heart  of  that  discussion.  To  the  consideration 
of  these  methods  we  now  proceed. 


CHAPTER  VIII. 

OF  THE  FOUR  METHODS  OF  EXPERIMENTAL  INQUIRY. 

§ 1.  The  simplest  and  most  obvious  modes  of  singling  out  from  among 
the  circumstances  which  precede  or  follow  a phenomenon,  those  with  which 
it  is  really  connected  by  an  invariable  law,  are  two  in  number.  One  is,  by 
comparing  together  different  instances  in  which  the  phenomenon  occurs. 
The  other  is,  by  comparing  instances  in  which  the  phenomenon  does  occur, 
with  instances  in  other  respects  similar  in  which  it  does  not.  These  two 
methods  may  be  respectively  denominated,  the  Method  of  Agreement,  and 
the  Method  of  Difference. 

In  illustrating  these  methods,  it  will  be  necessary  to  bear  in  mind  the 
twofold  character  of  inquiries  into  the  laws  of  phenomena;  which  may 
be  either  inquiries  into  the  cause  of  a given  effect,  or  into  the  effects  or 
-properties  of  a given  cause.  We  shall  consider  the  methods  in  their  ap- 
plication to  either  order  of  investigation,  and  shall  draw  our  examples 
equally  from  both. 

We  shall  denote  antecedents  by  the  large  letters  of  the  alphabet,  and 
the  consequents  corresponding  to  them  by  the  small.  Let  A,  then,  be  an 
agent  or  cause,  and  let  the  object  of  our  inquiry  be  to  ascertain  what  are 
the  effects  of  this  cause.  If  we  can  either  find,  or  produce,  the  agent  A in 
such  varieties  of  circumstances  that  the  different  cases  have  no  circumstance 
in  common  except  A ; then  whatever  effect  we  find  to  be  produced  in  all 
our  trials,  is  indicated  as  the  effect  of  A.  Suppose,  for  example,  that  A is 
tried  along  with  B and  C,  and  that  the  effect  is  a b c;  and  suppose  that 
A is  next  tried  with  D and  E,  but  without  B and  C,  and  that  the  effect  is 
a de.  Then  we  may  reason  thus : b and  c are  not  effects  of  A,  for  they  were 
not  produced  by  it  in  the  second  experiment;  nor  are  d and  e,  for  they 
were  not  produced  in  the  first.  Whatever  is  really  the  effect  of  A must 
have  been  produced  in  both  instances;  now  this  condition  is  fulfilled  by 
no  circumstance  except  a.  The  phenomenon  a can  not  have  been  the  ef- 
fect of  B or  C,  since  it  was  produced  where  they  were  not;  nor  of  D or  E, 
since  it  was  produced  where  they  were  not.  Therefore  it  is  the  effect 
of  A. 

For  example,  let  the  antecedent  A be  the  contact  of  an  alkaline  sub- 
stance and  an  oil.  This  combination  being  tried  under  several  varieties 
of  circumstances,  resembling  each  other  in  nothing  else,  the  results  agree  in 
the  production  of  a greasy  and  detersive  or  saponaceous  substance : it  is 
therefore  concluded  that  the  combination  of  an  oil  and  an  alkali  causes  the 
production  of  a soap.  It  is  thus  we  inquire,  by  the  Method  of  Agreement, 
into  the  effect  of  a given  cause. 

In  a similar  manner  we  may  inquire  into  the  cause  of  a given  effect. 
Let  a be  the  effect.  Here,  as  shown  in  the  last  chapter,  we  have  only  the 
resource  of  observation  without  experiment:  we  can  not  take  a phenome- 
non of  which  we  know  not  the  origin,  and  try  to  find  its  mode  of  produc- 


THE  FOUR  EXPERIMENTAL  METHODS. 


2*79 


tion  by  producing  it : if  we  succeeded  in  such  a random  trial  it  could  only 
be  by  accident.  But  if  we  can  observe  a in  two  different  combinations, 
abc  and  ade  ; and  if  we  know,  or  can  discover,  that  the  antecedent  cir- 
cumstances in  these  cases  respectively  were  ABC  and  ADE,  we  may 
conclude  by  a reasoning  similar  to  that  in  the  preceding  example,  that  A is 
the  antecedent  connected  with  the  consequent  a by  a law  of  causation. 
B and  C,  we  may  say,  can  not  be  causes  of  a,  since  on  its  second  occur- 
rence they  were  not  present;  nor  are  D and  E,  for  they  were  not  present  on 
its  first  occurrence.  A,  alone  of  the  five  circumstances,  was  found  among 
the  antecedents  of  a in  both  instances. 

For  example,  let  the  effect  a be  crystallization.  We  compare  instances 
in  which  bodies  are  known  to  assume  crystalline  structure,  but  which  have 
no  other  point  of  agreement;  and  we  find  them  to  have  one,  and  as  far  as 
we  can  observe,  only  one,  antecedent  in  common  : the  deposition  of  a solid 
matter  from  a liquid  state,  either  a state  of  fusion  or  of  solution.  We 
conclude,  therefore,  that  the  solidification  of  a substance  from  a liquid  state 
is  an  invariable  antecedent  of  its  crystallization. 

In  this  example  we  may  go  further,  and  say,  it  is  not  only  the  invariable 
antecedent  but  the  cause ; or  at  least  the  proximate  event  which  completes 
the  cause.  For  in  this  case  we  are  able,  after  detecting  the  antecedent  A, 
to  produce  it  artificially,  and  by  finding  that  a follows  it,  verify  the  result 
of  our  induction.  The  importance  of  thus  reversing  the  proof  was  strik- 
ingly manifested  when,  by  keeping  a phial  of  water  charged  with  siliceous 
particles  undisturbed  for  years,  a chemist  (I  believe  Dr.  Wollaston)  suc- 
ceeded in  obtaining  crystals  of  quartz;  and  in  the  equally  interesting  ex- 
periment in  which  Sir  James  Hall  produced  artificial  marble  by  the  cool- 
ing of  its  materials  from  fusion  under  immense  pressure:  two  admirable 
examples  of  the  light  which  may  be  thrown  upon  the  most  secret  processes 
of  Nature  by  well-contrived  interrogation  of  her. 

But  if  we  can  not  artificially  produce  the  phenomenon  A,  the  conclusion 
that  it  is  the  cause  of  a remains  subject  to  very  considerable  doubt. 
Though  an  invariable,  it  may  not  be  the  unconditional  antecedent  of  a,  but 
may  precede  it  as  day  precedes  night  or  night  day.  This  uncertainty  arises 
from  the  impossibility  of  assuring  ourselves  that  A is  the  only  immediate 
antecedent  common  to  both  the  instances.  If  we  could  be  certain  of  hav- 
ing ascertained  all  the  invariable  antecedents,  we  might  be  sure  that  the 
unconditional  invariable  antecedent,  or  cause,  must  be  found  somewhere 
among  them.  Unfortunately  it  is  hardly  ever  possible  to  ascertain  all  the 
antecedents,  unless  the  phenomenon  is  one  which  we  can  produce  artificial- 
ly. Even  then,  the  difficulty  is  merely  lightened,  not  removed : men  knew 
how  to  raise  water  in  pumps  long  before  they  adverted  to  what  was  really 
the  operating  circumstance  in  the  means  they  employed,  namely,  the  press- 
ure of  the  atmosphere  on  the  open  surface  of  the  water.  It  is,  however, 
much  easier  to  analyze  completely  a set  of  arrangements  made  by  our- 
selves, than  the  wThole  complex  mass  of  the  agencies  which  nature  happens 
to  be  exerting  at  the  moment  of  the  production  of  a given  phenomenon. 
We  may  overlook  some  of  the  material  circumstances  in  an  experiment 
with  an  eleetrical  machine ; but  we  shall,  at  the  worst,  be  better  acquainted 
with  them  than  with  those  of  a thunder-storm. 

The  mode  of  discovering  and  proving  laws  of  nature,  which  we  have 
now  examined,  proceeds  on  the  following  axiom : Whatever  circumstances 
can  be  excluded,  without  prejudice  to  the  phenomenon,  or  can  be  absent 
notwithstanding  its  presence,  is  not  connected  with  it  in  the  way  of  causa- 


2S0 


INDUCTION. 


tion.  The  casual  circumstances  being  thus  eliminated,  if  only  one  remains, 
that  one  is  the  cause  which  we  are  in  search  of : if  more  than  one,  they  ei- 
ther are,  or  contain  among  them,  the  cause;  and  so,  mutatis  mutandis,  of 
the  effect.  As  this  method  proceeds  by  comparing  different  instances  to 
ascertain  in  what  they  agree,  I have  termed  it  the  Method  of  Agreement; 
and  we  may  adopt  as  its  regulating  principal  the  following  canon  : 

First  Canon. 

If  two  or  more  instances  of  the  phenomenon  under  investigation  have 
only  one  circumstance  in  common,  the  circumstance  in  which  alone  all 
the  instances  agree,  is  the  cause  (or  effect)  of  the  given  phenomenon. 

Quitting  for  the  present  the  Method  of  Agreement,  to  which  we  shall 
almost  immediately  return,  we  proceed  to  a still  more  potent  instrument 
of  the  investigation  of  nature,  the  Method  of  Difference. 

§ 2.  In  the  Method  of  Agreement,  we  endeavored  to  obtain  instances 
which  agreed  in  the  given  circumstance  but  differed  in  every  other:  in  the 
present  method  we  require,  on  the  contrary,  two  instances  resembling  one 
another  in  every  other  respect,  but  differing  in  the  presence  or  absence  of 
the  phenomenon  we  wish  to  study.  If  our  object  be  to  discover  the  effects 
of  an  agent  A,  we  must  procure  A in  some  set  of  ascertained  circum- 
stances, as  A B C,  and  having  noted  the  effects  produced,  compare  them 
with  the  effect  of  the  remaining  circumstances  B C,  when  A is  absent.  If 
the  effect  of  A B C is  a h c,  and  the  effect  of  B C h c,  it  is  evident  that  the 
effect  of  A is  a.  So  again,  if  we  begin  at  the  other  end,  and  desire  to  in- 
vestigate the  cause  of  an  effect  a,  we  must  select  an  instance,  as  a b c,  in 
which  the  effect  occurs,  and  in  which  the  antecedents  were  ABC,  and  we 
must  look  out  for  another  instance  in  which  the  remaining  circumstances, 
b c,  occur  without  a.  If  the  antecedents,  in  that  instance,  are  B C,  we 
know  that  the  cause  of  a must  be  A:  either  A alone,  or  A in  conjunction 
with  some  of  the  other  circumstances  present. 

It  is  scarcely  necessary  to  give  examples  of  a logical  process  to  which 
we  owe  almost  all  the  inductive  conclusions  we  draw  in  daily  life.  When 
a man  is  shot  through  the  heart,  it  is  by  this  method  we  know  that  it  was 
the  gunshot  which  killed  him:  for  he  was  in  the  fullness  of  life  immedi- 
ately before,  all  circumstances  being  the  same,  except  the  wound. 

The  axioms  implied  in  this  method  are  evidently  the  following.  What- 
ever antecedent  can  not  be  excluded  without  preventing  the  phenome- 
non, is  the  cause,  or  a condition,  of  that  phenomenon  : whatever  consequent 
can  be  excluded,  with  no  other  difference  in  the  antecedents  than  the  ab- 
sence of  a particular  one,  is  the  effect  of  that  one.  Instead  of  comparing 
different  instances  of  a phenomenon,  to  discover  in  what  they  agree,  this 
method  compares  an  instance  of  its  occurrence  with  an  instance  of  its  non- 
occurrence, to  discover  in  what  they  differ.  The  canon  which  is  the  regu- 
lating principle  of  the  Method  of  Difference  may  be  expressed  as  follows : 

Second  Canon. 

If  an  instance  in  which  the  phenomenon  under  investigation  occurs, 
and  an  instance  in  which  it  does  not  occur , have  every  circumstance  in 
common  save  one,  that  one  occurring  only  in  the  former ; the  circum- 
stance in  which  alone  the  two  instances  differ,  is  the  effect,  or  the  cause,  or 
an  indispensable  part  of  the  cause , of  the  phenomenon. 


THE  FOUR  EXPERIMENTAL  METHODS. 


281 


§ 3.  The  two  methods  which  we  have  now  stated  have  many  features 
of  resemblance,  but  there  are  also  many  distinctions  between  them.  Both 
are  methods  of  elimination.  This  term  (employed  in  the  theory  of  equa- 
tions to  denote  the  process  by  which  one  after  another  of  the  elements  of 
a question  is  excluded,  and  the  solution  made  to  depend  on  the  relation 
between  the  remaining  elements  only)  is  well  suited  to  express  the  opera- 
tion, analogous  to  this,  which  has  been  understood  since  the  time  of  Bacon 
to  be  the  foundation  of  experimental  inquiry : namely,  the  successive  ex- 
clusion of  the  various  circumstances  which  are  found  to  accompany  a phe- 
nomenon in  a given  instance,  in  order  to  ascertain  what  are  those  among 
them  which  can  be  absent  consistently  with  the  existence  of  the  phenome- 
non. The  Method  of  Agreement  stands  on  the  ground  that  whatever  can 
be  eliminated,  is  not  connected  with  the  phenomenon  by  any  law.  The 
Method  of  Difference  has  for  its  foundation,  that  whatever  can  not  be 
eliminated,  is  connected  with  the  phenomenon  by  a law. 

Of  these  methods,  that  of  Difference  is  more  particularly  a method  of 
artificial  experiment ; while  that  of  Agreement  is  more  especially  the  re- 
source employed  where  experimentation  is  impossible.  A few  reflections 
will  prove  the  fact,  and  point  out  the  reason  of  it. 

It  is  inherent  in  the  peculiar  character  of  the  Method  of  Difference,  that 
the  nature  of  the  combinations  which  it  requires  is  much  more  strictly  de- 
fined than  in  the  Method  of  Agreement.  The  two  instances  which  are  to 
be  compared  with  one  another  must  be  exactly  similar,  in  all  circumstances 
except  the  one  which  we  are  attempting  to  investigate:  they  must  be  in 
the  relation  of  A B C and  B C,  or  of  a b c and  b c.  It  is  true  that  this 
similarity  of  circumstances  needs  not  extend  to  such  as  are  already  known 
to  be  immaterial  to  the  result.  And  in  the  case  of  most  phenomena  we 
learn  at  once,  from  the  commonest  experience,  that  most  of  the  co-existent 
phenomena  of  the  universe  may  be  either  present- or  absent  without  affect- 
ing the  given  phenomenon ; or,  if  present,  are  present  indifferently  when 
the  phenomenon  does  not  happen  and  when  it  does.  Still,  even  limiting 
the  identity  which  is  required  between  the  two  instances,  ABC  and  B C, 
to  such  circumstances  as  are  not  already  known  to  be  indifferent,  it  is 
very  seldom  that  nature  affords  two  instances,  of  which  we  can  be  assured 
that  they  stand  in  this  precise  relation  to  one  another.  In  the  spontane- 
ous operations  of  nature  there  is  generally  such  complication  and  such  ob- 
scurity, they  are  mostly  either  on  so  overwhelmingly  large  or  on  so  inac- 
cessibly minute  a scale,  we  are  so  ignorant  of  a great  part  of  the  facts 
which  really  take  place,  and  even  those  of  which  we  are  not  ignorant  are 
so  multitudinous,  and  therefore  so  seldom  exactly  alike  in  any  two  cases, 
that  a spontaneous  experiment,  of  the  kind  required  by  the  Method  of  Dif- 
ference, is  commonly  not  to  be  found.  When,  on  the  contrary,  we  obtain 
a phenomenon  by  an  artificial  experiment,  a pair  of  instances  such  as  the 
method  requires  is  obtained  almost  as  a matter  of  course,  provided  the 
process  does  not  last  a long  time.  A certain  state  of  surrounding  circum  - 
stances existed  before  we  commenced  the  experiment;  this  is  B C.  We 
then  introduce  A;  say,  for  instance,  by  merely  bringing  an  object  from 
another  part  of  the  room,  before  there  has  been  time  for  any  change  in  the 
other  elements.  It  is,  in  short  (as  M.  Comte  observes),  the  very  nature  of 
an  experiment,  to  introduce  into  the  pre-existing  state  of  circumstances  a 
change  perfectly  definite.  We  choose  a previous  state  of  things  with 
which  we  are  well  acquainted,  so  that  no  unforeseen  alteration  in  that  state 
is  likely  to  pass  unobserved ; and  into  this  we  introduce,  as  rapidly  as  pos- 


2S2 


INDUCTION. 


sible,  the  phenomenon  which  we  wish  to  study;  so  that  in  general  we  are 
entitled  to  feel  complete  assurance  that  the  pre-existing  state,  and  the  state 
which  we  have  produced,  differ  in  nothing  except  the  presence  or  absence 
of  that  phenomenon.  If  a bird  is  taken  from  a cage,  and  instantly  plunged 
into  carbonic  acid  gas,  the  experimentalist  may  be  fully  assured  (at  all 
events  after  one  or  two  repetitions)  that  no  circumstance  capable  of  caus- 
ing suffocation  had  supervened  in  the  interim,  except  the  change  from  im- 
mersion in  the  atmosphere  to  immersion  in  carbonic  acid  gas.  There  is 
one  doubt,  indeed,  which  may  remain  in  some  cases  of  this  description; 
the  effect  may  have  been  produced  not  by  the  change,  but  by  the  means 
employed  to  produce  the  change.  The  possibility,  however,  of  this  last 
supposition  generally  admits  of  being  conclusively  tested  by  other  experi- 
ments.* It  thus  appears  that  in  the  study  of  the  various  kinds  of  phenome- 
na which  we  can,  by  our  voluntary  agency,  modify  or  control,  we  can  in 
general  satisfy  the  requisitions  of  the  Method  of  Difference ; but  that  by 
the  spontaneous  operations  of  nature  those  requisitions  are  seldom  fulfilled. 

The  reverse  of  this  is  the  case  with  the  Method  of  Agreement.  We  do 
not  here  require  instances  of  so  special  and  determinate  a kind.  Any  in- 
stances whatever,  in  which  nature  presents  us  with  a phenomenon,  may  be 
examined  for  the  purposes  of  this  method;  and  if  all  such  instances  agree 
in  any  thing,  a conclusion  of  considerable  value  is  already  attained.  We 
can  seldom,  indeed,  be  sure  that  the  one  point  of  agreement  is  the  only 
one;  but  this  ignorance  does  not,  as  in  the  Method  of  Difference,  vitiate 
the  conclusion ; the  certainty  of  the  result,  as  far  as  it  goes,  is  not  affected. 
We  have  ascertained  one  invariable  antecedent  or  consequent,  however 
many  other  invariable  antecedents  or  consequents  may  still  remain  unas- 
certained. If  ABC,  AD E,  A FG,  are  all  equally  followed  by  a,  then  a is  an 
invariable  consequent  of  A.  If  abc,  ade,  afg,  all  number  A among  their 
antecedents,  then  A is  connected  as  an  antecedent,  by  some  invariable  law, 
with  a.  But  to  determine  whether  this  invariable  antecedent  is  a cause, 
or  this  invariable  consequent  an  effect,  we  must  be  able,  in  addition,  to 
produce  the  one  by  means  of  the  other ; or,  at  least,  to  obtain  that  which 
alone  constitutes  our  assurance  of  having  produced  any  thing,  namely,  an 
instance  in  which  the  effect,  a,  has  come  into  existence,  with  no  other 
change  in  the  pre-existing  circumstances  than  the  addition  of  A.  And 
this,  if  we  can  do  it,  is  an  application  of  the  Method  of  Difference,  not  of 
the  Method  of  Agreement. 

It  thus  appears  to  be  by  the  Method  of  Difference  alone  that  we  can 
ever,  in  the  way  of  direct  experience,  arrive  with  certainty  at  causes.  The 
Method  of  Agreement  leads  only  to  laws  of  phenomena  (as  some  writers 
call  them,  but  improperly,  since  laws  of  causation  are  also  laws  of  phenom- 
ena) : that  is,  to  uniformities,  which  either  are  not  laws  of  causation,  or  in 
which  the  question  of  causation  must  for  the  present  remain  undecided. 
The  Method  of  Agreement  is  chiefly  to  be  resorted  to,  as  a means  of  sug- 
gesting applications  of  the  Method  of  Difference  (as  in  the  last  example 
the  comparison  of  ABC,  ADE,AFG,  suggested  that  A was  the  ante- 
cedent on  which  to  try  the  experiment  whether  it  could  produce  a) ; or 
as  an  inferior  resource,  in  case  the  Method  of  Difference  is  impracticable; 
which,  as  we  before  showed,  generally  arises  from  the  impossibility  of  ar- 
tificially producing  the  phenomena.  And  hence  it  is  that  the  Method  of 
Agreement,  though  applicable  in  principle  to  either  case,  is  more  emphat- 
ically the  method  of  investigation  on  those  subjects  where  artificial  experi- 
mentation is  impossible ; because  on  those  it  is,  generally,  our  only  resource 


THE  FOUR  EXPERIMENTAL  METHODS. 


283 


of  a directly  inductive  nature;  while,  in  the  phenomena  which  we  can 
produce  at  pleasure,  the  Method  of  Difference  generally  affords  a more 
efficacious  process,  which  will  ascertain  causes  as  well  as  mere  laws. 

§ 4.  There  are,  however,  many  cases  in  which,  though  our  power  of 
producing  the  phenomenon  is  complete,  the  Method  of  Difference  either 
can  not  be  made  available  at  all,  or  not  without  a previous  employment  of 
the  Method  of  Agreement.  This  occurs  when  the  agency  by  which  we 
can  produce  the  phenomenon  is  not  that  of  one  single  antecedent,  but  a 
combination  of  antecedents,  which  we  have  no  power  of  separating  from 
each  other,  and  exhibiting  apart.  For  instance,  suppose  the  subject  of 
inquiry  to  be  the  cause  of  the  double  refraction  of  light.  We  can  produce 
this  phenomenon  at  pleasure,  by  employing  any  one  of  the  many  substances 
which  are  known  to  refract  light  in  that  peculiar  manner.  But  if,  taking- 
one  of  those  substances,  as  Iceland  spar,  for  example,  we  wish  to  determine 
on  which  of  the  properties  of  Iceland  sjjar  this  remarkable  phenomenon 
depends,  we  can  make  no  use,  for  that  purpose,  of  the  Method  of  Differ- 
ence ; for  we  can  not  find  another  substance  precisely  resembling  Iceland 
spar  except  in  some  one  property.  The  only  mode,  therefore,  of  prosecu- 
ting this  inquiry  is  that  afforded  by  the  Method  of  Agreement ; by  which, 
in  fact,  through  a comparison  of  all  the  known  substances  which  have  the 
property  of  doubly  refracting  light,  it  was  ascertained  that  they  agree  in 
the  circumstance  of  being  crystalline  substances ; and  though  the  converse 
does  not  hold,  though  all  crystalline  substances  have  not  the  property  of 
double  refraction,  it  was  concluded,  with  reason,  that  there  is  a real  con- 
nection between  these  two  properties;  that  either  crystalline  structure,  or 
the  cause  which  gives  rise  to  that  structure,  is  one  of  the  conditions  of 
double  refraction. 

Out  of  this  employment  of  the  Method  of  Agreement  arises  a peculiar 
modification  of  that  method,  which  is  sometimes  of  great  avail  in  the  in- 
vestigation of  nature.  In  cases  similar  to  the  above,  in  which  it  is  not 
possible  to  obtain  the  precise  pair  of  instances  which  our  second  canon 
requires  — instances  agreeing  in  every  antecedent  except  A,  or  in  every 
consequent  except  a , we  may  yet  be  able,  by  a double  employment  of  the 
Method  of  Agreement,  to  discover  in  what  the  instances  which  contain  A 
or  a differ  from  those  which  do  not. 

If  we  compare  various  instances  in  which  a occurs,  and  find  that  they  all 
have  in  common  the  circumstance  A,  and  (as  far  as  can  be  observed)  no 
other  circumstance,  the  Method  of  Agreement,  so  far,  bears  testimony  to  a 
connection  between  A and  a.  In  order  to  convert  this  evidence  of  connec- 
tion into  proof  of  causation  by  the  direct  Method  of  Difference,  we  ought 
to  be  able,  in  some  one  of  these  instances,  as  for  example,  AB  C,  to  leave 
out  A,  and  observe  whether  by  doing  so,  a is  prevented.  Now  supposing 
(what  is  often  the  case)  that  we  are  not  able  to  try  this  decisive  experi- 
ment; yet,  provided  we  can  by  any  means  discover  what  would  be  its  re- 
sult if  we  could  try  it,  the  advantage  will  be  the  same.  Suppose,  then, 
that  as  we  previously  examined  a variety  of  instances  in  which  a occurred, 
and  found  them  to  agree  in  containing  A,  so  we  now  observe  a variety  of 
instances  in  which  a does  not  occur,  and  find  them  agree  in  not  containing 
A ; which  establishes,  by  the  Method  of  Agreement,  the  same  connection 
between  the  absence  of  A and  the  absence  of  a,  which  was  before  estab- 
lished between  their  presence.  As,  then,  it  had  been  shown  that  whenever 
A is  present  a is  present,  so,  it  being  now  shown  that  when  A is  taken 


2S4 


INDUCTION. 


away  a is  removed  along  with  it,  we  have  by  the  one  proposition  ABC, 
a be,  by  the  oilier  BC,  b c,  the  positive  and  negative  instances  which  the 
Method  of  Difference  requires. 

This  method  may  be  called  the  Indirect  Method  of  Difference,  or  the 
Joint  Method  of  Agreement  and  Difference ; and  consists  in  a double  em- 
ployment of  the  Method  of  Agreement,  each  proof  being  independent  of 
the  other,  and  corroborating  it.  But  it  is  not  equivalent  to  a proof  by 
the  direct  Method  of  Difference.  For  the  requisitions  of  the  Method  of 
Difference  are  not  satisfied,  unless  we  can  be  quite  sure  either  that  the  in- 
stances affirmative  of  a agree  in  no  antecedent  whatever  but  A,  or  that  the 
instances  negative  of  a agree  in  nothing  but  the  negation  of  A.  Now,  if  it 
were  possible,  which  it  never  is,  to  have  this  assurance,  we  should  not  need 
the  joint  method;  for  either  of  the  two  sets  of  instances  separately  would 
then  be  sufficient  to  prove  causation.  This  indirect  method,  therefore,  can 
only  be  regarded  as  a great  extension  and  improvement  of  the  Method  of 
Agreement,  but  not  as  participating  in  the  more  cogent  nature  of  the  Meth- 
od of  Difference.  The  following  may  be  stated  as  its  canon  : 

Tiiied  Canon. 

If  two  or  more  instances  in  lohich  the  phenomenon  occurs  have  only 
one  circumstance  in  common , ichile  two  or  more  instances  in  which  it  does 
not  occur  have  nothing  in  common  save  the  absence  of  that  circumstance, 
the  circumstance  in  which  clone  the  two  sets  of  instances  differ,  is  the 
effect,  or  the  cause,  or  an  indispensable  part  of  the  cause,  of  the  phenomenon. 

We  shall  presently  see  that  the  Joint  Method  of  Agreement  and  Differ- 
ence constitutes,  in  another  respect  not  yet  adverted  to,  an  improvement 
upon  the  common  Method  of  Agreement,  namely,  in  being  unaffected  by 
a characteristic  imperfection  of  that  method,  the  nature  of  which  still  re- 
mains to  be  pointed  out.  But  as  we  can  not  enter  into  this  exposition 
without  introducing  a now  element  of  complexity  into  this  long  and  intri- 
cate discussion,  I shall  postpone  it  to  a subsequent  chapter,  and  shall  at 
once  proceed  to  a statement  of  two  other  methods,  which  will  complete 
the  enumeration  of  the  means  which  mankind  possess  for  exploring  the 
laws  of  nature  by  specific  observation  and  experience. 

§ 5.  The  first  of  these  has  been  aptly  denominated  the  Method  of  Resi- 
dues. Its  principle  is  very  simple.  Subducting  from  any  given  phenome- 
non all  the  portions  which,  by  virtue  of  preceding  inductions,  can  be  assigned 
to  known  causes,  the  remainder  will  be  the  effect  of  the  antecedents  which 
had  been  overlooked,  or  of  which  the  effect  was  as  yet  an  unknown  quantity. 

Suppose,  as  before,  that  we  have  the  antecedents  ABC,  followed  by  the 
consequents  ct  b c,  and  that  by  previous  inductions  (founded,  Ave  will  sup- 
pose, on  the  Method  of  Difference)  Ave  have  ascertained  the  causes  of  some 
of  these  effects,  or  the  effects  of  some  of  these  causes ; and  are  thence  ap- 
prised that  the  effect  of  A is  a,  and  that  the  effect  of  B is  b.  Subtracting 
the  sum  of  these  effects  from  the  total  phenomenon,  there  remains  c,  which 
now,  without  any  fresh  experiments,  we  may  know  to  be  the  effect  of  C. 
This  Method  of  Residues  is  in  truth  a peculiar  modification  of  the  Method 
of  Difference.  If  the  instance  ABC , abc,  could  have  been  compared 
with  a single  instance  AB ,ab,  we  should  have  proved  C to  be  the  cause 
of  c,  by  the  common  process  of  the  Method  of  Difference.  In  the  present 
case,  however,  instead  of  a single  instance  AB,  Ave  have  had  to  study  sep- 


THE  FOUR  EXPERIMENTAL  METHODS. 


285 


afately  the  causes  A and  B,  and  to  infer  from  the  effects  which  they  pro- 
duce separately  what  effect  they  must  produce  in  the  case  A B C,  where 
they  act  together.  Of  the  two  instances,  therefore,  which  the  Method  of 
Difference  requires  — the  one  positive,  the  other  negative  — the  negative 
one,  or  that  in  which  the  given  phenomenon  is  absent,  is  not  the  direct  re- 
sult of  observation  and  experiment,  but  has  been  arrived  at  by  deduction. 
As  one  of  the  forms  of  the  Method  of  Difference,  the  Method  of  Residues 
partakes  of  its  rigorous  certainty,  provided  the  previous  inductions,  those 
which  gave  the  effects  of  A and  B,  were  obtained  by  the  same  infallible 
method,  and  provided  we  are  certain  that  C is  the  only  antecedent  to 
which  the  residual  phenomenon  c can  be  referred;  the  only  agent  of  which 
we  had  not  already  calculated  and  subducted  the  effect.  But  as  we  can 
never  be  quite  certain  of  this,  the  evidence  derived  from  the  Method  of 
Residues  is  not  complete  unless  we  can  obtain  C artificially,  and  try  it  sep- 
arately, or  unless  its  agency,  when  once  suggested,  can  be  accounted  for, 
and  proved  deductively  from  known  laws. 

Even  with  these  reservations,  the  Method  of  Residues  is  one  of  the  most 
important  among  our  instruments  of  discovery.  Of  all  the  methods  of  in- 
vestigating laws  of  nature,  this  is  the  most  fertile  in  unexpected  results: 
often  informing  us  of  sequences  in  which  neither  the  cause  nor  the  effect 
were  sufficiently  conspicuous  to  attract  of  themselves  the  attention  of  ob- 
servers. The  agent  C may  be  an  obscure  circumstance,  not  likely  to  have 
been  perceived  unless  sought  for,  nor  likely  to  have  been  sought  for  until 
attention  had  been  awakened  by  the  insufficiency  of  the  obvious  causes  to 
account  for  the  whole  of  the  effect.  And  c may  be  so  disguised  by  its  in- 
termixture with  a and  b,  that  it  would  scarcely  have  presented  itself  spon- 
taneously as  a subject  of  separate  study.  Of  these  uses  of  the  method,  we 
shall  presently  cite  some-remarkable  examples.  The  canon  of  the  Method 
of  Residues  is  as  follows : 

Fourth  Canon. 

Subduct  from  any  phenomenon  such  part  as  is  known  by  previous  in- 
ductions to  be  the  effect  of  certain  antecedents , and  the  res  idue  of  the  phe- 
nomenon is  the  effect  of  the  remaining  antecedents. 

§ 6.  There  remains  a class  of  laws  which  it  is  impracticable  to  ascertain 
by  any  of  the  three  methods  which  I have  attempted  to  characterize: 
namely,  the  laws  of  those  Permanent  Causes,  or  indestructible  natural 
agents,  which  it  is  impossible  either  to  exclude  or  to  isolate;  which  we  can 
neither  hinder  from  being  present,  nor  contrive  that  they  shall  be  present 
alone.  It  would  appear  at  first  sight  that  we  could  by  no  means  separate 
the  effects  of  these  agents  from  the  effects  of  those  other  phenomena  with 
which  they  can  not  be  prevented  from  co-existing.  In  respect,  indeed,  to 
most  of  the  permanent  causes,  no  such  difficulty  exists ; since,  though  we 
can  not  eliminate  them  as  co-existing  facts,  we  can  eliminate  them  as  influ- 
encing agents,  by  simply  trying  our  experiment  in  a local  situation  beyond 
the  limits  of  their  influence.  The  pendulum,  for  example,  has  its  oscilla- 
tions disturbed  by  the  vicinity  of  a mountain:  we  remove  the  pendulum  to 
a sufficient  distance  from  the  mountain,  and  the  disturbance  ceases : from 
these  data  we  can  determine  by  the  Method  of  Difference,  the  amount  of  ef- 
fect due  to  the  mountain ; and  beyond  a certain  distance  every  thing  goes 
on  precisely  as  it  would  do  if  the  mountain  exercised  no  inlluence  what- 
ever, which,  accordingly,  we,  with  sufficient  reason,  conclude  to  be  the  fact. 


286 


INDUCTION. 


The  difficulty,  therefore,  in  applying  the  methods  already  treated  of  to 
determine  the  effects  of  Permanent  Causes,  is  confined  to  the  cases  in 
which  it  is  impossible  for  us  to  get  out  of  the  local  limits  of  their  influ- 
ence. The  pendulum  can  be  removed  from  the  influence  of  the  mountain, 
but  it  can  not  be  removed  from  the’ influence  of  the  earth : we  can  not  take 
away  the  earth  from  the  pendulum,  nor  the  pendulum  from  the  earth,  to 
ascertain  whether  it  would  continue  to  vibrate  if  the  action  which  the 
earth  exerts  upon  it  were  withdrawn.  On  what  evidence,  then,  do  we 
ascribe  its  vibrations  to  the  earth’s  influence?  Not  on  any  sanctioned  by 
the  Method  of  Difference ; for  one  of  the  two  instances,  the  negative  in- 
stance, is  wanting.  Nor  by  the  Method  of  Agreement;  for  though  all 
pendulums  agree  in  this,  that  during  their  oscillations  the  earth  is  always 
present,  why  may  we  not  as  well  ascribe  the  phenomenon  to  the  sun,  which 
is  equally  a co-existent  fact  in  all  the  experiments  ? It  is  evident  that  to 
establish  even  so  simple  a fact  of  causation  as  this,  there  was  required 
some  method  over  and  above  those  which  we  have  yet  examined. 

As  another  example,  let  us  take  the  phenomenon  Heat.  Independently 
of  all  hypothesis  as  to  the  real  nature  of  the  agency  so  called,  this  fact  is 
certain,  that  we  are  unable  to  exhaust  any  body  of  the  whole  of  its  heat. 
It  is  equally  certain  that  no  one  ever  perceived  heat  not  emanating  from  a 
body.  Being  unable,  then,  to  separate  Body  and  Heat,  we  can  not  effect 
such  a variation  of  circumstances  as  the  foregoing  three  methods  require ; 
we  can  not  ascertain,  by  those  methods,  what  portion  of  the  phenomena 
exhibited  by  any  body  is  due  to  the  heat  contained  in  it.  If  we  could  ob- 
serve a body  with  its  heat,  and  the  same  body  entirely  divested  of  heat, 
the  Method  of  Difference  would  show  the  effect  due  to  the  heat,  apart 
from  that  due  to  the  body.  If  we  could  observe  heat  under  circumstances 
agreeing  in  nothing  but  heat,  and  therefore  not  characterized  also  by  the 
presence  of  a body,  we  could  ascertain  the  effects  of  heat,  from  an  instance 
of  heat  with  a body  and  an  instance  of  heat  without  a body,  by  the  Meth- 
od of  Agreement;  or  we  could  determine  by  the  Method  of  Difference 
what  effect  was  due  to  the  body,  when  the  remainder  which  was  due  to  the 
heat  would  be  given  by  the  Method  of  Residues.  But  we  can  do  none  of 
these  things;  and  without  them  the  application  of  any  of  the  three  meth- 
ods to  the  solution  of  this  problem  would  be  illusory.  It  would  be  idle, 
for  instance,  to  attempt  to  ascertain  the  effect  of  heat  by  subtracting  from 
the  phenomena  exhibited  by  a body  all  that  is  due  to  its  other  properties; 
for  as  we  have  never  been  able  to  observe  any  bodies  without  a portion  of 
heat  in  them,  effects  due  to  that  heat  might  form  a part  of  the  very  re- 
sults which  we  were  affecting  to  subtract,  in  order  that  the  effect  of  heat 
might  be  shown  by  the  residue. 

If,  therefore,  there  were  no  other  methods  of  experimental  investigation 
than  these  three,  we  should  be  unable  to  determine  the  effects  due  to  heat 
as  a cause.  But  we  have  still  a resource.  Though  we  can  not  exclude  an 
antecedent  altogether,  we  may  be  able  to  produce,  or  nature  may  produce 
for  us  some  modification  in  it.  By  a modification  is  here  meant,  a change 
in  it  not  amounting  to  its  total  removal.  If  some  modification  in  the  an- 
tecedent A is  always  followed  by  a change  in  the  consequent  a,  the  other 
consequents  b and  c remaining  the  same;  or  vic&  versa,  if  every  change  in 
a is  found  to  have  been  preceded  by  some  modification  in  A,  none  being 
observable  in  any  of  the  other  antecedents,  we  may  safely  conclude  that  a 
is,  wholly  or  in  part,  an  effect  traceable  to  A,  or  at  least  in  some  way  con- 
nected with  it  through  causation.  For  example,  in  the  case  of  heat,  though 


THE  FOUR  EXPERIMENTAL  METHODS. 


287 


we  can  not  expel  it  altogether  from  any  body,  we  can  modify  it  in  quantity, 
we  can  increase  or  diminish  it ; and  doing  so,  we  find  by  the  various  meth- 
ods of  experimentation  or  observation  already  treated  of,  that  such  increase 
or  diminution  of  heat  is  followed  by  expansion  or  contraction  of  the  body. 
In  this  manner  we  arrive  at  the  conclusion,  otherwise  unattainable  by  us, 
that  one  of  the  effects  of  heat  is  to  enlarge  the  dimensions  of  bodies";  or, 
what  is  the  same  thing  in  other  words,  to  widen  the  distances  between  their 
particles. 

A change  in  a thing,  not  amounting  to  its  total  removal,  that  is,  a change 
which  leaves  it  still  the  same  thing  it  was,  must  be  a change  either  in  its 
quantity,  or  in  some  of  its  variable  relations  to  other  things,  of  which  va- 
riable relations  the  principal  is  its  position  in  space.  In  the  previous  ex- 
ample, the  modification  which  was  produced  in  the  antecedent  was  an  al- 
teration in  its  quantity.  Let  us  now  suppose  the  question  to  be,  what  in- 
fluence the  moon  exerts  on  the  surface  of  the  earth.  We  can  not  try  an 
experiment  in  the  absence  of  the  moon,  so  as  to  observe  what  terrestrial 
phenomena  her  annihilation  would  put  an  end  to;  but  when  we  find  that 
all  the  variations  in  the  position  of  the  moon  are  followed  by  correspond- 
ing variations  in  the  time  and  place  of  high  water,  the  place  being  always 
either  the  part  of  the  earth  which  is  nearest  to,  or  that  which  is  most  re- 
mote from,  the  moon,  we  have  ample  evidence  that  the  moon  is,  wholly  or 
partially,  the  cause  which  determines  the  tides.  It  very  commonly  hap- 
pens, as  it  does  in  this  instance,  that  the  variations  of  an  effect  are  corre- 
spondent, or  analogous,  to  those  of  its  cause ; as  the  moon  moves  farther 
toward  the  east,  the  high-water  point  does  the  same:  but  this  is  not  an  in- 
dispensable condition,  as  may  be  seen  in  the  same  example,  for  along  with 
that  high-water  point  there  is  at  the  same  instant  another  high-water  point 
diametrically  opposite  to  it,  and  which,  therefore,  of  necessity,  moves  toward 
the  west,  as  the  moon,  followed  by  the  nearer  of  the  tide  waves,  advances 
toward  the  east:  and  yet  both  these  motions  are  equally  effects  of  the 
moon’s  motion. 

That  the  oscillations  of  the  pendulum  are  caused  by  the  earth,  is  proved 
by  similar  evidence.  Those  oscillations  take  place  between  equidistant 
points  on  the  two  sides  of  a line,  which,  being  perpendicular  to  the  earth, 
varies  with  every  variation  in  the  earth’s  position,  either  in  space  or  rela- 
tively to  the  object.  Speaking  accurately,  we  only  know  by  the  method 
now  characterized,  that  all  terrestrial  bodies  tend  to  the  earth,  and  not  to 
some  unknown  fixed  point  lying  in  the  same  direction.  In  every  twenty- 
four  hours,  by  the  earth’s  rotation,  the  line  drawn  from  the  body  at  right 
angles  to  the  earth  coincides  successively  with  all  the  radii  of  a circle,  and 
in  the  course  of  six  months  the  place  of  that  circle  varies  by  nearly  two 
hundred  millions  of  miles;  yet  in  all  these  changes  of  the  earth’s  position, 
the  line  in  which  bodies  tend  to  fall  continues  to  be  directed  toward  it: 
which  proves  that  terrestrial  gravity  is  directed  to  the  earth,  and  not,  as 
was  once  fancied  by  some,  to  a fixed  point  of  space. 

The  method  by  which  these  results  were  obtained  may  be  termed  the 
Method  of  Concomitant  Variations  ; it  is  regulated  by  the  following  canon: 

Fifth  Canon. 

What  ever  phenomenon  varies  in  any  manner  whenever  another  phe- 
nomenon varies  in  some  particular  manner , is  either  a cause  or  an  effect 
of  that  phenomenon , or  is  connected  with  it  through  some  fact  of  causa- 
tion. 


28$ 


INDUCTION. 


The  last  clause  is  subjoined,  because  it  by  no  means  follows  when  two 
phenomena  accompany  each  other  in  their  variations,  that  the  one  is  cause 
and  the  other  effect.  The  same  thing  may,  and  indeed  must  happen,  sup- 
posing them  to  be  two  different  effects  of  a common  cause:  and  by  this 
method  alone  it  would  never  be  possible  to  ascertain  which  of  the  suppo- 
sitions is  the  true  one.  The  only  way  to  solve  the  doubt  would  be  that 
which  we  have  so  often  adverted  to,  viz.,  by  endeavoring  to  ascertain  wheth- 
er we  can  produce  the  one  set  of  variations  by  means  of  the  other.  In  the 
case  of  heat,  for  example,  by  increasing  the  temperature  of  a body  we  in- 
crease its  bulk,  but  by  increasing  its  bulk  we  do  not  increase  its  temper- 
ature; on  the  contrary  (as  in  the  rarefaction  of  air  under  the  receiver 
of  an  air-pump),  we  generally  diminish  it:  therefore  heat  is  not  an  effect, 
but  a cause,  of  increase  of  bulk.  If  we  can  not  ourselves  produce  the  va- 
riations, we  must  endeavor,  though  it  is  an  attempt  which  is  seldom  suc- 
cessful, to  find  them  produced  by  nature  in  some  case  in  which  the  pre- 
existing circumstances  are  perfectly  known  to  us. 

It  is  scarcely  necessary  to  say,  that  in  order  to  ascertain  the  uniform  con- 
comitance of  variations  in  the  effect  with  variations  in  the  cause,  the  same 
precautions  must  be  used  as  in  any  other  case  of  the  determination  of  an 
invariable  sequence.  We  must  endeavor  to  retain  all  the  other  anteced- 
ents unchanged,  while  that  particular  one  is  subjected  to  the  requisite  se- 
ries of  variations ; or,  in  other  words,  that  we  may  be  warranted  in  infer- 
ring causation  from  concomitance  of  variations,  the  concomitance  itself 
must  be  proved  by  the  Method  of  Difference. 

It  might  at  first  appear  that  the  Method  of  Concomitant  Variations  as- 
sumes a new  axiom,  or  law  of  causation  in  general,  namely,  that  every  mod- 
ification of  the  cause  is  followed  by  a change  in  the  effect.  And  it  does 
usually  happen  that  when  a phenomenon  A causes  a phenomenon  «,  any 
variation  in  the  quantity  or  in  the  various  relations  of  A,  is  uniformly  fol- 
lowed by  a variation  in  the  quantity  or  relations  of  a.  To  take  a familiar 
instance,  that  of  gravitation.  The  sun  causes  a certain  tendency  to  motion 
in  the  earth;  here  we  have  cause  and  effect;  but  that  tendency  is  toiocird 
the  sun,  and  therefore  varies  in  direction  as  the  sun  varies  in  the  relation 
of  position ; and,  moreover,  the  tendency  varies  in  intensity,  in  a certain 
numerical  correspondence  to  the  sun’s  distance  from  the  earth,  that  is,  ac- 
cording to  another  relation  of  the  sun.  Thus  we  see  that  there  is  not 
only  an  invariable  connection  between  the  sun  and  the  earth’s  gravitation, 
but  that  two  of  the  relations  of  the  sun,  its  position  with  respect  to  the 
earth  and  its  distance  from  the  earth,  are  invariably  connected  as  anteced- 
ents with  the  quantity  and  direction  of  the  earth’s  gravitation.  The  cause 
of  the  earth’s  gravitating  at  all,  is  simply  the  sun  ; but  the  cause  of  its 
gravitating  with  a given  intensity  and  in  a given  direction,  is  the  existence 
of  the  sun  in  a given  direction  and  at  a given  distance.  It  is  not  strange 
that  a modified  cause,  which  is  in  truth  a different  cause,  should  produce  a 
different  effect. 

Although  it  is  for  the  most  part  true  that  a modification  of  the  cause  is 
followed  by  a modification  of  the  effect,  the  Method  of  Concomitant  Varia- 
tions does  not,  however,  presuppose  this  as  an  axiom.  It  only  requires 
the  converse  proposition : that  any  thing  on  whose  modifications,  modifi- 
cations of  an  effect  are  invariably  consequent,  must  be  the  cause  (or  con- 
nected with  the  cause)  of  that  effect;  a proposition,  the  truth  of  which  is 
evident;  for  if  the  thing  itself  had  no  influence  on  the  effect,  neither  could 
the  modifications  of  the  thing  have  any  influence.  If  the  stars  have  no 


THE  FOUR  EXPERIMENTAL  METHODS. 


289 


power  over  the  fortunes  of  mankind,  it  is  implied  in  the  very  terms  that 
the  conjunctions  or  oppositions  of  different  stars  can  have  no  such  power. 

Although  the  most  striking  applications  of  the  Method  of  Concomitant 
Variations  take  place  in  the  cases  in  which  the  Method  of  Difference, 
strictly  so  called,  is  impossible,  its  use  is  not  confined  to  those  cases ; it 
may  often  usefully  follow  after  the  Method  of  Difference,  to  give  addition- 
al precision  to  a solution  which  that  has  found.  When  by  tfie  Method  of 
Difference  it  has  first  been  ascertained  that  a certain  object  produces  a 
certain  effect,  the  Method  of  Concomitant  Variations  may  be-  usefully  call- 
ed in,  to  determine  according  to  what  law  the  quantity  or  the  different  re- 
lations of  the  effect  follow  those  of  the  cause. 

§ V.  The  case  in  which  this  method  admits  of  the  most  extensive  em- 
ployment, is  that  in  which  the  variations  of  the  cause  are  variations  of 
quantity.  Of  such  variations  we  may  in  general  affirm,  with  safety,  that 
they  will  be  attended  not  only  with  variations,  but  with  similar  variations, 
of  the  effect : the  proposition  that  more  of  the  cause  is  followed  by  more 
of  the  effect,  being  a corollary  from  the  principle  of  the  Composition  of 
Causes,  which,  as  we  have  seen,  is  the  general  rule  of  causation ; cases  of 
the  opposite  description,  in  which  causes  change  their  properties  on  being- 
conjoined  with  one  another,  being,  on  the  contrary,  special  and  exceptional. 
Suppose,  then,  that  when  A changes  in  quantity,  a also  changes  in  quantity, 
and  in  such  a manner  that  we  can  trace  the  numerical  relation  which  the 
changes  of  the  one  bear  to  such  changes  of  the  other  as  take  place  within 
our  limits  of  observation.  We  may  then,  with  certain  precautions,  safely 
conclude  that  the  same  numerical  relation  will  hold  beyond  those  limits. 
If,  for  instance,  we  find  that  when  A is  double,  a is  double ; that  when  A is 
treble  or  quadruple,  a is  treble  or  quadruple;  we  may  conclude  that  if  A 
were  a half  or  a third,  a would  be  a half  or  a third,  and  finally,  that  if  A 
were  annihilated,  a would  be  annihilated  ; and  that  a is  wholly  the  effect  of 
A,  or  wholly  the  effect  of  the  same  cause  with  A.  And  so  with  any  other 
numerical  relation  according  to  which  A and  a would  vanish  simultaneous- 
ly ; as,  for  instance,  if  a were  proportional  to  the  square  of  A.  If,  on  the 
other  hand,  a is  not  wholly  the  effect  of  A,  but  yet  varies  when  A varies,  it 
is  probably  a mathematical  function  not  of  A alone,  but  of  A and  something 
else : its  changes,  for  example,  may  be  such  as  would  occur  if  part  of  it  re- 
mained constant,  or  varied  on  some  other  principle,  and  the  remainder  va- 
ried in  some  numerical  relations  to  the  variations  of  A.  In  that  case,  when 
A diminishes,  a will  be  seen  to  approach  not  toward  zero,  but  toward  some 
other  limit;  and  when  the  series  of  variations  is  such  as  to  indicate  what 
that  limit  is,  if  constant,  or  the  law  of  its  variation,  if  variable,  the  limit 
will  exactly  measure  how  much  of  a is  the  effect  of  some  other  and  inde- 
pendent cause,  and  the  remainder  will  be  the  effect  of  A (or  of  the  cause 
of  A). 

These  conclusions,  however,  must  not  be  drawn  without  certain  precau- 
tions. In  the  first  place,  the  possibility  of  drawing  them  at  all,  manifestly 
supposes  that  we  are  acquainted  not  only  with  the  variations,  but  with  the 
absolute  quantities  both  of  A and  a.  If  we  do  not  know  the  total  quan- 
tities, we  can  not,  of  course,  determine  the  real  numerical  relation  according 
to  which  those  quantities  vary.  It  is,  therefore,  an  error  to  conclude,  as 
some  have  concluded,  that  because  increase  of  heat  expands  bodies,  that 
is,  increases  the  distance  between  their  particles,  therefore  the  distance  is 
wholly  the  effect  of  heat,  and  that  if  we  could  entirely  exhaust  the  body  of 

19 


290 


INDUCTION. 


its  heat,  the  particles  would  be  in  complete  contact.  This  is  no  move  than 
a guess,  and  of  the  most  hazardous  sort,  not  a legitimate  induction : for 
since  we  neither  know  how  much  heat  there  is  in  any  body,  nor  what  is 
the  real  distance  between  any  two  of  its  particles,  we  can  not  judge  whether 
the  contraction  of  the  distance  does  or  does  not  follow  the  diminution  of 
the  quantity  of  heat  according  to  such  a numerical  relation  that  the  two 
quantities  would  vanish  simultaneously. 

In  contrast  with  this,  let  us  consider  a case  in  which  the  absolute  quan- 
tities are  known;  the  case  contemplated  in  the  first  law  of  motion:  viz., 
that  all  bodies  in  motion  continue  to  move  in  a straight  line  with  uniform 
velocity  until  acted  upon  by  some  new  force.  This  assertion  is  in  open  op- 
position to  first  appearances;  all  terrestrial  objects,  when  in  motion,  grad- 
ually abate  their  velocity,  and  at  last  stop;  which  accordingly  the  ancients, 
with  their  incluctio  per  enumerationem  simplicem,  imagined  to  be  the  law. 
Every  moving  body,  however,  encounters  various  obstacles,  as  friction,  the 
resistance  of  the  atmosphere,  etc.,  which  we  know  by  daily  experience  to 
be  causes  capable  of  destroying  motion.  It  was  suggested  that  the  whole 
of  the  retardation  might  be  owing  to  these  causes.  How  was  this  in- 
quired into  ? If  the  obstacles  could  have  been  entirely  removed,  the  case 
would  have  been  amenable  to  the  Method  of  Difference.  They  could  not 
be  removed,  they  could  only  be  diminished,  and  the  case,  therefore,  ad- 
mitted only  of  the  Method  of  Concomitant  Variations.  This  accordingly 
being  employed,  it  was  found  that  every  diminution  of  the  obstacles  di- 
minished the  retardation  of  the  motion : and  inasmuch  as  in  this  case  (un- 
like the  case  of  heat)  the  total  quantities  both  of  the  antecedent  and  of  the 
consequent  were  known,  it  was  practicable  to  estimate,  with  an  approach 
to  accuracy,  both  the  amount  of  the  retardation  and  the  amount  of  the 
retarding  causes,  or  resistances,  and  to  judge  how  near  they  both  were  to 
being  exhausted ; and  it  appeared  that  the  effect  dwindled  as  rapidly,  and 
at  each  step  was  as  far  on  the  road  toward  annihilation,  as  the  cause  was. 
The  simple  oscillation  of  a weight  suspended  from  a fixed  point,  and 
moved  a little  out  of  the  perpendicular,  which  in  ordinary  circumstances 
lasts  but  a few  minutes,  was  prolonged  in  Borda’s  experiments  to  more  than 
thirty  hours,  by  diminishing  as  much  as  possible  the  friction  at  the  point 
of  suspension,  and  by  making  the  body  oscillate  in  a space  exhausted  as 
nearly  as  possible  of  its  air.  There  coidd  therefore  be  no  hesitation  in  as- 
signing the  whole  of  the  retardation  of  motion  to  the  influence  of  the  ob- 
stacles ; and  since,  after  subducting  this  retardation  from  the  total  phenom- 
enon, the  remainder  was  a uniform  velocity,  the  result  was  the  proposition 
known  as  the  first  law  of  motion. 

There  is  also  another  characteristic  uncertainty  affecting  the  inference 
that  the  law  of  variation  which  the  quantities  observe  within  our  limits  of 
observation,  will  hold  beyond  those  limits.  There  is,  of  course,  in  the  first 
instance,  the  possibility  that  beyond  the  limits,  and  in  circumstances  there- 
fore of  which  we  have  no  direct  experience,  some  counteracting  cause 
might  develop  itself ; either  a new  agent  or  a new  property  of  the  agents 
concerned,  which  lies  dormant  in  the  circumstances  we  are  able  to  observe. 
This  is  an  element  of  uncertainty  which  enters  largely  into  all  our  predic- 
tions of  effects;  but  it  is  not  peculiarly  applicable  to  the  Method  of  Con- 
comitant Variations.  The  uncertainty,  however,  of  which  I am  about  to 
speak,  is  characteristic  of  that  method;  especially  in  the  cases  in  which 
the  extreme  limits  of  our  observation  are  very  narrow,  in  comparison  with 
the  possible  variations  in  the  quantities  of  the  phenomena.  Any  one  who 


THE  FOUR  EXPERIMENTAL  METHODS. 


291 


has  the  slightest  acquaintance  with  mathematics,  is  aware  that  very  differ- 
ent laws  of  variation  may  produce  numerical  results  which  differ  but  slight- 
ly from  one  another  within  narrow  limits;  and  it  is  often  only  when  the 
absolute  amounts  of  variation  are  considerable,  that  the  difference  between 
the  results  given  by  one  law  and  by  another  becomes  appreciable.  When, 
therefore,  such  variations  in  the  quantity  of  the  antecedents  as  we  have  the 
means  of  observing  are  small  in  comparison  with  the  total  quantities,  there 
is  much  danger  lest  we  should  mistake  the  numerical  law,  and  be  led  to 
miscalculate  the  variations  which  would  take  place  beyond  the  limits;  a 
miscalculation  which  would  vitiate  any  conclusion  respecting  the  depend- 
ence of  the  effect  upon  the  cause,  that  could  be  founded  on  those  varia- 
tions. Examples  are  not  wanting  of  such  mistakes.  “The  formulae,”  says 
Sir  John  Herschel,*  “ which  have  been  empirically  deduced  for  the  elas- 
ticity of  steam  (till  very  recently),  and  those  for  the  resistance  of  fluids,  and 
other  similar  subjects,”  when  relied  on  beyond  the  limits  of  the  observa- 
tions from  which  they  were  deduced,  “ have  almost  invariably  failed  to  sup- 
port the  theoretical  structures  which  have  been  erected  on  them.” 

In  this  uncertainty,  the  conclusion  we  may  draw  from  the  concomitant 
variations  of  a and  A,  to  the  existence  of  an  invariable  and  exclusive  con- 
nection between  them,  or  to  the  permanency  of  the  same  numerical  relation 
between  their  variations  when  the  quantities  are  much  greater  or  smaller 
than  those  which  we  have  had  the  means  of  observing,  can  not  be  consider- 
ed to  rest  on  a complete  induction.  All  that  in  such  a case  can  be  regard- 
ed as  proved  on  the  subject  of  causation  is,  that  there  is  some  connection 
between  the  two  phenomena;  that  A,  or  something  which  can  influence  A, 
must  be  one  of  the  causes  which  collectively  determine  a.  We  may,  how- 
ever, feel  assured  that  the  relation  which  we  have  observed  to  exist  be- 
tween the  variations  of  A and  a,  will  hold  true  in  all  cases  which  fall  be- 
tween the  same  extreme  limits;  that  is,  wherever  the  utmost  increase  or 
diminution  in  which  the  result  has  been  found  by  observation  to  coincide 
with  the  law,  is  not  exceeded. 

The  four  methods  which  it  has  now  been  attempted  to  describe,  are  the 
only  possible  modes  of  experimental  inquiry — of  direct  induction  a poste- 
riori, as  distinguished  from  deduction  : at  least,  I know  not,  nor  am  able  to 
imagine  any  others.  And  even  of  these,  the  Method  of  Residues,  as  we 
have  seen,  is  not  independent  of  deduction;  though,  as  it  also  requires 
specific  experience,  it  may,  without  impropriety,  be  included  among  meth- 
ods of  direct  observation  and  experiment. 

These,  then,  with  such  assistance  as  can  be  obtained  from  Deduction, 
compose  the  available  resources  of  the  human  mind  for  ascertaining  the 
laws  of  the  succession  of  phenomena.  Before  {proceeding  to  point  out  cer- 
tain circumstances  by  which  the  employment  of  these  methods  is  subjected 
to  an  immense  increase  of  complication  and  of  difficulty,  it  is  expedient  to 
illustrate  the  use  of  the  methods,  by  suitable  examples  drawn  from  actual 
physical  investigations.  These,  accordingly,  will  form  the  subject  of  the 
succeeding  chapter. 

* Discourse  on  the  Study  of  Natural  Philosophy , p.  179. 


292 


INDUCTION. 


CHAPTER  IX. 

MISCELLANEOUS  EXAMPLES  OF  THE  FOUR  METHODS. 

§ 1.  I shall  select,  as  a first  example,  an  interesting  speculation  of  one 
of  the  most  eminent  of  theoretical  chemists,  Baron  Liebig.  The  object  in 
view  is  to  ascertain  the  immediate  cause  of  the  death  produced  by  metal- 
lic poisons. 

Arsenious  acid,  and  the  salts  of  lead,  bismuth,  copper,  and  mercury,  if 
introduced  into  the  animal  organism,  except  in  the  smallest  doses,  destroy 
life.  These  facts  have  long  been  known,  as  insulated  truths  of  the  lowest 
order  of  generalization  ; but  it  was  reserved  for  Liebig,  by  an  apt  employ- 
ment of  the  first  two  of  our  methods  of  experimental  inquiry,  to  connect 
these  truths  together  by  a higher  induction,  pointing  out  what  property, 
common  to  all  these  deleterious  substances,  is  the  really  operating  cause  of 
their  fatal  effect. 

When  solutions  of  these  substances  are  placed  in  sufficiently  close  con- 
tact with  many  animal  products,  albumen,  milk,  muscular  fibre,  and  animal 
membranes,  the  acid  or  salt  leaves  the  water  in  which  it  was  dissolved, 
and  enters  into  combination  with  the  animal  substance,  which  substance, 
after  being  thus  acted  upon,  is  found  to  have  lost  its  tendency  to  sponta- 
neous decomposition,  or  putrefaction. 

Observation  also  shows,  in  cases  where  death  has  been  produced  by 
these  poisons,  that  the  parts  of  the  body  with  which  the  poisonous  sub- 
stances have  been  brought  into  contact,  do  not  afterward  putrefy. 

And,  finally,  when  the  poison  has  been  supplied  in  too  small  a quantity 
to  destroy  life,  eschars  are  produced,  that  is,  certain  superficial  portions  of 
the  tissues  are  destroyed,  which  are  afterward  thrown  off  by  the  reparative 
process  taking  place  in  the  healthy  parts. 

These  three  sets  of  instances  admit  of  being  treated  according  to  the 
Method  of  Agreement.  In  all  of  them  the  metallic  compounds  are 
brought  into  contact  with  the  substances  which  compose  the  human  or  ani- 
mal body;  and  the  instances  do  not  seem  to  agree  in  any  other  circum- 
stance. The  remaining  antecedents  are  as  different,  and  even  opposite,  as 
they  could  possibly  be  made;  for  in  some  the  animal  substances  exposed 
to  the  action  of  the  poisons  are  in  a state  of  life,  in  others  only  in  a state 
of  organization,  in  others  not  even  in  that.  And  what  is  the  result  which 
follows  in  all  the  cases?  The  conversion  of  the  animal  substance  (by  com- 
bination with  the  poison)  into  a chemical  compound,  held  together  by  so 
powerful  a force  as  to  resist  the  subsequent  action  of  the  ordinary  causes 
of  decomposition.  Now,  organic  life  (the  necessary  condition  of  sensitive 
life)  consisting  in  a continual  state  of  decomposition  and  recomposition  of 
the  different  organs  and  tissues,  whatever  incapacitates  them  for  this  de- 
composition destroys  life.  And  thus  the  proximate  cause  of  the  death  pro- 
duced by  this  description  of  poisons  is  ascertained,  as  far  as  the  Method 
of  Agreement  can  ascertain  it. 

Let  us  now  bring  our  conclusion  to  the  test  of  the  Method  of  Difference. 
Setting  out  from  the  cases  already  mentioned,  in  which  the  antecedent  is 
the  presence  of  substances  forming  with  the  tissues  a compound  incapable 


EXAMPLES  OF  THE  FOUR  METHODS. 


293 


of  putrefaction,  (and  a fortiori  incapable  of  the  chemical  actions  which 
constitute  life),  and  the  consequent  is  death,  either  of  the  whole  organism, 
or  of  some  portion  of  it ; let  us  compare  with  these  cases  other  cases,  as 
much  resembling  them  as  possible,  but  in  which  that  effect  is  not  produced. 
And,  first,  “many  insoluble  basic  salts  of  arsenious  acid  are  known  not  to 
be  poisonous.  The  substance  called  alkargen,  discovered  by  Bunsen,  which 
contains  a very  large  quantity  of  arsenic,  and  approaches  very  closely  in 
composition  to  the  organic  arsenious  compounds  found  in  the  body,  has 
not  the  slightest  injurious  action  upon  the  organism.”  Now  when  these 
substances  are  brought  into  contact  with  the  tissues  in  any  way,  they  do 
not  combine  with  them;  they  do  not  arrest  their  progress  to  decomposi- 
tion. As  far,  therefore,  as  these  instances  go,  it  appears  that  when  the 
effect  is  absent,  it  is  by  reason  of  the  absence  of  that  antecedent  which  we 
had  already  good  ground  for  considering  as  the  proximate  cause. 

But  the  rigorous  conditions  of  the  Method  of  Difference  are  not  yet  sat- 
isfied ; for  we  can  not  be  sure  that  these  unpoisonous  bodies  agree  with 
the  poisonous  substances  in  every  property,  except  the  particular  one  of 
entering  into  a difficultly  decomposable  compound  with  the  animal  tissues. 
To  render  the  method  strictly  applicable,  we  need  an  instance,  not  of  a 
different  substance,  but  of  one  of  the  very  same  substances,  in  circum- 
stances which  would  prevent  it  from  forming,  with  the  tissues,  the  sort 
of  compound  in  question ; and  then,  if  death  does  not  follow,  our  case  is 
made  out.  Now  such  instances  are  afforded  by  the  antidotes  to  these  poi- 
sons. For  example,  in  case  of  poisoning  by  arsenious  acid,  if  hydrated 
peroxide  of  iron  is  administered,  the  destructive  agency  is  instantly  check- 
ed. Now  this  peroxide  is  known  to  combine  with  the  acid,  and  form  a 
compound,  which,  being  insoluble,  can  not  act  at  all  on  animal  tissues.  So, 
again,  sugar  is  a well-known  antidote  to  poisoning  by  salts  of  copper;  and 
sugar  reduces  those  salts  either  into  metallic  copper,  or  into  the  red  sub- 
oxide, neither  of  which  enters  into  combination  with  animal  matter.  The 
disease  called  painter’s  colic,  so  common  in  manufactories  of  white-lead,  is 
unknown  where  the  workmen  are  accustomed  to  take,  as  a preservative, 
sulphuric  acid  lemonade  (a  solution  of  sugar  rendered  acid  by  sulphuric 
acid).  Now  diluted  sulphuric  acid  has  the  property  of  decomposing  all 
compounds  of  lead  with  organic  matter,  or  of  preventing  them  from  being 
formed. 

There  is  another  class  of  instances,  of  the  nature  required  by  the  Method 
of  Difference,  which  seem  at  first  sight  to  conflict  with  the  theory.  Solu- 
ble salts  of  silver,  such  for  instance  as  the  nitrate,  have  the  same  stiffening 
antiseptic  effect  on  decomposing  animal  substances  as  corrosive  sublimate 
and  the  most  deadly  metallic  poisons ; and  when  applied  to  the  external 
parts  of  the  body,  the  nitrate  is  a powerful  caustic,  depriving  those  parts  of 
all  active  vitality,  and  causing  them  to  be  thrown  off  by  the  neighboring 
living  structures,  in  the  form  of  an  eschar.  The  nitrate  and  the  other 
salts  of  silver  ought,  then,  it  would  seem,  if  the  theory  be  correct,  to  be 
poisonous ; yet  they  may  be  administered  internally  with  perfect  impunity. 
From  this  apparent  exception  arises  the  strongest  confirmation  which  the 
theory  has  yet  received.  Nitrate  of  silver,  in  spite  of  its  chemical  proper- 
ties, does  not  poison  when  introduced  into  the  stomach ; but  in  the  stom- 
ach, as  in  all  animal  liquids,  there  is  common  salt;  and  in  the  stomach 
there  is  also  free  muriatic  acid.  These  substances  operate  as  natural  anti- 
dotes, combining  with  the  nitrate,  and  if  its  quantity  is  not  too  great,  im- 
mediately converting  it  into  chloride  of  silver,  a substance  very  slightly 


294 


INDUCTION. 


soluble,  and  therefore  incapable  of  combining  with  the  tissues,  although  to 
the  extent  of  its  solubility  it  has  a medicinal  influence,  though  an  entirely 
different  class  of  organic  actions. 

The  preceding  instances  have  afforded  an  induction  of  a high  order  of 
conclusiveness,  illustrative  of  the  two  simplest  of  our  four  methods  ; though 
not  rising  to  the  maximum  of  certainty  which  the  Method  of  Difference, 
in  its  most  perfect  exemplification,  is  capable  of  affording.  For  (let  us 
not  forget)  the  positive  instance  and  the  negative  one  which  the  rigor  of 
that  method  requires,  ought  to  differ  only  in  the  presence  or  absence  of 
one  single  circumstance.  Now,  in  the  preceding  argument,  they  differ  in 
the  presence  or  absence  not  of  a single  circumstance , but  of  a single  sub- 
stance : and  as  every  substance  has  innumerable  properties,  there  is  no 
knowing  what  number  of  real  differences  are  involved  in  what  is  nominally 
and  apparently  only  one  difference.  It  is  conceivable  that  the  antidote, 
the  peroxide  of  iron  for  example,  may  counteract  the  poison  through  some 
other  of  its  properties  than  that  of  forming  an  insoluble  compound  with  it; 
and  if  so,  the  theory  would  fall  to  the  ground,  so  far  as  it  is  supported  by 
that  instance.  This  source  of  uncertainty,  which  is  a serious  hinderance  to 
all  extensive  generalizations  in  chemistry,  is,  however,  reduced  in  the  pres- 
ent case  to  almost  the  lowest  degree  possible,  when  we  find  that  not  only 
one  substance,  but  many  substances,  possess  the  capacity  of  acting  as  anti- 
dotes to  metallic  poisons,  and  that  all  these  agree  in  the  property  of  form- 
ing insoluble  compounds  with  the  poisons,  while  they  can  not  be  ascer- 
tained to  agree  in  any  other  property  whatsoever.  We  have  thus,  in  favor 
of  the  theory,  all  the  evidence  which  can  be  obtained  by  what  we  termed 
the  Indirect  Method  of  Difference,  or  the  Joint  Method  of  Agreement  and 
Difference;  the  evidence  of  which,  though  it  never  can  amount  to  that  of 
the  Method  of  Difference  properly  so  called,  may  approach  indefinitely  near 
to  it. 


§ 2.  Let  the  object  be*  to  ascertain  the  law  of  what  is  termed  induced 
electricity;  to  find  under  what  conditions  any  electrified  body,  whether 
positively  or  negatively  electrified,  gives  rise  to  a contrary  electric  state  in 
some  other  body  adjacent  to  it. 

The  most  familiar  exemplification  of  the  phenomenon  to  be  investigated 
is  the  following.  Around  the  prime  conductors  of  an  electrical  machine 
the  atmosphere  to  some  distance,  or  any  conducting  surface  suspended  in 
that  atmosphere,  is  found  to  be  in  an  electric  condition  opposite  to  that  of 
the  prime  conductor  itself.  Near  and  around  the  positive  prime  conductor 
there  is  negative  electricity,  and  near  and  around  the  negative  prime  con- 
ductor there  is  positive  electricity.  When  pith  balls  are  brought  near  to 
either  of  the  conductors,  they  become  electrified  with  the  opposite  electric- 
ity to  it;  either  receiving  a share  from  the  already  electrified  atmosphere 
by  conduction,  or  acted  upon  by  the  direct  inductive  influence  of  the  con- 
ductor itself:  they  are  then  attracted  by  the  conductor  to  which  they  are 
in  opposition ; or,  if  withdrawn  in  their  electrified  state,  they  will  be  at- 
tracted by  any  other  oppositely  charged  body.  In  like  manner  the  hand, 
if  brought  near  enough  to  the  conductor,  receives  or  gives  an  electric  dis- 
charge ; now  we  have  no  evidence  that  a charged  conductor  can  be  sud- 
denly discharged  unless  by  the  approach  of  a body  oppositely  electrified. 

* For  this  speculation,  as  for  many  other  of  my  scientific  illustrations,  I am  indebted  to 
Professor  Bain,  whose  subsequent  treatise  on  Logic  abounds  with  apt  illustrations  of  all  the 
inductive  methods. 


EXAMPLES  OE  THE  FOUR  METHODS. 


295 


In  the  case,  therefore,  of  the  electric  machine,  it  appears  that  the  accumula- 
tion of  electricity  in  an  insulated  conductor  is  always  accompanied  by  the 
excitement  of  the  contrary  electricity  in  the  surrounding  atmosphere,  and 
in  every  conductor  placed  near  the  former  conductor.  It  does  not  seem 
possible,  in  this  case,  to  produce  one  electricity  by  itself. 

Let  us  now  examine  all  the  other  instances  which  we  can  obtain,  resem- 
bling this  instance  in  the  given  consequent,  namely,  the  evolution  of  an  op- 
posite electricity  in  the  neighborhood  of  an  electrified  body.  As  one  re- 
markable instance  we  have  the  Leyden  jar;  and  after  the  splendid  experi- 
ments of  Faraday  in  complete  and  final  establishment  of  the  substantial 
identity  of  magnetism  and  electricity,  we  may  cite  the  magnet,  both  the 
natural  and  the  electro-magnet,  in  neither  of  which  it  is  possible  to  produce 
one  kind  of  electricity  by  itself,  or  to  charge  one  pole  without  charging  an 
opposite  pole  with  the  contrary  electricity  at  the  same  time.  We  can  not 
have  a magnet  with  one  pole:  if  we  break  a natural  loadstone  into  a thou- 
sand pieces,  each  piece  will  have  its  two  oppositely  electrified  poles  com- 
plete within  itself.  In  the  voltaic  circuit,  again,  we  can  not  have  one  cur- 
rent without  its  opposite.  In  the  ordinary  electric  machine,  the  glass  cyl- 
inder or  plate,  and  the  rubber,  acquire  opposite  electricities. 

F rom  all  these  instances,  treated  by  the  Method  of  Agreement,  a general 
law  appears  to  result.  The  instances  embrace  all  the  known  modes  in 
which  a body  can  become  charged  with  electricity ; and  in  all  of  them 
there  is  found,  as  a concomitant  or  consequent,  the  excitement  of  the  op- 
posite electric  state  in  some  other  body  or  bodies.  It  seems  to  follow  that 
the  two  facts  are  invariably  connected,  and  that  the  excitement  of  electric- 
ity in  any  body  has  for  one  of  its  necessary  conditions  the  possibility  of 
a simultaneous  excitement  of  the  opposite  electricity  in  some  neighbor- 
ing body. 

As  the  two  contrary  electricities  can  only  be  produced  together,  so  they 
can  only  cease  together.  This  may  be  shown  by  an  application  of  the  Meth- 
od of  Difference  to  the  example  of  the  Leyden  jar.  It  needs  scarcely  be 
here  remarked  that  in  the  Leyden  jar,  electricity  can  be  accumulated  and 
retained  in  considerable  quantity,  by  the  contrivance  of  having  two  conduct- 
ing surfaces  of  equal  extent,  and  parallel  to  each  other  through  the  whole 
of  that  extent,  with  a non-conducting  substance  such  as  glass  between  them. 
When  one  side  of  the  jar  is  charged  positively,  the  other  is  charged  nega- 
tively, and  it  was  by  virtue  of  this  fact  that  the  Leyden  jar  served  just  now 
as  an  instance  in  our  employment  of  the  Method  of  Agreement.  Now  it 
is  impossible  to  discharge  one  of  the  coatings  unless  the  other  can  be  dis- 
charged at  the  same  time.  A conductor  held  to  the  positive  side  can  not  con- 
vey away  any  electricity  unless  an  equal  quantity  be  allowed  to  pass  from 
the  negative  side : if  one  coating  be  perfectly  insulated,  the  charge  is  safe. 
The  dissipation  of  one  must  proceed  pari  passu  with  that  of  the  other. 

The  law  thus  strongly  indicated  admits  of  corroboration  by  the  Method 
of  Concomitant  Variations.  The  Leyden  jar  is  capable  of  receiving  a much 
higher  charge  than  can  ordinarily  be  given  to  the  conductor  of  an  electrical 
machine.  Now  in  the  case  of  the  Leyden  jar,  the  metallic  surface  which 
receives  the  induced  electricity  is  a conductor  exactly  similar  to  that  which 
receives  the  primary  charge,  and  is  therefore  as  susceptible  of  receiving 
and  retaining  the  one  electricity,  as  the  opposite  surface  of  receiving  and 
retaining  the  other ; but  in  the  machine,  the  neighboring  body  which  is  to 
be  oppositely  electrified  is  the  surrounding  atmosphere,  or  any  body  casu- 
ally brought  near  to  the  conductor ; and  as  these  are  generally  much  in- 


206 


INDUCTION. 


ferior  in  their  capacity  of  becoming  electrified,  to  the  conductor  itself,  theif 
limited  power  imposes  a corresponding  limit  to  the  capacity  of  the  con- 
ductor for  being  charged.  As  the  capacity  of  the  neighboring  body  for 
supporting  the  opposition  increases, a higher  charge  becomes  possible:  and 
to  this  appears  to  be  owing  the  great  superiority  of  the  Leyden  jar. 

A further  and  most  decisive  confirmation  by  the  Method  of  Difference, 
is  to  be  found  in  one  of  Faraday’s  experiments  in  the  course  of  his  re- 
searches on  the  subject  of  Induced  Electricity. 

Since  common  or  machine  electricity,  and  voltaic  electricity,  may  be  con- 
sidered for  the  present  purpose  to  be  identical,  Faraday  wished  to  know 
whether,  as  the  prime  conductor  develops  opposite  electricity  upon  a con- 
ductor in  its  vicinity,  so  a voltaic  current  running  along  a wire  would  in- 
duce an  opposite  current  upon  another  wire  laid  parallel  to  it  at  a short 
distance.  Now  this  case  is  similar  to  the  cases  previously  examined,  in 
every  circumstance  except  the  one  to  which  we  have  ascribed  the  effect. 
We  found  in  the  former  instances  that  whenever  electricity  of  one  kind 
was  excited  in  one  body,  electricity  of  the  opposite  kind  must  be  excited 
in  a neighboring  body.  But  in  Faraday’s  experiment  this  indispensable 
opposition  exists  within  the  wire  itself.  From  the  nature  of  a voltaic 
charge,  the  two  opposite  currents  necessary  to  the  existence  of  each  other 
are  both  accommodated  in  one  wire;  and  there  is  no  need  of  another  wire 
placed  beside  it  to  contain  one  of  them,  in  the  same  way  as  the  Leyden  jar 
must  have  a positive  and  a negative  surface.  The  exciting  cause  can  and 
does  produce  all  the  effect  which  its  laws  require,  independently  of  any 
electric  excitement  of  a neighboring  body.  Now  the  result  of  the  experi- 
ment with  the  second  wire  was,  that  no  opposite  current  was  produced. 
There  was  an  instantaneous  effect  at  the  closing  and  breaking  of  the  vol- 
taic circuit;  electric  inductions  appeared  when  the  two  wires  were  moved 
to  and  from  one  another;  but  these  are  phenomena  of  a different  class. 
There  was  no  induced  electricity  in  the  sense  in  which  this  is  predicated 
of  the  Leyden  jar;  there  was  no  sustained  current  running  up  the  one 
wire  while  an  opposite  current  ran  down  the  neighboring  wire ; and  this 
alone  would  have  been  a true  parallel  case  to  the  other. 

It  thus  appears  by  the  combined  evidence  of  the  Method  of  Agreement, 
the  Method  of  Concomitant  Variations,  and  the  most  rigorous  form  of  the 
Method  of  Difference,  that  neither  of  the  two  kinds  of  electricity  can  be 
excited  without  an  equal  excitement  of  the  other  and  opposite  kind : that 
both  are  effects  of  the  same  cause  ; that  the  possibility  of  the  one  is  a con- 
dition of  the  possibility  of  the  other,  and  the  quantity  of  the  one  an  im- 
passable limit  to  the  quantity  of  the  other.  A scientific  result  of  consider- 
able interest  in  itself,  and  illustrating  those  three  methods  in  a manner 
both  characteristic  and  easily  intelligible.* 

§ 3.  Our  third  example  shall  be  extracted  from  Sir  John  Herschel’s  Dis- 

* This  view  of  the  necessary  co-existence  of  opposite  excitements  involves  a great  extension 
of  the  original  doctrine  of  two  electricities.  The  early  theorists  assumed  that,  when  amber 
was  rubbed,  the  amber  was  made  positive  and  the  rubber  negative  to  the  same  degree ; but  it 
never  occurred  to  them  to  suppose  that  the  existence  of  the  amber  charge  was  dependent  on 
an  opposite  charge  in  the  bodies  with  which  the  amber  was  contiguous,  while  the  existence 
of  the  negative  charge  on  the  rubber  was  equally  dependent  on  a contrary  state  of  the  sur- 
faces that  might  accidentally  be  confronted  with  it ; that,  in  fact,  in  a case  of  electrical  ex- 
citement by  friction,  four  charges  were  the  minimum  that  could  exist.  But  tins  double  elec- 
trical action  is  essentially  implied  in  the  explanation  now  universally  adopted  in  regard  to 
the  phenomena  of  the  common  electric  machine. 


EXAMPLES  OF  THE  FOUR  METHODS. 


297 


course  on  the  Study  of  Natural  Philosophy , a work  replete  with  happily- 
selected  exemplifications  of  inductive  processes  from  almost  every  depart- 
ment of  physical  science,  and  in  which  alone,  of  all  books  which  I have  met 
with,  the  four  methods  of  induction  are  distinctly  recognized,  though  not 
so  clearly  characterized  and  defined,  nor  their  correlation  so  fully  shown, 
as  has  appeared  to  me  desirable.  The  present  example  is  described  by 
Sir  John  Herschel  as  “one  of  the  most  beautiful  specimens”  which  can  be 
cited  “ of  inductive  experimental  inquiry  lying  within  a moderate  com- 
pass;” the  theory  of  dew,  first  promulgated  by  the  late  Dr.  Wells,  and  now 
universally  adopted  by  scientific  authorities.  The  passages  in  inverted 
commas  are  extracted  verbatim  from  the  Discourse.* 

“ Suppose  deio  were  the  phenomenon  proposed,  whose  cause  we  would 
know.  In  the  first  place”  we  must  determine  precisely  what  we  mean  by 
dew:  what  the  fact  really  is  whose  cause  we  desire  to  investigate.  “We 
must  separate  dew  from  rain,  and  the  moisture  of  fogs,  and  limit  the  ap- 
plication of  the  term  to  what  is  really  meant,  which  is  the  spontaneous  ap- 
pearance of  moisture  on  substances  exposed  in  the  open  air  when  no  rain 
or  visible  wet  is  falling.”  This  answers  to  a preliminary  operation  which 
will  be  characterized  in  the  ensuing  book,  treating  of  operations  subsidiary 
to  induction.! 

“Now,  here  we  have  analogous  phenomena  in  the  moisture  which  be- 
dews a cold  metal  or  stone  when  we  breathe  upon  it;  that  which  appears 
on  a glass  of  water  fresh  from  the  well  in  hot  weather ; that  which  appears 
on  the  inside  of  windows  when  sudden  rain  or  hail  chills  the  external  ^iir ; 
that  which  runs  down  our  walls  when,  after  a long  frost,  a warm,  moist 
thaw  comes  on.”  Comparing  these  cases,  we  find  that  they  all  contain  the 
phenomenon  which  was  proposed  as  the  subject  of  investigation.  Now 
“all  these  instances  agree  in  one  point,  the  coldness  of  the  object  dewed, 
in  comparison  with  the  air  in  contact  with  it.”  But  there  still  remains  the 
most  important  case  of  all,  that  of  nocturnal  dew:  does  the  same  circum- 
stance exist  in  this  case?  “Is  it  a fact  that  the  object  dewed  is  colder 
than  the  air?  Certainly  not,  one  would  at  first  be  inclined  to  say;  for 
what  is  to  make  it  so  ? But  ....  the  experiment  is  easy  : we  have  only  to 
lay  a thermometer  in  contact  with  the  dewed  substance,  and  hang  one  at  a 
little  distance  above  it,  out  of  reach  of  its  influence.  The  experiment  has 
been  therefore  made,  the  question  has  been  asked,  and  the  answer  has  been 
invariably  in  the  affirmative.  Whenever  an  object  contracts  dew,  it  is 
colder  than  the  air.” 

Here,  then,  is  a complete  application  of  the  Method  of  Agreement,  estab- 
lishing the  fact  of  an  invariable  connection  between  the  deposition  of  dew 
on  a surface,  and  the  coldness  of  that  surface  compared  with  the  external 
air.  But  which  of  these  is  cause,  and  which  effect  ? or  are  they  both  ef- 
fects of  something  else?  On  this  subject  the  Method  of  Agreement  can 
afford  us  no  light:  we  must  call  in  a more  potent  method.  “We  must 
collect  more  facts,  or,  which  comes  to  the  same  thing,  vary  the  circum- 
stances; since  every  instance  in  which  the  circumstances  differ  is  a fresh 
fact : and  especially,  we  must  note  the  contrary  or  negative  cases,  i.  e ., 
where  no  dew  is  produced:”  a comparison  between  instances  of  dew  and 
instances  of  no  dew,  being  the  condition  necessary  to  bring  the  Method  of 
Difference  into  play. 

“ Now,  first,  no  dew  is  produced  on  the  surface  of  polished  metals,  but 


Pp.  110,  111. 


t Infra,  book  iv.,  chap,  ii.,  On  Abstraction. 


29S 


INDUCTION. 


it  is  very  copiously  on  glass,  both  exposed  with  their  faces  upward,  and  in 
some  cases  the  under  side  of  a horizontal  plate  of  glass  is  also  dewed.” 
Her  e is  an  instance  in  which  the  effect  is  produced,  and  another  instance  in 
which  it  is  not  produced ; but  we  can  not  yet  pronounce,  as  the  canon  of 
the  Method  of  Difference  requires,  that  the  latter  instance  agrees  with  the 
former  in  all  its  circumstances  except  one  ; for  the  differences  between 
glass  and  polished  metals  are  manifold,  and  the  only  thing  we  can  as  yet 
be  sure  of  is,  that  the  cause  of  dew  will  be  found  among  the  circumstances 
by  which  the  former  substance  is  distinguished  from  the  latter.  But  if 
we  could  be  sure  that  glass,  and  the  various  other  substances  on  which  dew 
is  deposited,  have  only  one  quality  in  common,  and  that  polished  metals 
and  the  other  substances  on  which  dew  is  not  deposited,  have  also  nothing 
in  common  but  the  one  circumstance  of  not  having  the  one  quality  which 
the  others  have;  the  requisitions  of  the  Method  of  Difference  would  be 
completely  satisfied,  and  we  should  recognize,  in  that  quality  of  the  sub- 
stances, the  cause  of  dew.  This,  accordingly,  is  the  path  of  inquiry  which 
is  next  to  be  pursued. 

“ In  the  cases  of  polished  metal  and  polished  glass,  the  contrast  shows 
evidently  that  the  substance  has  much  to  do  with  the  phenomenon  ; there- 
fore let  the  substance  alone  be  diversified  as  much  as  possible,  by  exposing 
polished  surfaces  of  various  kinds.  This  done,  a scale  of  intensity  becomes 
obvious.  Those  polished  substances  are  found  to  be  most  strongly  dewed 
which  conduct  heat  worst;  while  those  which  conduct  heat  well,  resist  dew 
most  effectually.”  The  complication  increases  ; here  is  the  Method  of 
Concomitant  Variations  called  to  our  assistance  ; and  no  other  method  was 
practicable  on  this  occasion  ; for  the  quality  of  conducting  heat  could  not 
be  excluded,  since  all  substances  conduct  heat  in  some  degree.  The  conclu- 
sion obtained  is,  that  caster  is  paribus  the  deposition  of  dew  is  in  some  pro- 
portion to  the  power  which  the  body  possesses  of  resisting  the  passage  of 
heat;  and  that  this,  therefore  (or  something  connected  with  this),  must  be 
at  least  one  of  the  causes  which  assist  in  producing  the  deposition  of  dew 
on  the  surface. 

“But  if  we  expose  rough  surfaces  instead  of  polished,  we  sometimes  find 
this  law  interfered  with.  Thus,  roughened  iron,  especially  if  painted  over 
or  blackened,  becomes  dewed  sooner  than  varnished  paper;  the  kind  of 
surface,  therefore,  has  a great  influence.  Expose,  then,  the  same  material 
in  very  diversified  states,  as  to  surface”  (that  is,  employ  the  Method  of  Dif- 
ference to  ascertain  concomitance  of  variations),  “ and  another  scale  of  in- 
tensity becomes  at  once  apparent ; those  surfaces  which  part  with  their 
heat  most  readily  by  radiation  are  found  to  contract  dew  most  copiously.” 
Here,  therefore,  are  the  requisites  for  a second  employment  of  the  Method 
of  Concomitant  Variations  ; which  in  this  case  also  is  the  only  method 
available,  since  all  substances  radiate  heat  in  some  degree  or  other.  The 
conclusion  obtained  by  this  new  application  of  the  method  is,  that  easterns 
paribus  the  deposition  of  dew  is  also  in  some  proportion  to  the  power  of 
radiating  heat;  and  that  the  quality  of  doing  this  abundantly  (or  some 
cause  on  which  that  quality  depends)  is  another  of  the  causes  which  pro- 
mote the  deposition  of  dew  on  the  substance. 

“Again,  the  influence  ascertained  to  exist  of  substance  and  surface  leads 
us  to  consider  that  of  texture:  and  here,  again,  we  are  presented  on  trial 
with  remarkable  differences,  and  with  a third  scale  of  intensity,  pointing 
out  substances  of  a close,  firm  texture,  such  as  stones,  metals,  etc.,  as  un- 
favorable, but  those  of  a loose  one,  as  cloth,  velvet,  wool,  eider-down,  cot- 


EXAMPLES  OF  THE  FOUR  METHODS. 


299 


ton,  etc.,  as  eminently  favorable  to  the  contraction  of  dew.”  The  Method 
of  Concomitant  Variations  is  here,  for  the  third  time,  had  recourse  to; 
and,  as  before,  from  necessity,  since  the  texture  of  no  substance  is  absolute- 
ly firm  or  absolutely  loose.  Looseness  of  texture,  therefore,  or  something 
which  is  the  cause  of  that  quality,  is  another  circumstance  which  promotes 
the  deposition  of  dew;  but  this  third  course  resolves  itself  into  the  first, 
viz.,  the  quality  of  resisting  the  passage  of  heat : for  substances  of  loose 
texture  “ are  precisely  those  which  are  best  adapted  for  clothing,  or  for  im- 
peding the  free  passage  of  heat  from  the  skin  into  the  air,  so  as  to  allow 
their  outer  surfaces  to  bo  very  cold,  while  they  remain  warm  within;”  and 
this  last  is,  therefore,  an  induction  (from  fresh  instances)  simply  corrobora- 
tive, of  a former  induction. 

It  thus  appears  that  the  instances  in  which  much  dew  is  deposited,  which 
are  very  various,  agree  in  this,  and,  so  far  as  we  are  able  to  observe,' in  this 
only,  that  they  either  radiate  heat  rapidly  or  conduct  it  slowly:  qualities 
between  which  there  is  no  other  circumstance  of  agreement  than  that  by 
virtue  of  either,  the  body  tends  to  lose  heat  from  the  surface  more  rapidly 
than  it  can  be  restored  from  within.  The  instances,  on  the  contrary,  in 
which  no  dew,  or  but  a small  quantity  of  it,  is  formed,  and  which  are  also 
extremely  various,  agree  (as  far  as  we  can  observe)  in  nothing  except  in 
not  having  this  same  property.  We  seem,  therefore,  to  have  detected  the 
characteristic  difference  between  the  substances  on  which  dew  is  pro- 
duced and  those  on  which  it  is  not  produced.  And  thus  have  been  real- 
ized the  requisitions  of  what  we  have  termed  the  Indirect  Method  of  Dif- 
ference, or  the  Joint  Method  of  Agreement  and  Difference.  The  example 
afforded  of  this  indirect  method,  and  of  the  manner  in  which  the  data  are 
prepared  for  it  by  the  Methods  of  Agreement  and  of  Concomitant  Varia- 
tions, is  the  most  important  of  all  the  illustrations  of  induction  afforded  by 
this  interesting  speculation. 

We  might  now  consider  the  question,  on  what  the  deposition  of  dew  de- 
pends, to  be  completely  solved,  if  we  could  be  quite  sure  that  the  sub- 
stances on  which  dew  is  produced  differ  from  those  on  which  it  is  not,  in 
nothing  but  in  the  property  of  losing  heat  from  the  surface  faster  than  the 
loss  can  be  repaired  from  within.  And  though  we  never  can  have  that 
complete  certainty,  this  is  not  of  so  much  importance  as  might  at  first  be 
supposed ; for  we  have,  at  all  events,  ascertained  that  even  if  there  be  any 
other  quality  hitherto  unobserved  which  is  present  in  all  the  substances 
which  contract  dew,  and  absent  in  those  which  do  not,  this  other  property 
must  be  one  which,  in  all  that  great  number  of  substances,  is  present  or  ab- 
sent exactly  where  the  property  of  being  a better  radiator  than  conductor 
is  present  or  absent;  an  extent  of  coincidence  which  affords  a strong  pre- 
sumption of  a community  of  cause,  and  a consequent  invariable  co-existence 
between  the  two  properties  ; so  that  the  property  of  being  a better  radiator 
than  conductor,  if  not  itself  the  cause,  almost  certainly  always  accompanies 
the  cause,  and  for  purposes  of  prediction,  no  error  is  likely  to  be  commit- 
ted by  treating  it  as  if  it  were  really  such. 

Reverting  now  to  an  earlier  stage  of  the  inquiry,  let  us  remember  that 
we  had  ascertained  that,  in  every  instance  where  dew  is  formed,  there  is 
actual  coldness  of  the  surface  below  the  temperature  of  the  surrounding 
air;  but  we  were  not  sure  whether  this  coldness  was  the  cause  of  dew,  or 
its  effect.  This  doubt  we  are  now  able  to  resolve.  We  have  found  that,  in 
every  such  instance,  the  substance  is  one  tvhicb,  by  its  own  properties  or 
laws,  would,  if  exposed  in  the  night,  become  colder  than  the  surrounding 


300 


INDUCTION. 


air.  The  coldness,  therefore,  being  accounted  for  independently  of  the  dew, 
while  it  is  proved  that  there  is  a connection  between  the  two,  it  must  be 
the  dew  which  depends  on  the  coldness;  or,  in  other  words,  the  coldness  is 
the  cause  of  the  dew. 

This  law  of  causation,  already  so  amply  established,  admits,  however,  of 
efficient  additional  corroboration  in  no  less  than  three  ways.  First,  by  de- 
duction from  the  known  laws  of  aqueous  vapor  when  diffused  through  air 
or  any  other  gas;  and  though  we  have  not  yet  come  to  the  Deductive 
Method,  we  will  not  omit  what  is  necessary  to  render  this  speculation  com- 
plete. It  is  known  by  direct  experiment  that  only  a limited  quantity  of 
water  can  remain  suspended  in  the  state  of  vapor  at  each  degree  of  tem- 
perature, and  that  this  maximum  grows  less  and  less  as  the  temperature 
diminishes.  From  this  it  follows,  deductively,  that  if  there  is  already  as 
much  vapor  suspended  as  the  air  will  contain  at  its  existing  temperature, 
any  lowering  of  that  temperature  will  cause  a portion  of  the  vapor  to  be 
condensed,  and  become  water.  But  again,  we  know  deductively,  from  the 
laws  of  heat,  that  the  contact  of  the  air  with  a body  colder  than  itself  will 
necessarily  lower  the  temperature  of  the  stratum  of  air  immediately  ap- 
plied to  its  surface ; and  will,  therefore,  cause  it  to  part  with  a portion  of 
its  water,  which  accordingly  will,  by  the  ordinary  laws  of  gravitation  or 
cohesion,  attach  itself  to  the  surface  of  the  body,  thereby  constituting  dew. 
This  deductive  proof,  it  will  have  been  seen,  has  the  advantage  of  at  once 
proving  causation  as  well  as  co-existence ; and  it  has  the  additional  advan- 
tage that  it  also  accounts  for  the  exceptions  to  the  occurrence  of  the  phe- 
nomenon, the  cases  in  which,  although  the  body  is  colder  than  the  air,  yet 
no  dew  is  deposited  ; by  showing  that  this  will  necessarily  be  the  case 
when  the  air  is  so  under-supplied  with  aqueous  vapor,  comparatively  to  its 
temperature,  that  even  when  somewhat  cooled  by  the  contact  of  the  cold- 
er body  it  can  still  continue  to  hold  in  suspension  all  the  vapor  which  was 
previously  suspended  in  it:  thus  in  a very  dry  summer  there  are  no  dews, 
in  a very  dry  winter  no  hoar-frost.  Here,  therefore,  is  an  additional  con- 
dition of  the  production  of  dew,  which  the  methods  we  previously  made 
use  of  failed  to  detect,  and  which  might  have  remained  still  undetected,  if 
recourse  had  not  been  had  to  the  plan  of  deducing  the  effect  from  the  as- 
certained properties  of  the  agents  known  to  be  present. 

The  second  corroboration  of  the  theory  is  by  direct  experiment,  accord- 
ing to  the  canon  of  the  Method  of  Difference.  We  can,  by  cooling  the  sur- 
face of  any  body,  find  in  all  cases  some  temperature  (more  or  less  inferior 
to  that  of  the  surrounding  air,  according  to  its  hygrometric  condition)  at 
which  dew  will  begin  to  be  deposited.  Here,  too,  therefore,  the  causation 
is  directly  proved.  We  can,  it  is  true,  accomplish  this  only  on  a small 
scale,  but  we  have  ample  reason  to  conclude  that  the  same  operation,  if 
conducted  in  nature’s  great  laboratory,  would  equally  produce  the  effect. 

And,  finally,  even  on  that  great  scale  we  are  able  to  verify  the  result. 
The  case  is  one  of  those  rare  cases,  as  we  have  shown  them  to  be,  in  which 
nature  works  the  experiment  for  us  in  the  same  manner  in  which  we  our- 
selves perform  it;  introducing  into  the  previous  state  of  things  a single 
and  perfectly  definite  new  circumstance,  and  manifesting  the  effect  so  rap- 
idly that  there  is  not  time  for  any  other  material  change  in  the  pre-existing 
circumstances.  “It  is  observed  that  dew  is  never  copiously  deposited  in 
situations  much  screened  from  the  open  sky,  and  not  at  all  in  a cloudy 
night;  but  if  the  clouds  withdraw  even  for  a few  minutes , and  leave  a 
clear  opening , a deposition  of  dew  presently  begins , and  goes  on  increas- 


EXAMPLES  OF  THE  FOUR  METHODS. 


SOI 


ing. ....  Dew  formed  in  clear  intervals  will  often  even  evaporate  again 
when  the  sky  becomes  thickly  overcast.”  The  proof,  therefore,  is  complete, 
that  the  presence  or  absence  of  an  uninterrupted  communication  with  the 
sky  causes  the  deposition  or  non-deposition  of  dew.  Now,  since  a clear  sky 
is  nothing  but  the  absence  of  clouds,  and  it  is  a known  property  of  clouds,  as 
of  all  other  bodies  between  which  and  any  given  object  nothing  intervenes 
but  an  elastic  fluid,  that  they  tend  to  raise  or  keep  up  the  superficial  tem- 
perature of  the  object  by  radiating  heat  to  it,  we  see  at  once  that  the  dis- 
appearance of  clouds  will  cause  the  surface  to  cool ; so  that  nature,  in  this 
case,  produces  a change  in  the  antecedent  by  definite  and  known  means, 
and  the  consequent  follows  accordingly : a natural  experiment  which  satis- 
fies the  requisitions  of  the  Method  of  Difference.* 

The  accumulated  proof  of  which  the  Theory  of  Dew  has  been  found 
susceptible,  is  a striking  instance  of  the  fullness  of  assurance  which  the  in- 
ductive evidence  of  laws  of  causation  may  attain,  in  cases  in  which  the  in- 
variable sequence  is  by  no  means  obvious  to  a superficial  view. 

§ 4.  The  admirable  physiological  investigations  of  Dr.  Brown-Sequard 
afford  brilliant  examples  of  the  application  of  the  Inductive  Methods  to  a 
class  of  inquiries  in  which,  for  reasons  which  will  presently  be  given,  di- 
rect induction  takes  place  under  peculiar  difficulties  and  disadvantages. 
As  one  of  the  most  apt  instances,  I select  his  speculation  (in  the  proceed- 
ings of  the  Royal  Society  for  May  16,  1861)  on  the  relations  between  mus- 
cular irritability,  cadaveric  rigidity,  and  putrefaction. 

The  law  which  Dr.  Brown-Sequard’s  investigation  tends  to  establish,  is 
the  following:  “ The  greater  the  degree  of  muscular  irritability  at  the  time  of 
death,  the  later  the  cadaveric  rigidity  sets  in,  and  the  longer  it  lasts,  and  the 
later  also  putrefaction  appears,  and  the  slower  it  progresses.”  One  would 
say  at  first  sight  that  the  method  here  required  must  be  that  of  Concomi- 
tant Variations.  But  this  is  a delusive  appearance,  arising  from  the  circum- 
stance that  the  conclusion  to  be  tested  is  itself  a fact  of  concomitant  varia- 
tions. For  the  establishment  of  that  fact  any  of  the  Methods  may  be  put 
in  requisition,  and  it  will  be  found  that  the  fourth  Method,  though  really 
employed,  lias  only  a subordinate  place  in  this  particular  investigation. 

The  evidences  by  which  Dr.  Brown-Sequard  establishes  the  law  may  be 
enumerated  as  follows : 

1st.  Paralyzed  muscles  have  greater  irritability  than  healthy  muscles. 
Now,  paralyzed  muscles  are  later  in  assuming  the  cadaveric  rigidity  than 
healthy  muscles,  the  rigidity  lasts  longer,  and  putrefaction  sets  in  later,  and 
proceeds  more  slowly. 

* I must,  however,  remark,  that  this  example,  which  seems  to  militate  against  the  assertion 
we  made  of  the  comparative  inapplicability  of  the  Method  of  Difference  to  cases  of  pure  ob- 
servation, is  really  one  of  those  exceptions  which,  according  to  a proverbial  expression,  prove 
the  general  rule/  For  in  this  case,  in  which  Nature,  in  her  experiment,  seems  to  have  imi- 
tated the  type  of  the  experiments  made  by  man,  she  has  only  succeeded  in  producing  the 
likeness  of  man's  most  imperfect  experiments;  namely,  those  in  which,  though  he  succeeds 
in  producing  the  phenomenon,  he  does  so  by  employing  complex  means,  which  he  is  unable 
perfectly  to  analyze,  and  can  form,  therefore,  no  sufficient  judgment  what  portion  of  the  effects 
may  be  due,  not  to  the  supposed  cause,  but  to  some  unknown  agency  of  the  means  by  which 
that  cause  was  produced.  In  the  natural  experiment  which  we  are  speaking  of,  the  means 
used  was  the  clearing  off  a canopy  of  clouds : and  we  certainly  do  not  know  sufficiently  in 
what  this  process  consists,  or  on  what  it  depends,  to  be  certain  a priori  that  it  might  not  oper- 
ate upon  the  deposition  of  dew  independently  of  any  thermometric  effect  at  the  earth’s  surface. 
Even,  therefore,  in  a case  so  favorable  ns  this  to  Nature's  experimental  talents,  her  experiment 
is  of  little  value  except  in  corroboration  of  a conclusion  already  attained  through  other  means. 


302 


INDUCTION. 


Both  these  propositions  had  to  be  proved  by  experiment;  and  for  the 
experiments  which  prove  them,  science  is  also  indebted  to  Dr.  Brown-S6- 
quard.  The  former  of  the  two — that  paralyzed  muscles  have  greater  irri- 
tability than  healthy  muscles  — he  ascertained  in  various  ways,  but  most 
decisively  by  “comparing  the  duration  of  irritability  in  a paralyzed  muscle 
and  in  the  corresponding  healthy  one  of  the  opposite  side,  while  they  are 
both  submitted  to  the  same  excitation.”  He  “often  found,  in  experiment- 
ing in  that  way,  that  the  paralyzed  muscle  remained  irritable  twice,  three 
times,  or  even  four  times  as  long  as  the  healthy  one.”  This  is  a case  of  in- 
duction by  the  Method  of  Difference.  The  two  limbs,  being  those  of  the 
same  animal,  were  presumed  to  differ  in  no  circumstance  material  to  the 
case  except  the  paralysis,  to  the  presence  and  absence  of  which,  therefore, 
the  difference  in  the  muscular  irritability  was  to  be  attributed.  This  as- 
sumption of  complete  resemblance  in  all  material  circumstances  save  one, 
evidently  could  not  be  safely  made  in  any  one  pair  of  experiments,  because 
the  two  legs  of  any  given  animal  might  be  accidentally  in  very  different 
pathological  conditions ; but  if,  besides  taking  pains  to  avoid  any  such  dif- 
ference, the  experiment  was  repeated  sufficiently  often  in  different  animals 
to  exclude  the  supposition  that  any  abnormal  circumstance  could  be  pres- 
ent in  them  all,  the  conditions  of  the  Method  of  Difference  were  adequate- 
ly secured. 

In  the  same  manner  in  which  Dr.  Brown-Sequard  proved  that  paralyzed 
muscles  have  greater  irritability,  he  also  proved  the  correlative  proposition 
respecting  cadaveric  rigidity  and  putrefaction.  Having,  by  section  of  the 
roots  of  the  sciatic  nerve,  and  again  of  a lateral  half  of  the  spinal  cord, 
produced  paralysis  in  one  hind  leg  of  an  animal  while  the  other  remained 
healthy,  he  found  that  not  only  did  muscular  irritability  last  much  longer 
in  the  paralyzed  limb,  but  rigidity  set  in  later  and  ended  later,  and  putre- 
faction began  later  and  was  less  rapid  than  on  the  healthy  side.  This  is  a 
common  case  of  the  Method  of  Difference,  requiring  no  comment.  A fur- 
ther and  very  important  corroboration  was  obtained  by  the  same  method. 
When  the  animal  was  killed,  not  shortly  after  the  section  of  the  nerve,  but 
a month  later,  the  effect  was  reversed;  rigidity  set  in  sooner,  and  lasted  a 
shorter  time,  than  in  the  healthy  muscles.  But  after  this  lapse  of  time,  the 
paralyzed  muscles,  having  been  kept  by  the  paralysis  in  a state  of  rest,  had 
lost  a great  part  of  their  irritability,  and  instead  of  more,  had  become  less 
irritable  than  those  on  the  healthy  side.  This  gives  the  ABC,  a be,  and 
B C,  be,  of  the  Method  of  Difference.  One  antecedent,  increased  irrita- 
bility, being  changed,  and  the  other  circumstances  being  the  same,  the  con- 
sequence did  not  follow;  and,  moreover,  when  a new  antecedent,  contrary 
to  the  first,  was  supplied,  it  was  followed  by  a contrary  consequent.  This 
instance  is  attended  with  the  special  advantage  of  proving  that  the  re- 
tardation and  prolongation  of  the  rigidity  do  not  depend  directly  on  the 
paralysis,  since  that  was  the  same  in  both  the  instances  ; but  specifically  on 
one  effect  of  the  paralysis,  namely,  the  increased  irritability  ; since  they 
ceased  when  it  ceased,  and  were  reversed  when  it  was  reversed. 

2d.  Diminution  of  the  temperature  of  muscles  before  death  increases 
their  irritability.  But  diminution  of  their  temperature  also  retards  cadav- 
eric rigidity  and  putrefaction. 

Both  these  truths  were  first  made  known  by  Dr.  Brown-Sequard  himself, 
through  experiments  which  conclude  according  to  the  Method  of  Differ- 
ence. There  is  nothing  in  the  nature  of  the  process  requiring  specific 
analysis. 


EXAMPLES  OF  THE  FOUR  METHODS. 


303 


3d.  Muscular  exercise,  prolonged  to  exhaustion,  diminishes  the  muscu- 
lar irritability.  This  is  a well-known  truth,  dependent  on  the  most  gener- 
al laws  of  muscular  action,  and  proved  by  experiments  under  the  Method 
of  Difference,  constantly  repeated.  Now,  it  lias  been  shown  by  observa- 
tion that  overdriven  cattle,  if  killed  before  recovery  from  their  fatigue, 
become  rigid  and  putrefy  in  a surprisingly  short  time.  A similar  fact  has 
been  observed  in  the  case  of  animals  hunted  to  death ; cocks  killed  during 
or  shortly  after  a fight ; and  soldiers  slain  in  the  field  of  battle.  These  va- 
rious cases  agree  in  no  circumstance,  directly  connected  with  the  muscles, 
except  that  these  have  just  been  subjected  to  exhausting  exercise.  Under 
the  canon,  therefore,  of  the  Method  of  Agreement,  it  may  be  inferred  that 
there  is  a connection  between  the  two  facts.  The  Method  of  Agreement, 
indeed,  as  has  been  shown,  is  not  competent  to  prove  causation.  The  pres- 
ent case,  however,  is  already  known  to  be  a case  of  causation,  it  being  cer- 
tain that  the  state  of  the  body  after  death  must  somehow  depend  upon  its 
state  at  the  time  of  death.  We  are,  therefore,  warranted  in  concluding  that 
the  single  circumstance  in  which  all  the  instances  agree,  is  the  part  of  the 
antecedent  which  is  the  cause  of  that  particular  consequent. 

4th.  In  proportion  as  the  nutrition  of  muscles  is  in  a good  state,  their 
irritability  is  high.  This  fact  also  rests  on  the  general  evidence  of  the 
laws  of  physiology,  grounded  on  many  familiar  applications  of  the  Method 
of  Difference.  Now,  in  the  case  of  those  who  die  from  accident  or  vio- 
lence, with  their  muscles  in  a good  state  of  nutrition,  the  muscular  irrita- 
bility continues  long  after  death,  rigidity  sets  in  late,  and  persists  long 
without  the  putrefactive  change.  On  the  contrary,  in  cases  of  disease  in 
which  nutrition  has  been  diminished  for  a long  time  before  death,  all  these 
effects  are  reversed.  These  are  the  conditions  of  the  Joint  Method  of 
Agreement  and  Difference.  The  cases  of  retarded  and  long  continued 
rigidity  here  in  question  agree  only  in  being  preceded  by  a high  state  of 
nutrition  of  the  muscles;  the  cases  of  rapid  and  brief  rigidity  agree  only 
in  being  preceded  by  a low  state  of  muscular  nutrition;  a connection  is, 
therefore,  inductively  proved  between  the  degree  of  the  nutrition,  and  the 
slowness  and  prolongation  of  the  rigidity. 

5th.  Convulsions,  like  exhausting  exercise,  but  in  a still  greater  degree, 
diminish  the  muscular  irritability.  Now,  when  death  follows  violent  and 
prolonged  convulsions,  as  in  tetanus,  hydrophobia,  some  cases  of  cholera, 
and  certain  poisons,  rigidity  sets  in  very  rapidly,  and  after  a very  brief  du- 
ration, gives  place  to  putrefaction.  This  is  another  example  of  the  Meth- 
od of  Agreement,  of  the  same  character  with  No.  3. 

6th.  The  series  of  instances  which  we  shall  take  last,  is  of  a more  com- 
plex character,  and  requires  a more  minute  analysis. 

It  has  long  been  observed  that  in  some  cases  of  death  by  lightning,  ca- 
daveric rigidity  either  does  not  take  place  at  all,  or  is  of  such  extremely 
brief  duration  as  to  escape  notice,  and  that  in  these  cases  putrefaction  is 
very  rapid.  In  other  cases,  however,  the  usual  cadaveric  rigidity  appears. 
There  must  be  some  difference  in  the  cause,  to  account  for  this  difference 
in  the  effect.  Now,  “death  by  lightning  may  be  the  result  of,  1st,  a syn- 
cope bjr  fright,  or  in  consequence  of  a direct  or  reflex  influence  of  light- 
ning on  the  par  vagum ; 2d,  hemorrhage  in  or  around  the  brain,  or  in  the 
lungs,  the  pericardium,  etc. ; 3d,  concussion,  or  some  other  alteration  in 
the  brain ;”  none  of  which  phenomena  have  any  known  property  capable  of 
accounting  for  the  suppression,  or  almost  suppression,  of  the  cadaveric  ri- 
gidity. But  the  cause  of  death  may  also  be  that  the  lightning  produces 


304 


INDUCTION. 


“a  violent  convulsion  of  every  muscle  in  the  body,”  of  which,  if  of  suffi- 
cient intensity,  the  known  effect  would  be  that  “muscular  irritability 
ceases  almost  at  once.”  If  Dr.  Brown-Sequard’s  generalization  is  a true 
law,  these  will  be  the  very  cases  in  which  rigidity  is  so  much  abridged  as 
to  escape  notice ; and  the  cases  in  which,  on  the  contrary,  rigidity  takes 
place  as  usual,  will  be  those  in  which  the  stroke  of  lightning  operates  in 
some  of  the  other  modes  which  have  been  enumerated.  How,  then,  is  this 
brought  to  the  test?  By  experiments,  not  on  lightning,  which  can  not  be 
commanded  at  pleasure,  but  on  the  same  natural  agency  in  a manageable 
form,  that  of  artificial  galvanism.  Dr.  Brown-Sequard  galvanized  the  en- 
tire bodies  of  animals  immediately  after  death.  Galvanism  can  not  operate 
in  any  of  the  modes  in  which  the  stroke  of  lightning  may  have  operated, 
except  the  single  one  of  producing  muscular  convulsions.  If,  therefore,  af- 
ter the  bodies  have  been  galvanized,  the  duration  of  rigidity  is  much  short- 
ened and  putrefaction  much  accelerated,  it  is  reasonable  to  ascribe  the 
same  effects  when  produced  by  lightning  to  the  property  which  galvanism 
shares  with  lightning,  and  not  to  those  which  it  does  not.  Now  this  Dr. 
Brown-Sequard  found  to  be  the  fact.  The  galvanic  experiment  was  tried 
with  charges  of  very  various  degrees  of  strength  ; and  the  more  powerful  the 
charge,  the  shorter  was  found  to  be  the  duration  of  rigidity,  and  the  more 
speedy  and  rapid  the  putrefaction.  In  the  experiment  in  which  the  charge 
was  strongest,  and  the  muscular  irritability  most  promptly  destroyed,  the 
rigidity  only  lasted  fifteen  minutes.  On  the  principle,  therefore,  of  the 
Method  of  Concomitant  Variations,  it  may  be  inferred  that  the  duration 
of  the  rigidity  depends  on  the  degree  of  the  irritability ; and  that  if  the 
charge  had  been  as  much  stronger  than  Dr.  Brown-Sequard’s  strongest,  as 
a stroke  of  lightning  must  be  stronger  than  any  electric  shock  which  we 
can  produce  artificially,  the  rigidity  would  have  been  shortened  in  a corre- 
sponding ratio,  and  might  have  disappeared  altogether.  This  conclusion 
having  been  arrived  at,  the  case  of  an  electric  shock,  whether  natural  or 
artificial,  becomes  an  instance,  in  addition  to  all  those  already  ascertained, 
of  correspondence  between  the  irritability  of  the  muscle  and  the  duration 
of  rigidity. 

All  these  instances  are  summed  up  in  the  following  statement : “ That 
when  the  degree  of  muscular  irritability  at  the  time  of  death  is  considera- 
ble, either  in  consequence  of  a good  state  of  nutrition,  as  in  persons  who 
die  in  full  health  from  an  accidental  cause,  or  in  consequence  of  rest,  as  in 
cases  of  paralysis,  or  on  account  of  the  influence  of  cold,  cadaveric  rigidity 
in  all  these  cases  sets  in  late  and  lasts  long,  and  putrefaction  appears  late, 
and  progresses  slowly;”  but  “that  when  the  degree  of  muscular  irritability 
at  the  time  of  death  is  slight,  either  in  consequence  of  a bad  state  of  nu- 
trition, or  of  exhaustion  from  overexertion,  or  from  convulsions  caused  by 
disease  or  poison,  cadaveric  rigidity  sets  in  and  ceases  soon,  and  putrefac- 
tion appears  and  progresses  quickly.”  These  facts  present,  in  all  their 
completeness,  the  conditions  of  the  Joint  Method  of  Agreement  and  Dif- 
ference. Early  and  brief  rigidity  takes  place  in  cases  which  agree  only  in 
the  circumstance  of  a low  state  of  muscular  irritability.  Rigidity  begins 
late  and  lasts  long  in  cases  which  agree  only  in  the  contrary  circumstance, 
of  a muscular  irritability  high  and  unusually  prolonged.  It  follows  that 
there  is  a connection  through  causation  between  the  degree  of  muscular  ir- 
ritability after  death,  and  the  tardiness  and  prolongation  of  the  cadaveric 
rigidity. 

This  investigation  places  in  a strong  light  the  value  and  efficacy  of  the 


EXAMPLES  OF  THE  FOUR  METHODS. 


305 


Joint  Method.  For,  ns  we  have  already  seen,  the  defect  of  that  Method  is, 
that  like  the  Method  of  Agreement,  of  which  it  is  only  an  improved  form, 
it  can  not  prove  causation.  But  in  the  present  case  (as  in  one  of  the  steps 
in  the  argument  which  led  up  to  it)  causation  is  already  proved  ; since 
there  could  never  be  any  doubt  that  the  rigidity  altogether,  and  the  putre- 
faction which  follows  it,  are  caused  by  the  fact  of  death:  the  observations 
and  experiments  on  which  this  rests  are  too  familiar  to  need  analysis,  and 
fall  under  the  Method  of  Difference.  It  being,  therefore,  beyond  doubt 
that  the  aggregate  antecedent,  the  death,  is  the  actual  cause  of  the  whole 
train  of  consequents,  whatever  of  the  circumstances  attending  the  death 
can  be  shown  to  be  followed  in  all  its  variations  by  variations  in  the  effect 
under  investigation,  must  be  the  particular  feature  of  the  fact  of  death  on 
which  that  effect  depends.  The  degree  of  muscular  irritability  at  the 
time  of  death  fulfills  this  condition.  The  only  point  that  could  be  brought 
into  question,  would  be  whether  the  effect  depended  on  the  irritability  it- 
self, or  on  something  which  always  accompanied  the  irritability:  and  this 
doubt  is  set  at  rest  by  establishing,  as  the  instances  do,  that  by  whatever 
cause  the  high  or  low  irritability  is  produced,  the  effect  equally  follows ; 
and  can  not,  therefore,  depend  upon  the  causes  of  irritability,  nor  upon  the 
other  effects  of  those  causes,  which  are  as  various  as  the  causes  them- 
selves, but  upon  the  irritability,  solely. 

§ 5.  The  last  two  examples  will  have  conveyed  to  any  one  by  whom 
they  have  been  duly  followed,  so  clear  a conception  of  the  use  and  practi- 
cal management  of  three  of  the  four  methods  of  experimental  inquiry,  as 
to  supersede  the  necessity  of  any  further  exemplification  of  them.  The 
remaining  method,  that  of  Residues,  not  having  found  a place  in  any  of 
the  preceding  investigations,  I shall  quote  from  Sir  John  Herschel  some 
examples  of  that  method,  with  the  remarks  by  which  they  are  introduced. 

“ It  is  by  this  process,  in  fact,  that  science,  in  its  present  advanced  state, 
is  chiefly  promoted.  Most  of  the  phenomena  which  Nature  presents  are 
very  complicated;  and  when  the  effects  of  all  known  causes  are  estimated 
with  exactness,  and  subducted,  the  residual  facts  are  constantly  appearing 
in  the  form  of  phenomena  altogether  new,  and  leading  to  the  most  impor- 
tant conclusions. 

“For  example:  the  return  of  the  comet  predicted  by  Professor  Encke  a 
great  many  times  in  succession,  and  the  general  good  agreement  of  its  cal- 
culated with  its  observed  place  during  any  one  of  its  periods  of  visibility, 
would  lead  us  to  say  that  its  gravitation  toward  the  sun  and  planets  is  the 
sole  and  sufficient  cause  of  all  the  phenomena  of  its  orbitual  motion  ; but 
when  the  effect  of  this  cause  is  strictly  calculated  and  subducted  from  the 
observed  motion,  there  is  found  to  remain  behind  a residual  phenomenon, 
which  would  never  have  been  otherwise  ascertained  to  exist,  which  is  a 
small  anticipation  of  the  time  of  its  re-appearance,  or  a diminution  of  its 
periodic  time,  which  can  not  be  accounted  for  by  gravity,  and  whose  cause 
is  therefore  to  be  inquired  into.  Such  an  anticipation  would  be  caused  by 
the  resistance  of  a medium  disseminated  through  the  celestial  regions; 
and  as  there  are  other  good  reasons  for  believing  this  to  be  a vera  causa'1'1 
(an  actually  existing  antecedent),  “ it  has  therefore  been  ascribed  to  such  a 
resistance.* 

“M.  Arago,  having  suspended  a magnetic  needle  by  a silk  thread,  and  set 

* In  his  subsequent  work,  Outlines  of  Astronomy  (§  570),  Sir  John  Herschel  suggests  an- 
other possible  explanation  of  the  acceleration  of  the  revolution  of  a comet. 

20 


300 


INDUCTION. 


it  in  vibration,  observed,  that  it  came  much  sooner  to  a state  of  rest  when 
suspended  over  a plate  of  copper,  than  when  no  such  plate  was  beneath  it. 
Now,  in  both  cases  there  were  two  verve  causae’1’’  (antecedents  known  to 
exist)  “ why  it  should  come  at  length  to  rest,  viz.,  the  resistance  of  the  air, 
which  opposes,  and  at  length  destroys,  all  motions  performed  in  it;  and  the 
want  of  perfect  mobility  in  the  silk  thread.  But  the  effect  of  these  causes 
being  exactly  known  by  the  observation  made  in  the  absence  of  the  cop- 
per, and  being  thus  allowed  for  and  subducted,  a residual  phenomenon 
appeared,  in  the  fact  that  a retarding  influence  was  exerted  by  the  copper 
itself;  and  this  fact,  once  ascertained,  speedily  led  to  the  knowledge  of 
an  entirely  new  and  unexpected  class  of  relations.”  This  example  belongs, 
however,  not  to  the  Method  of  Residues  but  to  the  Method  of  Difference, 
the  law  being  ascertained  by  a direct  comparison  of  the  results  of  two  ex- 
periments, which  differed  in  nothing  but  the  presence  or  absence  of  the 
plate  of  copper.  To  have  made  it  exemplify  the  Method  of  Residues,  the 
effect  of  the  resistance  of  the  air  and  that  of  the  rigidity  of  the  silk  should 
have  been  calculated  a priori,  from  the  laws  obtained  by  separate  and  fore- 
gone experiments. 

“Unexpected  and  peculiarly  striking  confirmations  of  inductive  laws 
frequently  occur  in  the  form  of  residual  phenomena,  in  the  course  of  in- 
vestigations of  a widely  different  nature  from  those  which  gave  rise  to  the 
inductions  themselves.  A very  elegant  example  may  be  cited  in  the  unex- 
pected confirmation  of  the  law  of  the  development  of  heat  in  elastic  fluids 
by  compression,  which  is  afforded  by  the  phenomena  of  sound.  The  in- 
quiry into  the  cause  of  sound  had  led  to  conclusions  respecting  its  mode 
of  propagation,  from  which  its  velocity  in  the  air  could  be  precisely  cal- 
culated. The  calculations  were  performed ; but,  when  compared  with 
fact,  though  the  agreement  was  quite  sufficient  to  show  the  general  cor- 
rectness of  the  cause  and  mode  of  propagation  assigned,  yet  the  whole  ve- 
locity could  not  be  shown  to  arise  from  this  theory.  There  was  still  a 
residual  velocity  to  be  accounted  for,  which  placed  dynamical  philosophers 
for  a long  time  in  great  dilemma.  At  length  Laplace  struck  on  the  happy 
idea,  that  this  might  arise  from  the  heat  developed  in  the  act  of  that  con- 
densation which  necessarily  takes  place  at  every  vibration  by  which  sound 
is  conveyed.  The  matter  was  subjected  to  exact  calculation,  and  the  result 
was  at  once  the  complete  explanation  of  the  residual  phenomenon,  and  a 
striking  confirmation  of  the  general  law  of  the  development  of  heat  by 
compression,  under  circumstances  beyond  artificial  imitation.” 

“Many  of  the  new  elements  of  chemistry  have  been  detected  in  the 
investigation  of  residual  phenomena.  Thus  Arfwedson  discovered  lithia 
by  perceiving  an  excess  of  weight  in  the  sulphate  produced  from  a small 
portion  of  what  he  considered  as  magnesia  present  in  a mineral  he  had  an- 
alyzed. It  is  on  this  principle,  too,  that  the  small  concentrated  residues  of 
great  operations  in  the  arts  are  almost  sure  to  be  the  lurking-places  of  new 
chemical  ingredients:  witness  iodine,  brome,  selenium,  and  the  new  metals 
accompanying  platina  in  the  experiments  of  Wollaston  and  Tennant.  It 
was  a happy  thought  of  Glauber  to  examine  what  every  body  else  threw 
away.”* 

“Almost  all  the  greatest  discoveries  in  Astronomy,”  says  the  same  au- 
thor,f “ have  resulted  from  the  consideration  of  residual  phenomena  of  a 
quantitative  or  numerical  kind It  was  thus  that  the  grand  discovery 


Discourse,  pp.  156-8,  and  171. 


t Outlines  of  Astronomy,  § 856. 


EXAMPLES  OF  THE  FOUR  METHODS. 


307 


of  the  precession  of  the  equinoxes  resulted  as  a residual  phenomenon,  from 
the  imperfect  explanation  of  the  return  of  the  seasons  by  the  return  of  the 
sun  to  the  same  apparent  place  among  the  fixed  stars.  Thus,  also,  aberra- 
tion and  nutation  resulted  as  residual  phenomena  from  that  portion  of  the 
changes  of  the  apparent  places  of  the  fixed  stars  which  was  left  unaccounted 
for  by  precession.  And  thus  again  the  apparent  proper  motions  of  the  stars 
are  the  observed  residues  of  their  apparent  movements  outstanding  and 
unaccounted  for  by  strict  calculation  of  the  effects  of  precession,  nutation, 
and  aberration.  The  nearest  approach  which  human  theories  can  make  to 
perfection  is  to  diminish  this  residue,  this  caput  mortuum  of  observation, 
as  it  may  be  considered,  as  much  as  practicable,  and,  if  possible,  to  reduce 
it  to  nothing,  either  by  showing  that  something  has  been  neglected  in  our 
estimation  of  known  causes,  or  by  reasoning  upon  it  as  a new  fact,  and  on 
the  principle  of  the  inductive  philosophy  ascending  from  the  effect  to  its 
cause  or  causes.” 

The  disturbing  effects  mutually  produced  by  the  earth  and  planets  upon 
each  other’s  motions  were  first  brought  to  light  as  residual  phenomena,  by  the 
difference  which  appeared  between  the  observed  places  of  those  bodies,  and 
the  places  calculated  on  a consideration  solely  of  their  gravitation  toward  the 
sun.  It  was  this  which  determined  astronomers  to  consider  the  law  of  gravi- 
tation as  obtaining  between  all  bodies  whatever,  and  therefore  between  all 
particles  of  matter  ; their  first  tendency  having  been  to  regard  it  as  a force 
acting  only  between  each  planet  or  satellite  and  the  central  body  to  whose 
system  it  belonged.  Again,  the  catastrophists,  in  geology,  be  their  opinion 
right  or  wrong,  support  it  on  the  plea,  that  after  the  effect  of  all  causes  now 
in  operation  has  been  allowed  for,  there  remains  in  the  existing  constitu- 
tion of  the  earth  a large  residue  of  facts,  proving  the  existence  at  former 
periods  either  of  other  forces,  or  of  the  same  forces  in  a much  greater  de- 
gree of  intensity.  To  add  one  more  example : those  who  assert,  what  no 
one  has  shown  any  real  ground  for  believing,  that  there  is  in  one  human 
individual,  one  sex,  or  one  race  of  mankind  over  another,  an  inherent  and 
inexplicable  superiority  in  mental  faculties,  could  only  substantiate  their 
proposition  by  subtracting  from  the  differences  of  intellect  which  we  in 
fact  see,  all  that  can  be  traced  by  known  laws  either  to  the  ascertained 
differences  of  physical  organization,  or  to  the  differences  which  have  ex- 
isted in  the  outward  circumstances  in  which  the  subjects  of  the  comparison 
have  hitherto  been  placed.  What  these  causes  might  fail  to  account  for 
would  constitute  a residual  phenomenon,  which  and  which  alone  would  be 
evidence  of  an  ulterior  original  distinction,  and  the  measure  of  its  amount. 
But  the  asserters  of  such  supposed  differences  have  not  provided  them- 
selves with  these  necessary  logical  conditions  of  the  establishment  of  their 
doctrine. 

The  spirit  of  the  Method  of  Residues  being,  it  is  hoped,  sufficiently  in- 
telligible from  these  examples,  and  the  other  three  methods  having  already 
been  so  fully  exemplified,  we  may  here  close  our  exposition  of  the  four 
methods,  considered  as  employed  in  the  investigation  of  the  simpler  and 
more  elementary  order  of  the  combinations  of  phenomena. 

§ 6.  Dr.  Whewell  has  expressed  a very  unfavorable  opinion  of  the  utili- 
ty of  the  Four  Methods,  as  well  as  of  the  aptness  of  the  examples  by  which 
I have  attempted  to  illustrate  them.  His  words  are  these  :* 


Philosophy  of  Discovery , pp.  263,  264. 


30S 


INDUCTION. 


“ Upon  these  methods,  the  obvious  thing  to  remark  is,  that  they  take  for 
granted  the  very  thing  which  is  most  difficult  to  discover,  the  reduction  of 
the  phenomena  to  formulas  such  as  are  here  presented  to  us.  When  we 
have  any  set  of  complex  facts  offered  to  us;  for  instance, those  which  were 
offered  in  the  cases  of  discovery  which  I have  mentioned — the  facts  of  the 
planetary  paths,  of  falling  bodies,  of  refracted  rays,  of  cosmical  motions,  of 
chemical  analysis;  and  when,  in  any  of  these  cases,  we  would  discover  the 
law  of  nature  which  governs  them,  or,  if  any  one  chooses  so  to  term  it,  the 
feature  in  which  all  the  cases  agree,  where  are  we  to  look  for  our  A,  B,  C, 
and  a,b,c ? Nature  does  not  present  to  us  the  cases  in  this  form;  and 
how  are  we  to  reduce  them  to  this  form?  You  say  when  we  find  the  com- 
bination' of  A B C with  ah  c and  A B D with  a b cl,  then  we  may  draw  our 
inference.  Granted;  but  when  and  where  are  we  to  find  such  combina- 
tions? Even  now  that  the  discoveries  are  made,  who  will  point  out  to  us 
what  are  the  A,  B,  C,  and  a,  b,  c,  elements  of  the  cases  which  have  just  been 
enumerated  ? Who  will  tell  us  which  of  the  methods  of  inquiry  those 
historically  real  and  successful  inquiries  exemplify  ? Who  will  carry  these 
formulas  through  the  history  of  the  sciences,  as  they  have  really  grown  up, 
and  show  us  that  these  four  methods  have  been  operative  in  their  forma- 
tion; or  that  any  light  is  thrown  upon  the  steps  of  their  progress  by  refer- 
ence to  these  formulae  ?” 

He  adds  that,  in  this  work,  the  methods  have  not  been  applied  “ to  a 
large  body  of  conspicuous  and  undoubted  examples  of  discovery,  extending 
along  the  whole  history  of  science;”  which  ought  to  have  been  done  in  or- 
der that  the  methods  might  be  shown  to  possess  the  “advantage”  (which 
he  claims  as  belonging  to  his  own)  of  being  those  “ by  which  all  great  dis- 
coveries in  science  have  really  been  made.” — (P.  2T 7.) 

There  is  a striking  similarity  between  the  objections  here  made  against 
Canons  of  Induction,  and  what  was  alleged,  in  the  last  century,  by  as  able 
men  as  Dr.  Whewell,  against  the  acknowledged  Canon  of  Ratiocination. 
Those  who  protested  against  the  Aristotelian  Logic  said  of  the  Syllogism, 
what  Dr.  Whewell  says  of  the  Inductive  Methods,  that  it  “ takes  for  grant- 
ed the  very  thing  which  is  most  difficult  to  discover,  the  reduction  of  the 
argument  to  formulae  such  as  are  here  presented  to  us.”  The  grand  diffi- 
culty, they  said,  is  to  obtain  your  syllogism,  not  to  judge  of  its  correctness 
when  obtained.  On  the  matter  of  fact,  both  they  and  Dr.  Whewell  are 
right.  The  greatest  difficulty  in  both  cases  is,  first,  that  of  obtaining  the 
evidence,  and  next,  of  reducing  it  to  the  form  which  tests  its  conclusive- 
ness. But  if  we  try  to  reduce  it  without  knowing  what  it  is  to  be  reduced 
to,  we  are  not  likely  to  make  much  progress.  It  is  a more  difficult  thing 
to  solve  a geometrical  problem,  than  to  judge  whether  a proposed  solution 
is  correct:  but  if  people  were  not  able  to  judge  of  the  solution  when  found, 
they  would  have  little  chance  of  finding  it.  And  it  can  not  be  pretended 
that  to  judge  of  an  induction  when  found  is  perfectly  easy,  is  a thing  for 
which  aids  and  instruments  are  superfluous;  for  erroneous  inductions, false 
inferences  from  experience,  are  quite  as  common,  on  some  subjects  much 
commoner  than  true  ones.  The  business  of  Inductive  Logic  is  to  provide 
rules  and  models  (such  as  the  Syllogism  and  its  rules  are  for  ratiocination) 
to  which  if  inductive  arguments  conform,  those  arguments  are  conclusive, 
and  not  otherwise.  This  is  what  the  Four  Methods  profess  to  be,  and 
what  1 believe  they  are  universally  considered  to  be  by  experimental  phi- 
losophers, who  had  practiced  all  of  them  long  before  any  one  sought  to  re- 
duce the  practice  to  theory. 


EXAMPLES  OE  THE  FOUR  METHODS. 


309 


The  assailants  of  the  Syllogism  had  also  anticipated  Dr.  Whewell  in  the 
other  branch  of  his  argument.  They  said  that  no  discoveries  were  ever 
made  by  syllogism  ; and  Dr.  Whewell  says,  or  seems  to  say,  that  none  were 
ever  made  by  the  Four  Methods  of  Induction.  To  the  former  objectors, 
Archbishop  Whately  very  pertinently  answered,  that  their  argument,  if 
good  at  all,  was  good  against  the  reasoning  process  altogether  ; for  what- 
ever can  not  be  reduced  to  syllogism,  is  not  reasoning.  And  Dr.  Whewell’s 
argument,  if  good  at  all,  is  good  against  all  inferences  from  experience.  In 
saying  that  no  discoveries  were  ever  made  by  the  Four  Methods,  he  affirms 
that  none  were  ever  made  by  observation  and  experiment ; for  assuredly  if 
any  were,  it  was  by  processes  reducible  to  one  or  other  of  those  methods. 

This  difference  between  us  accounts  for  the  dissatisfaction  which  my  ex- 
amples give  him  ; for  I did  not  select  them  with  a view  to  satisfy  any  one 
who  required  to  be  convinced  that  observation  and  experiment  are  modes 
of  acquiring  knowledge : I confess  that  in  the  choice  of  them  I thought 
only  of  illustration,  and  of  facilitating  the  conception  of  the  Methods  by 
concrete  instances.  If  it  had  been  my  object  to  justify  the  processes  them- 
selves as  means  of  investigation,  there  would  have  been  no  need  to  look 
far  off,  or  make  use  of  recondite  or  complicated  instances.  As  a specimen 
of  a truth  ascertained  by  the  Method  of  Agreement,  I might  have  chosen 
the  proposition,  “ Dogs  bark.”  This  dog,  and  that  dog,  and  the  other  dog, 
answer  to  A B C,  A D E,  A F G.  The  circumstance  of  being  a dog  an- 
swers to  A.  Barking  answers  to  a.  As  a truth  made  known  by  the  Meth- 
od of  Difference,  “ Fire  burns  ” might  have  sufficed.  Before  I touch  the 
fire  I am  not  burned;  this  is  B C : I touch  it,  and  am  burned  ; this  is  A B 
C,  a B C. 

Such  familiar  experimental  processes  are  not  regarded  as  inductions  by 
Dr.  Whewell ; but  they  are  perfectly  homogeneous  with  those  by  which, 
even  on  his  own  showing,  the  pyramid  of  science  is  supplied  with  its  base. 
In  vain  he  attempts  to  escape  from  this  conclusion  by  laying  the  most  ar- 
bitrary restrictions  on  the  choice  of  examples  admissible  as  instances  of 
Induction  : they  must  neither  be  such  as  are  still  matter  of  discussion 
(p.  265),  nor  must  any  of  them  be  drawn  from  mental  and  social  subjects 
(p.  269),  nor  from  ordinary  observation  and  practical  life  (pp.  241-24'7). 
They  must  be  taken  exclusively  from  the  generalizations  by  which  scientific 
thinkers  have  ascended  to  great  and  comprehensive  laws  of  natural  phe- 
nomena. Now  it  is  seldom  possible,  in  these  complicated  inquiries,  to  go 
much  beyond  the  initial  steps,  without  calling  in  the  instrument  of  Deduc- 
tion, and  the  temporary  aid  of  hypothesis ; as  I myself,  in  common  with 
Dr.  Whewell,  have  maintained  against  the  purely  empirical  school.  Since, 
therefore,  such  cases  could  not  conveniently  be  selected  to  illustrate  the 
principles  of  mere  observation  and  experiment,  Dr.  Whewell  is  misled  by 
their  absence  into  representing  the  Experimental  Methods  as  serving  no 
purpose  in  scientific  investigation ; forgetting  that  if  those  methods  had 
not  supplied  the  first  generalizations,  there  would  have  been  no  materials 
for  his  own  conception  of  Induction  to  work  upon. 

His  challenge, however,  to  point  out  which  of  the  four  methods  are  exem- 
plified in  certain  important  cases  of  scientific  inquiry,  is  easily  answered. 
“The  planetary  paths,”  as  far  as  they  are  a case  of  induction  at  all,*  fall 
under  the  Method  of  Agreement.  The  law  of  “ falling  bodies,”  namely,* 
that  they  describe  spaces  proportional  to  the  squares  of  the  times,  was  his- 


* See,  on  this  point,  the  second  chapter  of  the  present  hook. 


310 


INDUCTION. 


torically  a deduction  from  the  first  law  of  motion  ; but  the  experiments  by 
which  it  was  verified,  and  by  which  it  might  have  been  discovered,  were 
examples  of  the  Method  of  Agreement;  and  the  apparent  variation  from 
the  true  law,  caused  by  the  resistance  of  the  air,  was  cleared  up  by  experi- 
ments in,  vacuo,  constituting  an  application  of  the  Method  of  Difference. 
The  law  of  “ refracted  rays”  (the  constancy  of  the  ratio  between  the  sines 
of  incidence  and  of  refraction  for  each  refracting  substance)  was  ascertained 
by  direct  measurement,  and  therefore  by  the  Method  of  Agreement.  The 
“ cosmical  motions  ” were  determined  by  highly  complex  processes  of 
thought,  in  which  Deduction  was  predominant,  but  the  Methods  of  Agree- 
ment and  of  Concomitant  Variations  had  a large  part  in  establishing  the 
empirical  laws.  Every  case  without  exception  of  “ chemical  analysis”  con- 
stitutes a well-marked  example  of  the  Method  of  Difference.  To  any  one 
acquainted  with  the  subjects — to  Dr.  Whewell  himself,  there  would  not  be 
the  smallest  difficulty  in  setting  out  “ the  ABC  and  a b c elements  ” of 
these  cases. 

If  discoveries  are  ever  made  by  observation  and  experiment  without  De- 
duction, the  four  methods  are  methods  of  discovery  : but  even  if  they  were 
not  methods  of  discovery,  it  would  not  be  the  less  true  that  they  are  the 
sole  methods  of  Proof  ; and  in  that  character,  even  the  results  of  deduction 
are  amenable  to  them.  The  great  generalizations  which  begin  as  Hypo- 
theses, must  end  by  being  proved,  and  are  in  reality  (as  will  be  shown 
hereafter)  proved,  by  the  Four  Methods.  Now  it  is  with  Proof,  as  such, 
that  Logic  is  principally  concerned.  This  distinction  has  indeed  no  chance 
of  finding  favor  with  Dr.  Whewell;  for  it  is  the  peculiarity  of  his  system, 
not  to  recognize,  in  cases  of  Induction,  any  necessity  for  proof.  If,  after 
assuming  an  hypothesis  and  carefully  collating  it  with  facts,  nothing  is 
brought  to  light  inconsistent  with  it,  that  is,  if  experience  does  not  disprove 
it, he  is  content:  at  least  until  a simpler  hypothesis, equally  consistent  with 
experience,  presents  itself.  If  this  be  Induction,  doubtless  there  is  no  ne- 
cessity for  the  four  methods.  But  to  suppose  that  it  is  so,  appears  to  me  a 
radical  misconception  of  the  nature  of  the  evidence  of  physical  truths. 

So  real  and  practical  is  the  need  of  a test  for  induction,  similar  to  the 
syllogistic  test  of  ratiocination,  that  inferences  which  bid  defiance  to  the 
most  elementary  notions  of  inductive  logic  are  put  forth  without  misgiv- 
ing by  persons  eminent  in  physical  science,  as  soon  as  they  are  off  the 
ground  on  which  they  are  conversant  with  the  facts,  and  not  reduced  to 
judge  only  by  the  arguments;  and  as  for  educated  persons  in  general,  it 
may  be  doubted  if  they  are  better  judges  of  a good  or  a bad  induction 
than  they  were  before  Bacon  wrote.  The  improvement  in  the  results  of 
thinking  has  seldom  extended  to  the  processes;  or  has  reached,  if  any  proc- 
ess, that  of  investigation  only,  not  that  of  proof.  A knowledge  of  many 
laws  of  nature  has  doubtless  been  arrived  at,  by  framing  hypotheses  and 
finding  that  the  facts  corresponded  to  them;  and  many  errors  have  been 
got  rid  of  by  coming  to  a knowledge  of  facts  which  were  inconsistent  with 
them,  but  not  by  discovering  that  the  mode  of  thought  which  led  to  the 
errors  was  itself  faulty,  and  might  have  been  known  to  be  such  independ- 
ently of  the  facts  which  disproved  the  specific  conclusion.  Hence  it  is, 
that  while  the  thoughts  of  mankind  have  on  many  subjects  worked  them- 
selves practically  right,  the  thinking  power  remains  as  weak  as  ever : and 
on  all  subjects  on  which  the  facts  which  would  check  the  result  are  not  ac- 
cessible, as  in  what  relates  to  the  invisible  world,  and  even,  as  has  been 
seen  lately,  to  the  visible  world  of  the  planetary  regions,  men  of  the  great- 


PLURALITY  OF  CAUSES. 


311 


est  scientific  acquirements  argue  as  pitiably  as  the  merest  ignoramus.  For 
though  they  have  made  many  sound  inductions,  they  have  not  learned  from 
them  (and  Dr.  Whewell  thinks  there  is  no  necessity  that  they  should  learn) 
the  principles  of  inductive  evidence. 


CHAPTER  X. 

OF  PLURALITY  OF  CAUSES,  AND  OF  THE  INTERMIXTURE  OF  EFFECTS. 

§ 1.  In  the  preceding  exposition  of  the  four  methods  of  observation 
and  experiment,  by  which  we  contrive  to  distinguish  among  a mass  of  co- 
existent phenomena  the  particular  effect  due  to  a given  cause,  or  the  par- 
ticular cause  which  gave  birth  to  a given  effect,  it  has  been  necessary  to 
suppose,  in  the  first  instance,  for  the  sake  of  simplification,  that  this  ana- 
lytical operation  is  encumbered  by  no  other  difficulties  than  what  are  essen- 
tially inherent  in  its  nature ; and  to  represent  to  ourselves,  therefore,  every 
effect,  on  the  one  hand  as  connected  exclusively  with  a single  cause,  and 
on  the  other  hand  as  incapable  of  being  mixed  and  confounded  with  any 
other  co-existent  effect.  We  have  regarded  abcde,  the  aggregate  of 
the  phenomena  existing  at  any  moment,  as  consisting  of  dissimilar  facts, 
a , b , c,  d,  and  e,  for  each  of  which  one,  and  only  one,  cause  needs  be  sought; 
the  difficulty  being  only  that  of  singling  out  this  one  cause  from  the  mul- 
titude of  antecedent  circumstances,  A,B,C,D,  and  E.  The  cause  indeed 
may  not  be  simple ; it  may  consist  of  an  assemblage  of  conditions ; but  we 
have  supposed  that  there  was  only  one  possible  assemblage  of  conditions 
from  which  the  given  effect  could  result. 

If  such  were  the  fact,  it  would  be  comparatively  an  easy  task  to  investi- 
gate the  laws  of  nature.  But  the  supposition  does  not  hold  in  either  of 
its  parts.  In  the  first  place,  it  is  not  true  that  the  same  phenomenon  is 
always  produced  by  the  same  cause : the  effect  a may  sometimes  arise 
from  A,  sometimes  from  B.  And,  secondly,  the  effects  of  different  causes 
are  often  not  dissimilar,  but  homogeneous,  and  marked  out  by  no  assign- 
able boundaries  from  one  another : A and  B may  produce  not  a and  b,  but 
different  portions  of  an  effect  a.  The  obscurity  and  difficulty  of  the  inves- 
tigation of  the  laws  of  phenomena  is  singularly  increased  by  the  necessi- 
ty of  adverting  to  these  two  circumstances : Intermixture  of  Effects,  and 
Plurality  of  Causes.  To  the  latter,  being  the  simpler  of  the  two  considera- 
tions, we  shall  first  direct  our  attention. 

It  is  not  true,  then,  that  one  effect  must  be  connected  with  only  one 
cause,  or  assemblage  of  conditions;  that  each  phenomenon  can  be  pro- 
duced only  in  one  way.  There  are  often  several  independent  modes  in 
which  the  same  phenomenon  could  have  originated.  One  fact  may  be  the 
consequent  in  several  invariable  sequences ; it  may  follow,  with  equal  uni- 
formity, any  one  of  several  antecedents,  or  collections  of  antecedents. 
Many  causes  may  produce  mechanical  motion;  many  causes  may  produce 
some  kinds  of  sensation  ; many  causes  may  produce  death.  A given  effect 
may  really  be  produced  by  a certain  cause,  and  yet  be  perfectly  capable  of 
being  produced  without  it. 

§ 2.  One  of  the  principal  consequences  of  this  fact  of  Plurality  of  Causes 
is,  to  render  the  first  of  the  inductive  methods,  that  of  Agreement,  uncer- 


312 


INDUCTION. 


tain.  To  illustrate  that  method,  we  supposed  two  instances,  A B C follow- 
ed by  a be,  and  ADE  followed  by  ade.  From  these  instances  it  might 
apparently  be  concluded  that  A is  an  invariable  antecedent  of  a , and  even 
that  it  is  the  unconditional  invariable  antecedent,  or  cause,  if  we  could  be 
sure  that  there  is  no  other  antecedent  common  to  the  two  cases.  That  this 
difficulty  may  not  stand  in  the  way,  let  us  suppose  the  two  cases  positive- 
ly ascertained  to  have  no  antecedent  in  common  except  A.  The  moment, 
however,  that  we  let  in  the  possibility  of  a plurality  of  causes,  the  conclu- 
sion fails.  For  it  involves  a tacit  supposition,  that  a must  have  been  pro- 
duced in  both  instances  by  the  same  cause.  If  there  can  possibly  have 
been  two  causes,  those  two  may,  for  example,  be  C and  E:  the  one  may 
have  been  the  cause  of  a in  the  former  of  the  instances,  the  other  in  the 
latter,  A having  no  influence  in  either  case. 

Suppose,  for  example,  that  two  great  artists  or  great  philosophers,  that 
two  extremely  selfish  or  extremely  generous  characters,  were  compared 
together  as  to  the  circumstances  of  their  education  and  history,  and  the 
two  cases  were  found  to  agree  only  in  one  circumstance:  would  it  follow 
that  this  one  circumstance  was  the  cause  of  the  quality  which  characterized 
both  those  individuals?  Not  at  all;  for  the  causes  which  may  produce 
any  type  of  character  are  very  numerous;  and  the  two  persons  might 
equally  have  agreed  in  their  character,  though  there  had  been  no  manner 
of  resemblance  in  their  previous  history. 

This,  therefore,  is  a characteristic  imperfection  of  the  Method  of  Agree- 
ment, from  which  imperfection  the  Method  of  Difference  is  free.  For  if 
we  have  two  instances,  ABC  and  B C,  of  which  B C gives  b c,  and  A being 
added  converts  it  into  a b c,  it  is  certain  that  in  this  instance  at  least,  A was 
either  the  cause  of  a,  or  an  indispensable  portion  of  its  cause,  even  though 
the  cause  which  produces  it  in  other  instances  may  be  altogether  different. 
Plurality  of  Causes,  therefore,  not  only  does  not  diminish  the  reliance  due 
to  the  Method  of  Difference,  but  does  not  even  render  a greater  number 
of  observations  or  experiments  necessary : two  instances,  the  one  positive 
and  the  other  negative,  are  still  sufficient  for  the  most  complete  and  rigor- 
ous induction.  Not  so,  however,  with  the  Method  of  Agreement.  The 
conclusions  which  that  yields,  when  the  number  of  instances  compared  is 
small,  are  of  no  real  value,  except  as,  in  the  character  of  suggestions,  they 
may  lead  either  to  experiments  bringing  them  to  the  test  of  the  Method 
of  Difference,  or  to  reasonings  which  may  explain  and  verify  them  de- 
ductively. 

It  is  only  when  the  instances,  being  indefinitely  multiplied  and  varied, 
continue  to  suggest  the  same  result,  that  this  result  acquires  any  high  de- 
gree of  independent  value.  If  there  are  but  two  instances,  A B C and 
A D E,  though  these  instances  have  no  antecedent  in  common  except  A,  yet 
as  the  effect  may  possibly  have  been  produced  in  the  two  cases  by  differ- 
ent causes,  the  result  is  at  most  only  a slight  probability  in  favor  of  A; 
there  may  be  causation,  but  it  is  almost  equally  probable  that  there  was 
only  a coincidence.  But  the  oftener  we  repeat  the  observation,  varying 
the  circumstances,  the  more  we  advance  toward  a solution  of  this  doubt. 
For  if  we  try  A F G,  A H K,  etc.,  all  unlike  one  another  except  in  contain- 
ing the  circumstance  A,  and  if  we  find  the  effect  a entering  into  the  re- 
sult in  all  these  cases,  we  must  suppose  one  of  two  things,  either  that  it  is 
caused  by  A,  or  that  it  has  as  many  different  causes  as  there  are  instances. 
With  each  addition,  therefore,  to  the  number  of  instances,  the  presump- 
tion is  strengthened  in  favor  of  A.  The  inquirer,  of  course,  will  not  neg- 


PLURALITY  OF  CAUSES. 


313 


lect,  if  an  opportunity  present  itself,  to  exclnde  A from  some  one  of  these 
combinations,  from  A H K for  instance,  and  by  trying  H K separately,  ap- 
peal to  the  Method  of  Difference  in  aid  of  the  Method  of  Agreement.  By 
the  Method  of  Difference  alone  can  it  be  ascertained  that  A is  the  cause 
of  a;  but  that  it  is  either  the  cause,  or  another  effect  of  the  same  cause, 
may  be  placed  beyond  any  reasonable  doubt  by  the  Method  of  Agreement, 
provided  the  instances  are  very  numerous  as  well  as  sufficiently  various. 

After  how  great  a multiplication,  then,  of  varied  instances,  all  agreeing 
in  no  other  antecedent  except  A,  is  the  supposition  of  a plurality  of  causes 
sufficiently  rebutted,  and  the  conclusion  that  a is  connected  with  A divest- 
ed of  the  characteristic  imperfection,  and  reduced  to  a virtual  certainty? 
This  is  a question  which  we  can  not  be  exempted  from  answering : but 
the  consideration  of  it  belongs  to  what  is  called  the  Theory  of  Probability, 
which  will  form  the  subject  of  a chapter  hereafter.  It  is  seen,  however,  at 
once,  that  the  conclusion  does  amount  to  a practical  certainty  after  a suffi- 
cient number  of  instances,  and  that  the  method,  therefore,  is  not  radically 
vitiated  by  the  characteristic  imperfection.  The  reshit  of  these  considera- 
tions is  only,  in  the  first  place,  to  point  out  a new  source  of  inferiority  in 
the  Method  of  Agreement  as  compared  with  other  modes  of  investigation, 
and  new  reasons  for  never  resting  contented  with  the  results  obtained  by 
it,  without  attempting  to  confirm  them  either  by  the  Method  of  Difference, 
or  by  connecting  them  deductively  with  some  law  or  laws  already  ascer- 
tained by  that  superior  method.  And,  in  the  second  place,  we  learn  from 
this  the  true  theory  of  the  value  of  mere  number  of  instances  in  inductive 
inquiry.  The  Plurality  of  Causes  is  the  only  reason  why  mere  number  is 
of  any  importance.  The  tendency  of  unscientific  inquirers  is  to  rely  too 
much  on  number,  without  analyzing  the  instances ; without  looting  closely 
enough  into  their  nature  to  ascertain  what  circumstances  are  or  are  not 
eliminated  by  means  of  them.  Most  people  hold  their  conclusions  with  a 
degree  of  assurance  proportioned  to  the  mere  mass  of  the  experience  on 
which  they  appear  to  rest ; not  considering  that  by  the  addition  of  in- 
stances to  instances,  all  of  the  same  kind,  that  is,  differing  from  one  another 
only  in  points  already  recognized  as  immaterial,  nothing  whatever  is  add- 
ed to  the  evidence  of  the  conclusion.  A single  instance  eliminating  some 
antecedent  which  existed  in  all  the  other  cases,  is  of  more  value  than  the 
greatest  multitude  of  instances  which  are  reckoned  by  their  number  alone. 
It  is  necessary,  no  doubt,  to  assure  ourselves,  by  repetition  of  the  observa- 
tion or  experiment,  that  no  error  has  been  committed  concerning  the  indi- 
vidual facts  observed ; and  until  we  have  assured  ourselves  of  this,  instead 
of  varying  the  circumstances,  we  can  not  too  scrupulously  repeat  the  same 
experiment  or  observation  without  any  change.  But  when  once  this  as- 
surance has  been  obtained,  the  multiplication  of  instances  which  do  not  ex- 
clude any  more  circumstances  is  entirely  useless,  provided  there  have  been' 
already  enough  to  exclude  the  supposition  of  Plurality  of  Causes. 

It  is  of  importance  to  remark,  that  the  peculiar  modification  of  the 
Method  of  Agreement,  which,  as  partaking  in  some  degree  of  the  nature 
of  the  Method  of  Difference,  I have  called  the  Joint  Method  of  Agreement 
and  Difference,  is  not  affected  by  the  characteristic  imperfection  now 
pointed  out.  For,  in  the  joint  method,  it  is  supposed  not  only  that  the  in- 
stances in  which  a is,  agree  only  in  containing  A,  but  also  that  the  in- 
stances in  which  a is  not,  agree  only  in  not  containing  A.  Now,  if  this  be 
so,  A must  be  not  only  the  cause  of  a,  but  the  only  possible  cause : for  if 
there  were  another,  as  for  example  B,  then  in  the  instances  in  which  a is 


31-i 


INDUCTION. 


not,  B must  have  been  absent  as  well  as  A,  and  it  would  not  be  true  that 
these  instances  agree  only  in  not  containing  A.  This,  therefore,  consti- 
tutes an  immense  advantage  of  the  joint  method  over  the  simple  Method 
of  Agreement.  It  may  seem,  indeed,  that  the  advantage  does  not  belong 
so  much  to  the  joint  method,  as  to  one  of  its  two  premises  (if  they  may  be 
so  called),  the  negative  premise.  The  Method  of  Agreement,  when  applied 
•to  negative  instances,  or  those  in  which  a phenomenon  does  not  take  place, 
is  certainly  free  from  the  characteristic  imperfection  which  affects  it  in  the 
affirmative  case.  The  negative  premise,  it  might  therefore  be  supposed, 
could  be  worked  as  a simple  case  of  the  Method  of  Agreement,  without  re- 
quiring an  affirmative  premise  to  be  joined  with  it.  But  though  this  is 
true  in  principle,  it  is  generally  altogether  impossible  to  work  the  Method 
of  Agreement  by  negative  instances  without  positive  ones:  it  is  so  much 
more  difficult  to  exhaust  the  field  of  negation  than  that  of  affirmation. 
For  instance,  let  the  question  be  what  is  the  cause  of  the  transparency  of 
bodies;  with  what  prospect  of  success  could  wre  set  ourselves  to  inquire 
directly  in  what  the  multifarious  substances  which  are  not  transparent 
agree  ? But  we  might  hope  much  sooner  to  seize  some  point  of  resem- 
blance among  the  comparatively  few  and  definite  species  of  objects  which 
are  transparent ; and  this  being  attained,  we  should  quite  naturally  be  put 
upon  examining  whether  the  absence  of  this  one  circumstance  be  not  pre- 
cisely the  point  in  which  all  opaque  substances  will  be  found  to  resemble. 

The  Joint  Method  of  Agreement  and  Difference,  therefore,  or  as  I have 
otherwise  called  it,  the  Indirect  Method  of  Difference  (because,  like  the 
Method  of  Difference  properly  so-called,  it  proceeds  by  ascertaining  how  and 
in  what  the  cases  where  the  phenomenon  is  present  differ  from  those  in  which 
it  is  absent)  is,  after  the  Direct  Method  of  Difference,  the  most  powerful 
of  the  remaining  instruments  of  inductive  investigation  ; and  in  the  sciences 
which  depend  on  pure  observation,  with  little  or  no  aid  from  experiment, 
this  method,  so  well  exemplified  in  the  speculation  on  the  cause  of  dew,  is 
the  primary  resource,  so  far  as  direct  appeals  to  experience  are  concerned. 

§ 3.  We  have  thus  far  treated  Plurality  of  Causes  only  as  a possible  sup- 
position, which,  until  removed,  renders  our  inductions  uncertain  ; and  have 
only  considered  by  what  means,  where  the  plurality  does  not  really  exist, 
we  may  be  enabled  to  disprove  it.  But  we  must  also  consider  it  as  a case 
actually  occurring  in  nature,  and  which,  as  often  as  it  does  occur,  our 
methods  of  induction  ought  to  be  capable  of  ascertaining  and  establishing. 
For  this,  however,  there  is  required  no  peculiar  method.  When  an  effect 
is  really  producible  by  two  or  more  causes,  the  process  for  detecting  them 
is  in  no  way  different  from  that  by  which  we  discover  single  causes.  They 
may  (first)  be  discovered  as  separate  sequences,  by  separate  sets  of  in- 
stances. One  set  of  observations  or  experiments  shows  that  the  sun  is  a 
cause  of  heat,  another  that  friction  is  a source  of  it,  another  that  percus- 
sion, another  that  electricity,  another  that  chemical  action  is  such  a source. 
Or  (secondly)  the  plurality  may  come  to  light  in  the  course  of  collating  a 
number  of  instances,  when  we  attempt  to  find  some  circumstance  in  which 
they  all  agree,  and  fail  in  doing  so.  We  find  it  impossible  to  trace,  in  all 
the  cases  in  which  the  effect  is  met  with,  any  common  circumstance.  We 
find  that  we  can  eliminate  all  the  antecedents ; that  no  one  of  them  is 
present  in  all  the  instances,  no  one  of  them  indispensable  to  the  effect. 
On  closer  scrutiny,  however,  it  appears  that  though  no  one  is  always  pres- 
ent, one  or  other  of  several  always  is.  If,  on  further  analysis,  we  can  de- 


INTERMIXTURE  OF  EFFECTS. 


315 


tect  in  these  any  common  element,  we  may  be  able  to  ascend  from  them 
to  some  one  cause  which  is  the  really  operative  circumstance  in  them  all. 
Thus  it  is  now  thought  that  in  the  production  of  heat  by  friction,  percus- 
sion, chemical  action,  etc.,  the  ultimate  source  is  one  and  the  same.  But  if 
(as  continually  happens)  we  can  not  take  this  ulterior  step,  the  different 
antecedents  must  be  set  down  provisionally  as  distinct  causes,  each  suffi- 
cient of  itself  to  produce  the  effect. 

We  here  close  our  remarks  on  the  Plurality  of  Causes,  and  proceed  to 
the  still  more  peculiar  and  more  complex  case  of  the  Intermixture  of  Ef- 
fects, and  the  interference  of  causes  with  one  another:  a case  constituting 
the  principal  part  of  the  complication  and  difficulty  of  the  study  of  nature ; 
and  with  which  the  four  only  possible  methods  of  directly  inductive  inves- 
tigation by  observation  and  experiment,  are,  for  the  most  part,  as  will  ap- 
pear presently,  quite  unequal  to  cope.  The  instrument  of  Deduction  alone 
is  adequate  to  unravel  the  complexities  proceeding  from  this  source;  and 
the  four  methods  have  little  more  in  their  power  than  to  supply  premises 
for,  and  a verification  of,  our  deductions. 

§ 4.  A concurrence  of  two  or  more  causes,  not  separately  producing  each 
its  own  effect,  but  interfering  with  or  modifying  the  effects  of  one  anoth- 
er, takes  place,  as  has  already  been  explained  in  two  different  ways.  In 
the  one,  which  is  exemplified  by  the  joint  operation  of  different  forces  in 
mechanics,  the  separate  effects  of  all  the  causes  continue  to  be  produced, 
but  are  compounded  with  one  another,  and  disappear  in  one  total.  In  the 
other,  illustrated  by  the  case  of  chemical  action,  the  separate  effects  cease 
entirely,  and  are  succeeded  by  phenomena  altogether  different,  and  govern- 
ed by  different  laws. 

Of  these  cases  the  former  is  by  far  the  more  frequent,  and  this  case  it  is 
which,  for  the  most  part,  eludes  the  grasp  of  our  experimental  methods. 
The  other  and  exceptional  case  is  essentially  amenable  to  them.  When  the 
laws  of  the  original  agents  cease  entirely,  and  a phenomenon  makes  its 
appearance,  which,  with  reference  to  those  laws,  is  quite  heterogeneous; 
when,  for  example,  two  gaseous  substances,  hydrogen  and  oxygen,  on  be- 
ing brought  together,  throw  off  their  peculiar  properties,  and  produce  the 
substance  called  water;  in  such  cases  the  new  fact  may  be  subjected  to 
experimental  inquiry,  like  any  other  phenomenon  ; and  the  elements  which 
are  said  to  compose  it  may  be  considered  as  the  mere  agents  of  its  pro- 
duction— the  conditions  on  which  it  depends,  the  facts  which  make  up  its 
cause. 

The  effects  of  the  new  phenomenon,  the  'properties  of  water,  for  instance, 
are  as  easily  found  by  experiment  as  the  effects  of  any  other  cause.  But 
to  discover  the  cause  of  it,  that  is,  the  particular  conjunction  of  agents 
from  which  it  results,  is  often  difficult  enough.  In  the  first  place,  the  ori- 
gin and  actual  production  of  the  phenomenon  are  most  frequently  inacces- 
sible to  our  observation.  If  we  could  not  have  learned  the  composition  of 
water  until  we  found  instances  in  which  it  was  actually  produced  from 
oxygen  and  hydrogen,  we  should  have  been  forced  to  wait  until  the  casual 
thought  struck  some  one  of  passing  an  electric  spark  through  a mixture 
of  the  two  gases,  or  inserting  a lighted  taper  into  it,  merely  to  try  what 
would  happen.  Besides,  many  substances,  though  they  can  be  analyzed, 
can  not  by  any  known  artificial  means  be  recompounded.  Further,  even 
if  we  could  have  ascertained,  by  the  Method  of  Agreement,  that  oxygen 
and  hydrogen  were  both  present  when  water  is  produced,  no  experimenta- 


316 


INDUCTION. 


tion  on  oxygen  and  hydrogen  separately,  no  knowledge  of  their  laws,  could 
have  enabled  us  deductively  to  infer  that  they  would  produce  water.  We 
require  a specific  experiment  on  the  two  combined. 

Under  these  difficulties,  we  should  generally  have  been  indebted  for  our 
knowledge  of  the  causes  of  this  class  of  effects,  not  to  any  inquiry  direct- 
ed specifically  toward  that  end,  but  either  to  accident,  or  to  the  gradual 
progress  of  experimentation  on  the  different  combinations  of  which  the 
producing  agents  are  susceptible;  if  it  were  not  for  a peculiarity  belonging 
to  effects  of  this  description,  that  they  often,  under  some  particular  com- 
bination of  circumstances,  reproduce  their  causes.  If  water  results  from 
the  juxtaposition  of  hydrogen  and  oxygen  whenever  this  can  be  made  suf- 
ficiently close  and  intimate,  so,  on  the  other  hand,  if  water  itself  be  placed 
in  certain  situations,  hydrogen  and  oxygen  are  reproduced  from  it:  an 
abrupt  termination  is  put  to  the  new  laws,  and  the  agents  re-appear  sepa- 
rately with  their  own  properties  as  at  first.  What  is  called  chemical  anal- 
ysis is  the  process  of  searching  for  the  causes  of  a phenomenon  among  its 
effects,  or  rather  among  the  effects  produced  by  the  action  of  some  other 
causes  upon  it. 

Lavoisier,  by  heating  mercury  to  a high  temperature  in  a close  vessel 
containing  air,  found  that  the  mercury  increased  in  weight,  and  became 
what  was  then  called  red  precipitate,  while  the  air,  on  being  examined 
after  the  experiment,  proved  to  have  lost  weight,  and  to  have  become  in- 
capable of  supporting  life  or  combustion.  When  red  precipitate  was  ex- 
posed to  a still  greater  heat,  it  became  mercury  again,  and  gave  off  a gas 
which  did  support  life  and  fiame.  Thus  the  agents  which  by  their  com- 
bination produced  red  precipitate,  namely,  the  mercury  and  the  gas,  re- 
appear as  effects  resulting  from  that  precipitate  when  acted  upon  by  heat. 
So,  if  we  decompose  water  by  means  of  iron  filings,  we  produce  two  effects, 
rust  and  hydrogen.  Now  rust  is  already  known,  by  experiments  upon  the 
component  substances,  to  be  an  effect  of  the  union  of  iron  and  oxygen : 
the  iron  we  ourselves  supplied,  but  the  oxygen  must  have  been  produced 
from  the  water.  The  result,  therefore,  is  that  water  has  disappeared,  and 
hydrogen  and  oxygen  have  appeared  in  its  stead  ; or,  in  other  words,  the 
original  laws  of  these  gaseous  agents,  which  had  been  suspended  by  the 
superinduction  of  the  new  laws  called  the  properties  of  water,  have  again 
started  into  existence,  and  the  causes  of  water  are  found  among  its  effects. 

Where  two  phenomena,  between  the  laws  or  properties  of  which,  con- 
sidered in  themselves,  no  connection  can  be  traced,  are  thus  reciprocally 
cause  and  effect,  each  capable  in  its  turn  of  being  produced  from  the  oth- 
er, and  each,  when  it  produces  the  other,  ceasing  itself  to  exist  (as  water 
is  produced  from  oxygen  and  hydrogen,  and  oxygen  and  hydrogen  are  re- 
produced from  water) ; this  causation  of  the  two  phenomena  by  one  an- 
other, each  being  generated  by  the  other’s  destruction,  is  properly  trans- 
formation. The  idea  of  chemical  composition  is  an  idea  of  transformation, 
but  of  a transformation  which  is  incomplete;  since  we  consider  the  oxy- 
gen and  hydrogen  to  be  present  in  the  water  as  oxygen  and  hydrogen,  and 
capable  of  being  discovered  in  it  if  our  senses  were  sufficiently  keen : a 
supposition  (for  it  is  no  more)  grounded  solely  on  the  fact  that  the  weight 
of  the  water  is  the  sum  of  the  separate  weights  of  the  two  ingredients.  If 
there  had  not  been  this  exception  to  the  entire  disappearance,  in  the  com- 
pound, of  the  laws  of  the  separate  ingredients;  if  the  combined  agents  had 
not,  in  this  one  particular  of  weight,  preserved  their  own  laws,  and  produced 
a joint  result  equal  to  the  sum  of  their  separate  results;  we  should  never, 


INTERMIXTURE  OF  EFFECTS. 


317 


probably,  have  had  the  notion  now  implied  by  the  words  chemical  compo- 
sition ; and,  in  the  facts  of  water  produced  from  hydrogen  and  oxygen, 
and  hydrogen  and  oxygen  produced  from  water,  as  the  transformation 
would  have  been  complete,  we  should  have  seen  only  a transformation. 

In  these  cases,  where  the  heteropathic  effect  (as  we  called  it  in  a former 
chapter)*  is  but  a transformation  of  its  cause,  or  in  other  words,  where 
the  effect  and  its  cause  are  reciprocally  such,  and  mutually  convertible  into 
each  other;  the  problem  of  finding  the  cause  resolves  itself  into  the  far 
easier  one  of  finding  an  effect,  which  is  the  kind  of  inquiry  that  admits  of 
being  prosecuted  by  direct  experiment.  But  there  are  other  cases  of 
heteropathic  effects  to  which  this  mode  of  investigation  is  not  applicable. 
Take,  for  instance,  the  heteropathic  laws  of  mind ; that  portion  of  the  phe- 
nomena of  our  mental  nature  which  are  analogous  to  chemical  rather  than 
to  dynamical  phenomena;  as  when  a complex  passion  is  formed  by  the  co- 
alition of  several  elementary  impulses,  or  a complex  emotion  by  several 
simple  pleasures  or  pains,  of  which  it  is  the  result  without  being  the  ag- 
gregate, or  in  any  respect  homogeneous  with  them.  The  product,  in  these 
cases,  is  generated  by  its  various  factors ; but  the  factors  can  not  be  re- 
produced from  the  product;  just  as  a youth  can  grow  into  an  old  man, 
but  an  old  man  can  not  grow  into  a youth.  We  can  not  ascertain  from 
what  simple  feelings  any  of  our  complex  states  of  mind  are  generated,  as 
we  ascertain  the  ingredients  of  a chemical  compound,  by  making  it,  in  its 
turn,  generate  them.  We  can  only,  therefore,  discover  these  laws  by  the 
slow  process  of  studying  the  simple  feelings  themselves,  and  ascertaining 
synthetically,  by  experimenting  on  the  various  combinations  of  which  they 
are  susceptible,  what  they,  by  their  mutual  action  upon  one  another,  are 
capable  of  generating. 

§ 5.  It  might  have  been  supposed  that  the  other,  and  apparently  simpler 
variety  of  the  mutual  interference  of  causes,  where  each  cause  continues 
to  produce  its  own  proper  effect  according  to  the  same  laws  to  which  it 
conforms  in  its  separate  state,  would  have  presented  fewer  difficulties  to 
the  inductive  inquirer  than  that  of  which  we  have  just  finished  the  consid- 
eration. It  presents,  however,  so  far  as  direct  induction  apart  from  de- 
duction is  concerned,  infinitely  greater  difficulties.  When  a concurrence 
of  causes  gives  rise  to  a new  effect,  bearing  no  relation  to  the  separate 
effects  of  those  causes,  the  resulting  phenomenon  stands  forth  undisguised, 
inviting  attention  to  its  peculiarity,  and  presenting  no  obstacle  to  our  rec- 
ognizing its  presence  or  absence  among  any  number  of  surrounding  phe- 
nomena. It  admits,  therefore,  of  being  easily  brought  under  the  canons  of 
Induction,  provided  instances  can  be  obtained  such  as  those  canons  require ; 
and  the  non-occurrence  of  such  instances,  or  the  want  of  means  to  pro- 
duce them  artificially,  is  the  real  and  only  difficulty  in  such  investigations ; 
a difficulty  not  logical  but  in  some  sort  physical.  It  is  otherwise  with  cases 
of  what,  in  a preceding  chapter,  has  been  denominated  the  Composition  of 
Causes.  There,  the  effects  of  the  separate  causes  do  not  terminate  and  give 
place  to  others,  thereby  ceasing  to  form  any  part  of  the  phenomenon  to  be 
investigated ; on  the  contrary,  they  still  take  place,  but  are  intermingled 
with,  and  disguised  by,  the  homogeneous  and  closely  allied  effects  of  other 
causes.  They  are  no  longer  a,  b,  c,  d,  e,  existing  side  by  side,  and  continu- 
ing to  be  separately  discernible ; they  are  +«,  — a,  \ b,  —b,  2 b,  etc, ; some  of 


Ante,  chap,  vii.,  § 1. 


31S 


INDUCTION. 


which  cancel  one  another,  while  many  others  do  not  appear  distinguisha- 
bly,  but  merge  in  one  sum;  forming  altogether  a result,  between  which 
and  the  causes  whereby  it  was  produced  there  is  often  an  insurmountable 
difficulty  in  tracing  by  observation  any  fixed  relation  whatever. 

The  general  idea  of  the  Composition  of  Causes  has  been  seen  to  be,  that 
though  two  or  more  laws  interfere  with  one  another,  and  apparently  frus- 
trate or  modify  one  another’s  operation,  yet  in  reality  all  are  fulfilled,  the 
collective  effect  being  the  exact  sum  of  the  effects  of  the  causes  taken  sepa- 
rately. A familiar  instance  is  that  of  a body  kept  in  equilibrium  by  two 
equal  and  contrary  forces.  One  of  the  forces  if  acting  alone  would  carry 
the  body  in  a given  time  a certain  distance  to  the  west,  the  other  if  acting 
alone  would  carry  it  exactly  as  far  toward  the  east;  and  the  result  is  the 
same  as  if  it  had  been  first  carried  to  the  west  as  far  as  the  one  force  would 
carry  it,  and  then  back  toward  the  east  as  far  as  the  other  would  carry 
it — that  is,  precisely  the  same  distance;  being  ultimately  left  where  it  was 
found  at  first. 

All  laws  of  causation  are  liable  to  be  in  this  manner  counteracted,  and 
seemingly  frustrated,  by  coming  into  confiict  with  other  laws,  the  separate 
result  of  which  is  opposite  to  theirs,  or  more  or  less  inconsistent  with  it. 
And  hence,  with  almost  every  law,  many  instances  in  which  it  really  is' 
entirely  fulfilled,  do  not,  at  first  sight,  appear  to  be  cases  of  its  operation 
at  all.  It  is  so  in  the  example  just  adduced:  a force  in  mechanics  means 
neither  more  nor  less  than  a cause  of  motion,  yet  the  sum  of  the  effects  of 
two  causes  of  motion  may  be  rest.  Again,  a body  solicited  by  two  forces 
in  directions  making  an  angle  with  one  another,  moves  in  the  diagonal; 
and  it  seems  a paradox  to  say  that  motion  in  the  diagonal  is  the  sum  of  two 
motions  in  two  other  lines.  Motion,  however,  is  but  change  of  place,  and 
at  every  instant  the  body  is  in  the  exact  place  it  would  have  been  in  if  the 
forces  had  acted  during  alternate  instants  instead  of  acting  in  the  same 
instant  (saving  that  if  we  suppose  two  forces  to  act  successively  which  are 
in  truth  simultaneous  we  must  of  course  allow  them  double  the  time).  It 
is  evident,  therefore,  that  each  force  has  had,  during  each  instant,  all  the 
effect  which  belonged  to  it;  and  that  the  modifying  influence  which  one 
of  two  concurrent  causes  is  said  to  exercise  with  respect  to  the  other  may 
be  considered  as  exerted  not  over  the  action  of  the  cause  itself,  but  over 
the  effect  after  it  is  completed.  For  all  purposes  of  predicting,  calcula- 
ting, or  explaining  their  joint  result,  causes  which  compound  their  effects 
may  be  treated  as  if  they  produced  simultaneously  each  of  them  its  own 
effect,  and  all  these  effects  co-existed  visibly. 

Since  the  laws  of  causes  are  as  really  fulfilled  when  the  causes  are  said 
to  be  counteracted  by  opposing  causes,  as  when  they  are  left  to  their  own 
undisturbed  action,  we  must  be  cautious  not  to  express  the  laws  in  such 
terms  as  would  render  the  assertion  of  their  being  fulfilled  in  those  cases  a 
contradiction.  If,  for  instance,  it  were  stated  as  a law  of  nature  that  a 
body  to  which  a force  is  applied  moves  in  the  direction  of  the  force,  with  a 
velocity  proportioned  to  the  force  directly,  and  to  its  own  mass  inversely; 
when  in  point  of  fact  some  bodies  to  which  a force  is  applied  do  not  move 
at  all,  and  those  which  do  move  (at  least  in  the  region  of  our  earth)  are, 
from  the  very  first,  retarded  by  the  action  of  gravity  and  other  resisting 
forces,  and  at  last  stopped  altogether;,  it  is  clear  that  the  general  proposi- 
tion, though  it  would  be  true  under  a certain  hypothesis,  would  not  ex- 
press the  facts  as  they  actually  occur.  To  accommodate  tbe  expression  of 
the  law  to  the  real  phenomena,  we  must  say,  not  that  the  object  moves,  but 


INTERMIXTURE  OF  EFFECTS. 


319 


that  it  tends  to  move,  in  the  direction  and  with  the  velocity  specified. 
We  might,  indeed,  guard  our  expression  in  a different  mode,  by  saying 
that  tire  body  moves  in  that  manner  unless  prevented,  or  except  in  so  far 
as  prevented,  by  some  counteracting  cause.  But  the  body  does  not  only 
move  in  that  manner  unless  counteracted ; it  tends  to  move  in  that  manner 
even  when  counteracted;  it  still  exerts,  in  the  original  direction,  the  same 
energy  of  movement  as  if  its  first  impulse  had  been  undisturbed,  and  pro- 
duces, by  that  energy,  an  exactly  equivalent  quantity  of  effect.  This  is 
true  even  when  the  force  leaves  the  body  as  it  found  it,  in  a state  of  abso- 
lute rest;  as  when  we  attempt  to  raise  a body  of  three  tons’ weight  with 
a force  equal  to  one  ton.  For  if,  while  we  are  applying  this  force,  wind  or 
water  or  any  other  agent  supplies  an  additional  force  just  exceeding  two 
tons,  the  body  will  be  raised;  thus  proving  that  the  force  we  applied  ex- 
erted its  full  effect,  by  neutralizing  an  equivalent  jjortion  of  the  weight 
which  it  was  insufficient  altogether  to  overcome.  And  if,  while  we  are 
exerting  this  force  of  one  ton  upon  the  object  in  a direction  contrary  to 
that  of  gravity,  it  be  put  into  a scale  and  weighed,  it  will  be  found  to  have 
lost  a ton  of  its  weight,  or,  in  other  words,  to  press  downward  with  a force 
only  equal  to  the  difference  of  the  two  forces. 

These  facts  are  correctly  indicated  by  the  expression  tendency.  All  laws 
of  causation,  in  consequence  of  their  liability  to  be  counteracted,  require  to 
be  stated  in  words  affirmative  of  tendencies  only,  and  not  of  actual  results. 
In  those  sciences  of  causation  which  have  an  accurate  nomenclature,  there 
are  special  words  which  signify  a tendency  to  the  particular  effect  with 
which  the  science  is  conversant;  thus  pressure,  in  mechanics,  is  synony- 
mous with  tendency  to  motion,  and  forces  are  not  reasoned  on  as  causing 
actual  motion,  but  as  exerting  pressure.  A similar  improvement  in  termi- 
nology would  be  very  salutary  in  many  other  branches  of  science. 

The  habit  of  neglecting  this  necessary  element  in  the  precise  expression 
of  the  laws  of  nature,  has  given  birth  to  the  popular  prejudice  that  all  gen- 
eral truths  have  exceptions  ; and  much  unmerited  distrust  has  thence  ac- 
crued to  the  conclusions  of  science,  when  they  have  been  submitted  to  the 
judgment  of  minds  insufficiently  disciplined  and  cultivated.  The  rough 
generalizations  suggested  by  common  observation  usually  have  exceptions; 
but  principles  of  science,  or,  in  other  words,  laws  of  causation,  have  not. 
“What  is  thought  to  be  an  exception  to  a principle”  (to  quote  words  used 
on  a different  occasion),  “ is  always  some  other  and  distinct  principle  cut- 
ting into  the  former;  some  other  force  which  impinges*  against  the  first 
force,  and  deflects  it  from  its  direction.  There  are  not  a law  and  an  excep- 
tion to  that  law,  the  law  acting  in  ninety-nine  cases,  and  the  exception  in 
one.  There  are  two  laws,  each  possibly  acting  in  the  whole  hundred  cases, 
and  bringing  about  a common  effect  by  their  conjunct  operation.  If  the 
force  which,  being  the  less  conspicuous  of  the  two,  is  called  the  disturbing 
force,  prevails  sufficiently  over  the  other  force  in  some  one  case,  to  consti- 
tute that  case  what  is  commonly  called  an  exception,  the  same  disturbing 
force  probably  acts  as  a modifying  cause  in  many  other  cases  which  no  one 
will  call  exceptions. 

“ Thus  if  it  were  stated  to  be  a law  of  nature  that  all  heavy  bodies  fall 
to  the  ground,  it  would  probably  be  said  that  the  resistance  of  the  atmos- 
phere, which  prevents  a balloon  from  falling,  constitutes  the  balloon  an  ex- 

* It  seems  hardly  necessary  to  say  that  the  word  impinae.  as  a general  term  to  express  col- 
lision of  forces,  is  here  used  by  a figure  of  speech,  and  not  as  expressive  of  any  theory  respect- 
ing the  nature  of  force. 


320 


INDUCTION. 


ception  to  that  pretended  law  of  nature.  But  the  real  law  is,  that  all  heavy 
bodies  tend  to  fall ; and  to  this  there  is  no  exception,  not  even  the  sun  and 
moon  ; for  even  they,  as  every  astronomer  knows,  tend  toward  the  earth, 
with  a force  exactly  equal  to  that  with  which  the  earth  tends  toward  them. 
The  resistance  of  the  atmosphere  might,  in  the  particular  case  of  the  bal- 
loon, from  a misapprehension  of  what  the  law  of  gravitation  is,  be  said  to 
prevail  over  the  law  ; but  its  disturbing  effect  is  quite  as  real  in  every 
other  case,  since  though  it  does  not  prevent,  it  retards  the  fall  of  all  bodies 
whatever.  The  rule,  and  the  so-called  exception,  do  not  divide  the  cases 
between  them ; each  of  them  is  a comprehensive  rule  extending  to  all  cases. 
To  call  one  of  these  concurrent  principles  an  exception  to  the  other,  is  su- 
perficial, and  contrary  to  the  correct  principles  of  nomenclature  and  ar- 
rangement. An  effect  of  precisely  the  same  kind,  and  arising  from  the 
same  cause,  ought  not  to  be  placed  in  two  different  categories,  merely  as 
there  does  or  does  not  exist  another  cause  preponderating  over  it.”* 

§ 6.  We  have  now  to  consider  according  to  what  method  these  complex 
effects,  compounded  of  the  effects  of  many  causes,  are  to  be  studied  ; how 
we  are  enabled  to  trace  each  effect  to  the  concurrence  of  causes  in  which 
it  originated,  and  ascertain  the  conditions  of  its  recurrence — the  circum- 
stances in  which  it  may  be  expected  again  to  occur.  The  conditions  of  a 
phenomenon  which  arises  from  a composition  of  causes,  may  be  investi- 
gated either  deductively  or  experimentally. 

The  case,  it  is  evident,  is  naturally  susceptible  of  the  deductive  mode  of 
investigation.  The  law  of  an  effect  of  this  description  is  a result  of  the 
laws  of  the  separate  causes  on  the  combination  of  which  it  depends,  and  is, 
therefore,  in  itself  capable  of  being  deduced  from  these  laws.  This  is  call- 
ed the  method  a priori.  The  other,  or  a jyosteriori  method,  professes  to 
proceed  according  to  the  canons  of  experimental  inquiry.  Considering 
the  whole  assemblage  of  concurrent  causes  which  produced  the  phenome- 
non, as  one  single  cause,  it  attempts  to  ascertain  the  cause  in  the  ordinary 
manner,  by  a comparison  of  instances.  This  second  method  subdivides 
itself  into  two  different  varieties.  If  it  merely  collates  instances  of  the 
effect,  it  is  a method  of  pure  observation.  If  it  operates  upon  the  causes, 
and  tries  different  combinations  of  them,  in  hopes  of  ultimately  hitting  the 
precise  combination  which  will  produce  the  given  total  effect,  it  is  a method 
of  experiment. 

In  order  more  completely  to  clear  up  the  nature  of  each  of  these  three 
methods,  and  determine  which  of  them  deserves  the  preference,  it  will  be 
expedient  (conformably  to  a favorite  maxim  of  Lord  Chancellor  Eldon,  to 
which,  though  it  has  often  incurred  philosophical  ridicule,  a deeper  phi- 
losophy will  not  refuse  its  sanction)  to  “clothe  them  in  circumstances.” 
We  shall  select  for  this  purpose  a case  which  as  yet  furnishes  no  very  brill- 
iant example  of  the  success  of  any  of  the  three  methods,  but  which  is  all 
the  more  suited  to  illustrate  the  difficulties  inherent  in  them.  Let  the  sub- 
ject of  inquiry  be,  the  conditions  of  health  and  disease  in  the  human  body; 
or  (for  greater  simplicity)  the  conditions  of  recovery  from  a given  disease ; 
and  in  order  to  narrow  the  question  still  more,  let  it  be  limited,  in  the  first 
instance,  to  this  one  inquiry:  Is,  or  is  not,  some  particular  medicament 
(mercury,  for  instance)  a remedy  for  the  given  disease. 

Now,  the  deductive  method  would  set  out  from  known  properties  of 


Essays  on  some  Unsettled  Questions  of  Political  Economy , Essay  V. 


INTERMIXTURE  OF  EFFECTS. 


321 


mercury,  and  known  laws  of  the  human  body,  and  by  reasoning  from  these, 
would  attempt  to  discover  whether  mercury  will  act  upon  the  body  when 
in  the  morbid  condition  supposed,  in  such  a manner  as  would  tend  to  re- 
store health.  The  experimental  method  would  simply  administer  mercury 
in  as  many  cases  as  possible,  noting  the  age,  sex,  temperament,  and  other 
peculiarities  of  bodily  constitution,  the  particular  form  or  variety  of  the 
disease,  the  particular  stage  of  its  progress,  etc.,  remarking  in  which  of 
these  cases  it  was  attended  with  a salutary  effect,  and  with  what  circum- 
stances it  was  on  those  occasions  combined.  The  method  of  simple  obser- 
vation would  compare  instances  of  recovery,  to  find  whether  they  agreed 
in  having  been  preceded  by  the  administration  of  mercury ; or  would  com- 
pare instances  of  recovery  with  instances  of  failure,  to  find  cases  which, 
agreeing  in  all  other  respects,  differed  only  in  the  fact  that  mercury  had 
been  administered,  or  that  it  had  not. 

§ V.  That  the  last  of  these  three  modes  of  investigation  is  applicable  to 
the  case,  no  one  has  ever  seriously  contended.  No  conclusions  of  value  on 
a subject  of  such  intricacy  ever  were  obtained  in  that  way.  The  utmost 
that  could  result  would  be  a vague  general  impression  for  or  against  the 
efficacy  of  mercury,  of  no  avail  for  guidance  unless  confirmed  by  one  of  the 
other  two'  methods.  Not  that  the  results,  wThich  this  method  strives  to  ob- 
tain, would  not  be  of  the  utmost  possible  value  if  they  could  be  obtained. 
If  all  the  cases  of  recovery  which  presented  themselves,  in  an  examination 
extending  to  a great  number  of  instances,  were  cases  in  which  mercury  had 
been  administered,  we  might  generalize  with  confidence  from  this  expe- 
rience, and  should  have  obtained  a conclusion  of  real  value.  But  no  such 
basis  for  generalization  can  we,  in  a case  of  this  description,  hope  to  obtain. 
The  reason  is  that  which  we  have  spoken  of  as  constituting  the  character- 
istic imperfection  of  the  Method  of  Agreement,  Plurality  of  Causes.  Sup- 
posing even  that  mercury  does  tend  to  cure  the  disease,  so  many  other 
causes,  both  natural  and  artificial,  also  tend  to  cure  it,  that  there  are  sure 
to  be  abundant  instances  of  recovery  in  which  mercury  has  not  been  ad- 
ministered, unless,  indeed,  the  practice  be  to  administer  it  in  all  cases;  on 
which  supposition  it  will  equally  be  found  in  the  cases  of  failure. 

When  an  effect  results  from  the  union  of  many  causes,  the  share  which 
each  has  in  the  determination  of  the  effect  can  not  in  general  be  great, 
and  the  effect  is  not  likely,  even  in  its  presence  or  absence,  still  less  in  its 
variations,  to  follow,  even  approximately,  any  one  of  the  causes.  Recov- 
ery from  a disease  is  an  event  to  which,  in  every  case,  many  influences 
must  concur.  Mercury  may  be  one  such  influence  ; but  from  the  very  fact 
that  there  are  many  other  such,  it  will  necessarily  happen  that  although 
mercury  is  administered,  the  patient,  for  want  of  other  concurring  influ- 
ences, will  often  not  recover,  and  that  he  often  will  recover  when  it  is 
not  administered,  the  other  favorable  influences  being  sufficiently  powerful 
without  it.  Neither,  therefore,  will  the  instances  of  recovery  agree  in  the 
administration  of  mercury,  nor  will  the  instances  of  failure  agree  in  its 
non  - administration.  It  is  much  if,  by  multiplied  and  accurate  returns 
from  hospitals  and  the  like,  we  can  collect  that  there  are  rather  more  re- 
coveries and  rather  fewer  failures  when  mercury  is  administered  than  when 
it  is  not ; a result  of  very  secondary  value  even  as  a guide  to  practice,  and 
almost  worthless  as  a contribution  to  the  theory  of  the  subject.* 

* It  is  justly  remarked  by  Professor  Bain,  that  though  the  Methods  of  Agreement  and  Dif- 
ference are  not  applicable  to  these  cases,  they  are  not  wholly  inaccessible  to  the  Method  of 

21 


322 


INDUCTION. 


§ 8.  The  inapplicability  of  the  method  of  simple  observation  to  ascertain 
the  conditions  of  effects  dependent  on  many  concurring  causes,  being  thus 
recognized,  we  shall  next  inquire  whether  any  greater  benefit  can  be  ex- 
pected from  the  other  branch  of  the  a posteriori  method,  that  which  pro- 
ceeds by  directly  trying  different  combinations  of  causes,  either  artificially 
produced  or  found  in  nature,  and  taking  notice  what  is  their  effect;  as,  for 
example,  by  actually  trying  the  effect  of  mercury  in  as  many  different  cir- 
cumstances as  possible.  This  method  differs  from  the  one  which  we  have 
just  examined  in  turning  our  attention  directly  to  the  causes  or  agents, 
instead  of  turning  it  to  the  effect,  recovery  from  the  disease.  And  since, 
as  a general  rule,  the  effects  of  causes  are  far  more  accessible  to  our  study 
than  the  causes  of  effects,  it  is  natural  to  think  that  this  method  has  a 
much  better  chance  of  proving  successful  than  the  former. 

The  method  now  under  consideration  is  called  the  Empirical  Method  ; 
and  in  order  to  estimate  it  fairly,  we  must  suppose  it  to  be  completely,  not 
incompletely,  empirical.  We  must  exclude  from  it  every  thing  which  par- 
takes of  the  nature  not  of  an  experimental  but  of  a deductive  operation. 
If,  for  instance,  we  try  experiments  with  mercury  upon  a person  in  health, 
in  order  to  ascertain  the  general  laws  of  its  action  upon  the  human  body, 
and  then  reason  from  these  laws  to  determine  how  it  will  act  upon  persons 
affected  with  a particular  disease,  this  may  be  a really  effectual  method ; 
but  this  is  deduction.  The  experimental  method  does  not  derive  the  law 
of  a complex  case  from  the  simpler  laws  which  conspire  to  produce  it,  but 
makes  its  experiments  directly  upon  the  complex  case.  We  must  make 
entire  abstraction  of  all  knowledge  of  the  simpler  tendencies,  the  modi 
operandi  of  mercury  in  detail.  Our  experimentation  must  aim  at  obtain- 
ing a direct  answer  to  the  specific  question,  Does  or  does  not  mercury  tend 
to  cure  the  particular  disease? 

Let  us  see,  therefore,  how  far  the  case  admits  of  the  observance  of  those 
rules  of  experimentation  which  it  is  found  necessary  to  observe  in  other 
cases.  When  we  devise  an  experiment  to  ascertain  the  effect  of  a given 
agent,  there  are  certain  precautions  which  we  never,  if  we  can  help  it,  omit. 
In  the  first  place,  we  introduce  the  agent  into  the  midst  of  a set  of  circum- 
stances which  we  have  exactly  ascertained.  It  needs  hardly  be  remarked 
how  far  this  condition  is  from  being  realized  in  any  case  connected  with 
the  phenomena  of  life;  how  far  we  are  from  knowing  what  are  all  the  cir- 
cumstances which  pre-exist  in  any  instance  in  which  mercury  is  adminis- 
tered to  a living  being.  This  difficulty,  however,  though  insuperable  in 

Concomitant  Variations.  “If  a cause  happens  to  vary  alone,  the  effect  will  also  vary  alone: 
a cause  and  effect  may  be  thus  singled  out  under  the  greatest  complications.  Thus,  when  the 
appetite  for  food  increases  with  the  cold,  we  have  a strong  evidence  of  connection  between 
these  two  facts,  although  other  circumstances  may  operate  in  the  same  direction.  The  as- 
signing of  the  respective  parts  of  the  sun  and  moon  in  the  action  of  the  tides  may  be  effected, 
to  a certain  degree  of  exactness,  by  the  variations  of  the  amount  according  to  the  positions 
of  the  two  attractive  bodies.  By  a series  of  experiments  of  Concomitant  Variations,  directed 
to  ascertain  the  elimination  of  nitrogen  from  the  human  body  under  varieties  of  muscular  ex- 
ercise, Dr.  Parkes  obtained  the  remarkable  conclusion,  that  a muscle  grows  during  exercise, 
and  loses  bulk  during  the  subsequent  rest.”  {Logic,  ii.,  83.) 

It  is,  no  doubt,  often  possible  to  single  out  the  influencing  causes  from  among  a great  num- 
ber of  mere  concomitants,  by  noting  what  are  the  antecedents,  a variation  in  which  is  followed 
by  a variation  in  the  effect.  But  when  there  are  many  influencing  causes,  no  one  of  their, 
greatly  predominating  over  the  rest,  and  especially  when  some  of  these  are  continually  chan- 
ging, it  is  scarcely  ever  possible  to  trace  such  a relation  between  the  variations  of  the  effect 
and  those  of  any  one  cause  as  would  enable  us  to  assign  to  that  cause  its  real  share  in  the 
production  of  the  effect. 


INTERMIXTURE  OF  EFFECTS. 


323 


most  cases,  may  not  be  so  in  all ; there  are  sometimes  concurrences  of 
many  causes,  in  which  we  yet  know  accurately  what  the  causes  are.  More- 
over, the  difficulty  may  be  attenuated  by  sufficient  multiplication  of  experi- 
ments, in  circumstances  rendering  it  improbable  that  any  of  the  unknown 
causes  should  exist  in  them  all.  But  when  we  have  got  clear  of  this  ob- 
stacle, we  encounter  another  still  more  serious.  In  other  cases,  when  we 
intend  to  try  an  experiment,  we  do  not  reckon  it  enough  that  there  be  no 
circumstance  in  the  case  the  presence  of  which  is  unknown  to  us.  We  re- 
quire, also,  that  none  of  the  circumstances  which  we  do  know  shall  have 
effects  susceptible  of  being  confounded  with  those  of  the  agents  whose 
properties  we  wish  to  study.  We  take  the  utmost  pains  to  exclude  all 
causes  capable  of  composition  with  the  given  cause;  or,  if  forced  to  let  in 
any  such  causes,  we  take  care  to  make  them  such  that  we  can  compute 
and  allow  for  their  influence,  so  that  the  effect  of  the  given  cause  may,  af- 
ter the  subduction  of  those  other  effects,  be  apparent  as  a residual  phe- 
nomenon. 

These  precautions  are  inapplicable  to  such  cases  as  we  are  now  consid- 
ering. The  mercury  of  our  experiment  being  tried  with  an  unknown  mul- 
titude (or  even  let  it  be  a known  multitude)  of  other  influencing  circum- 
stances, the  mere  fact  of  their  being  influencing  circumstances  implies  that 
they  disguise  the  effect  of  the  mercury,  and  preclude  us  from  knowing 
whether  it  has  any  effect  or  not.  Unless  we  already  knew  what  and  how 
much  is  owing  to  every  other  circumstance  (that  is,  unless  wre  suppose  the 
very  problem  solved  which  we  are  considering  the  means  of  solving),  we 
can  not  tell  that  those  other  circumstances  may  not  have  produced  the 
whole  of  the  effect,  independently  or  even  in  spite  of  the  mercury.  The 
Method  of  Difference,  in  the  ordinary  mode  of  its  use,  namely,  by  com- 
paring the  state  of  things  following  the  experiment  with  the  state  which 
preceded  it,  is  thus,  in  the  case  of  intermixture  of  effects,  entirely  unavail- 
ing; because  other  causes  than  that  whose  effect  we  are  seeking  to  deter- 
mine have  been  operating  during  the  transition.  As  for  the  other  mode 
of  employing  the  Method  of  Difference,  namely,  by  comparing,  not  the 
same  case  at  two  different  periods,  but  different  cases,  this  in  the  present 
instance  is  quite  chimerical.  In  phenomena  so  complicated  it  is  question- 
able if  two  cases,  similar  in  all  respects  but  one,  ever  occurred ; and  were 
they  to  occur,  we  could  not  possibly  know  that  they  were  so  exactly 
similar. 

Any  thing  like  a scientific  use  of  the  method  of  experiment,  in  these  com- 
plicated cases,  is  therefore  out  of  the  question.  We  can  generally,  even  in 
the  most  favorable  cases,  only  discover  by  a succession  of  trials,  that  a cer- 
tain cause  is  very  often  followed  by  a certain  effect.  For,  in  one  of  these 
conjunct  effects,  the  portion  which  is  determined  by  any  one  of  the  in- 
fluencing agents,  is  usually,  as  wre  before  remarked,  but  small ; and  it  must 
be  a more  potent  cause  than  most,  if  even  the  tendency  which  it  really  ex- 
erts is  not  thwarted  by  other  tendencies  in  nearly  as  many  cases  as  it  is  ful- 
filled. Some  causes  indeed  there  are  which  are  more  potent  than  any 
counteracting  causes  to  which  they  are  commonly  exposed ; and  according- 
ly there  are  some  truths  in  medicine  which  are  sufficiently  proved  by  direct 
experiment.  Of  these  the  most  familiar  are  those  that  relate  to  the  efficacy 
of  the  substances  known  as  Specifics  for  particular  diseases,  “ quinine, 
colchicum,  lime-juice,  cod-liver  oil,”*  and  a few  others.  Even  these  are 


Bain’s  Logic,  ii. , 360. 


324 


INDUCTION. 


not  invariably  followed  by  success ; but  they  succeed  in  so  large  a propor- 
tion of  cases,  and  against  such  powerful  obstacles,  that  their  tendency  to 
restore  health  in  the  disorders  for  which  they  are  prescribed  may  be  re- 
garded as  an  experimental  truth.* 

If  so  little  can  be  done  by  the  experimental  method  to  determine  the 
conditions  of  an  effect  of  many  combined  causes,  in  the  case  of  medical 
science;  still  less  is  this  method  applicable  to  a class  of  phenomena  more 
complicated  than  even  those  of  physiology,  the  phenomena  of  politics  and 
history.  There,  Plurality  of  Causes  exists  in  almost  boundless  excess,  and 
effects  are,  for  the  most  part,  inextricably  interwoven  with  one  another.  To 
add  to  the  embarrassment,  most  of  the  inquiries  in  political  science  relate 
to  the  production  of  effects  of  a most  comprehensive  description,  such  as 
the  public  wealth,  public  security,  public  morality,  and  the  like:  results 
liable  to  be  affected  directly  or  indirectly  either  in  plus  or  in  mimes  by 
nearly  every  fact  which  exists,  or  event  which  occurs,  in  human  society. 
The  vulgar  notion,  that  the  safe  methods  on  political  subjects  are  those  of 
Baconian  induction — that  the  true  guide  is  not  general  reasoning,  but  spe- 
cific experience— will  one  day  be  quoted  as  among  the  most  unequivocal 
marks  of  a low  state  of  the  speculative  faculties  in  any  age  in  which  it  is 
accredited.  Nothing  can  be  more  ludicrous  than  the  sort  of  parodies  on 
experimental  reasoning  which  one  is  accustomed  to  meet  with,  not  in  pop- 
ular discussion  only,  but  in  grave  treatises,  when  the  affairs  of  nations 
are  the  theme.  “How,”  it  is  asked,  “can  an  institution  be  bad,  when  the 
country  has  prospered  under  it?”  “How  can  such  or  such  causes  have 
contributed  to  the  prosperity  of  one  country,  when  another  has  prospered 
without  them?”  Whoever  makes  use  of  an  argument  of  this  kind,  not  in- 
tending to  deceive,  should  be  sent  back  to  learn  the  elements  of  some  one 
of  the  more  easy  physical  sciences.  Such  reasoners  ignore  the  fact  of 
Plurality  of  Causes  in  the  very  case  which  affords  the  most  signal  example 
of  it.  So  little  could  be  concluded,  in  such  a case,  from  any  possible  colla- 
tion of  individual  instances,  that  even  the  impossibility,  in  social  phenomena, 
of  making  artificial  experiments,  a circumstance  otherwise  so  prejudicial  to 
directly  inductive  inquiry,  hardly  affords,  in  this  case,  additional  reason  of 
regret.  For  even  if  we  could  try  experiments  upon  a nation  or  upon  the 
human  race,  with  as  little  scruple  as  M.  Magendie  tried  them  on  dogs  and 
rabbits,  we  should  never  succeed  in  making  two  instances  identical  in  every 
respect  except  the  presence  or  absence  of  some  one  definite  circumstance. 
The  nearest  approach  to  an  experiment  in  the  philosophical  sense,  which 
takes  place  in  politics,  is  the  introduction  of  a new  operative  element  into 
national  affairs  by  some  special  and  assignable  measure  of  government, 
such  as  the  enactment  or  repeal  of  a particular  law.  But  where  there  are 
so  many  influences  at  work,  it  requires  some  time  for  the  influence  of  any 
new  cause  upon  national  phenomena  to  become  apparent;  and  as  the  causes 
operating  in  so  extensive  a sphere  are  not  only  infinitely  numerous,  but  in 
a state  of  perpetual  alteration,  it  is  always  certain  that  before  the  effect  of 

* What  is  said  in  the  text  on  the  applicability  of  the  experimental  methods  to  resolve  par- 
ticular questions  of  medical  treatment,  does  not  detract  from  their  efficacy  in  ascertaining  the 
general  laws  of  the  animal  or  human  system.  The  functions,  for  example,  of  the  different 
classes  of  nerves  have  been  discovered,  and  probably  could  only  have  been  discovered,  by  ex- 
periments on  living  animals.  Observation  and  experiment  are  the  ultimate  basis  of  all  knowl- 
edge : from  them  we  obtain  the  elementary  laws  of  life,  as  we  obtain  all  other  elementary  truths. 
It  is  in  dealing  with  the  complex  combinations  that  the  experimental  methods  are  for  the  most 
part  illusory,  and  the  deductive  mode  of  investigation  must  be  invoked  to  disentangle  the  com- 
plexity. 


THE  DEDUCTIVE  METHOD. 


325 


the  new  cause  becomes  conspicuous  enough  to  be  a subject  of  induction,  so 
many  of  the  other  influencing  circumstances  will  have  changed  as  to  vitiate 
the  experiment.* 

Two,  therefore,  of  the  three  possible  methods  for  the  study  of  phenomena 
resulting  from  the  composition  of  many  causes,  being,  from  the  very  nature 
of  the  case,  inefficient  and  illusory,  there  remains  only  the  third — that  which 
considers  the  causes  separately,  and  infers  the  effect  from  the  balance  of 
the  different  tendencies  which  produce  it : in  short,  the  deductive,  or  a pri- 
ori method.  The  more  particular  consideration  of  this  intellectual  process 
requires  a chapter  to  itself. 


CHAPTER  XI. 

OF  THE  DEDUCTIVE  METHOD. 

§ 1.  The  mode  of  investigation  which,  from  the  proved  inapplicability 
of  direct  methods  of  observation  and  experiment,  remains  to  us  as  the 
main  source  of  the  knowledge  we  possess  or  can  acquire  respecting  the 
conditions  and  laws  of  recurrence,  of  the  more  complex  phenomena,  is 
called,  in  its  most  general  expression,  the  Deductive  Method  ; and  consists 
of  three  operations : the  first,  one  of  direct  induction ; the  second,  of  ra- 
tiocination ; the  third,  of  verification. 

I call  the  first  step  in  the  process  an  inductive  operation,  because  there 
must  be  a direct  induction  as  the  basis  of  the  whole ; though  in  many  par- 
ticular investigations  the  place  of  the  induction  may  be  supplied  by  a prior 
deduction ; but  the  premises  of  this  prior  deduction  must  have  been  de- 
rived from  induction. 

The  problem  of  the  Deductive  Method  is,  to  find  the  law  of  an  effect, 
from  the  laws  of  the  different  tendencies  of  which  it  is  the  'joint  result. 
The  first  requisite,  therefore,  is  to  know  the  laws  of  those  tendencies;  the 
law  of  each  of  the  concurrent  causes : and  this  supposes  a previous  proc- 
ess of  observation  or  experiment  upon  each  cause  separately;  or  else  a pre- 
vious deduction,  which  also  must  depend  for  its  ultimate  premises  on  ob- 
servation or  experiment.  Thus,  if  the  subject  be  social  or  historical  phe- 
nomena, the  premises  of  the  Deductive  Method  must  be  the  laws  of  the 
causes  which  determine  that  class  of  phenomena ; and  those  causes  are  hu- 
man actions,  together  with  the  general  outward  circumstances  under  the 

* Professor  Bain,  though  concurring  generally  in  the  views  expressed  in  this  chapter,  seems 
to  estimate  more  highly  than  I do  the  scope  for  specific  experimental  evidence  in  politics. 
{Logic,  ii. , 333-337.)  There  are,  it  is  true,  as  he  remarks  (p.  336),  some  cases  “when  an 
agent  suddenly  introduced  is  almost  instantaneously  followed  by  some  other  changes,  as  when 
the  announcement  of  a diplomatic  rupture  between  two  nations  is  followed  the  same  day  by  a 
derangement  of  the  money-market.”  But  this  experiment  would  be  quite  inconclusive  merely 
as  an  experiment.  It  can  only  serve,  as  any  experiment  may,  to  verify  the  conclusion  of  a 
deduction.  Unless  we  already  knew  by  our  knowledge  of  the  motives  which  act  on  business 
men,  that  the  prospect  of  war  tends  to  derange  the  money-market,  we  should  never  have  been 
able  to  prove  a connection  between  the  two  facts,  unless  after  having  ascertained  historically 
that  the  one  followed  the  other  in  too  great  a number  of  instances  to  be  consistent  with  their 
having  been  recorded  with  due  precautions.  Whoever  has  carefully  examined  any  of  the  at- 
tempts continually  made  to  prove  economic  doctrines  by  such  a recital  of  instances,  knows 
well  how  futile  they  are.  It  always  turns  out  that  the  circumstances  of  scarcely  any  of  the 
cases  have  been  fully  stated ; and  that  cases,  in  equal  or  greater  numbers,  have  been  omitted 
which  would  have  tended  to  an  opposite  conclusion. 


326 


INDUCTION. 


influence  of  which  mankind  are  placed,  and  which  constitute  man’s  posi- 
tion on  the  earth.  The  Deductive  Method,  applied  to  social  phenomena, 
must  begin,  therefore,  by  investigating,  or  must  suppose  to  have  been  al- 
ready investigated,  the  laws  of  human  action,  and  those  properties  of  out- 
ward things  by  which  the  actions  of  human  beings  in  society  are  deter- 
mined. Some  of  these  general  truths  will  naturally  be  obtained  by  obser- 
vation and  experiment,  others  by  deduction : the  more  complex  laws  of 
human  action,  for  example,  may  be  deduced  from  the  simpler  ones;  but 
the  simple  or  elementary  laws  will  always,  and  necessarily,  have  been  ob- 
tained by  a directly  inductive  process. 

To  ascertain,  then,  the  laws  of  each  separate  cause  which  takes  a share 
in  producing  the  effect,  is  the  first  desideratum  of  the  Deductive  Method. 
To  know  what  the  causes  are  which  must  be  subjected  to  this  process  of 
study,  may  or  may  not  be  difficult.  In  the  case  last  mentioned,  this  first 
condition  is  of  easy  fulfillment.  That  social  phenomena  depend  on  the  acts 
and  mental  impressions  of  human  beings,  never  could  have  been  a matter 
of  any  doubt,  however  imperfectly  it  may  have  been  known  either  by  what 
laws  those  impressions  and  actions  are  governed,  or  to  what  social  conse- 
quences their  laws  naturally  lead.  Neither,  again,  after  physical  science 
had  attained  a certain  development,  could  there  be  any  real  doubt  where  to 
look  for  the  laws  on  which  the  phenomena  of  life  depend,  since  they  must 
be  the  mechanical  and  chemical  laws  of  the  solid  and  fluid  substances  com 
posing  the  organized  body  and  the  medium  in  which  it  subsists,  together 
with  the  peculiar  vital  laws  of  the  different  tissues  constituting  the  organic 
structure.  In  other  cases,  really  far  more  simple  than  these,  it  was  much 
less  obvious  in  what  quarter  the  causes  were  to  be  looked  for:  as  in  the 
case  of  the  celestial  phenomena.  Until,  by  combining  the  laws  of  certain 
causes,  it  was  found  that  those  laws  explained  all  the  facts  which  experi- 
ence had  proved  concerning  the  heavenly  motions,  and  led  to  predictions 
which  it  always  verified,  mankind  never  knew  that  those  were  the  causes. 
But  whether  we  are  able  to  put  the  question  before,  or  not  until  after,  we 
have  become  capable  of  answering  it,  in  either  case  it  must  be  answered ; 
the  laws  of  the  different  causes  must  be  ascertained,  before  we  can  proceed 
to  deduce  from  them  the  conditions  of  the  effect. 

The  mode  of  ascertaining  those  laws  neither  is,  nor  can  be  any  other 
than  the  fourfold  method  of  experimental  inquiry,  already  discussed.  A 
few  remarks  on  the  application  of  that  method  to  cases  of  the  Composition 
of  Causes  are  all  that  is  requisite. 

It  is  obvious  that  we  can  not  expect  to  find  the  law  of  a tendency  by 
an  induction  from  cases  in  which  the  tendency  is  counteracted.  The  laws 
of  motion  could  never  have  been  brought  to  light  from  the  observation  of 
bodies  kept  at  rest  by  the  equilibrium  of  opposing  forces.  Even  where  the 
tendency  is  not,  in  the  ordinary  sense  of  the  word,  counteracted,  but  only 
modified,  by  having  its  effects  compounded  with  the  effects  arising  from 
some  other  tendency  or  tendencies,  we  are  still  in  an  unfavorable  position 
for  tracing,  by  means  of  such  cases,  the  law  of  the  tendency  itself.  It 
M'ould  have  been  scarcely  possible  to  discover  the  law  that  every  body  in 
motion  tends  to  continue  moving  in  a straight  line,  by  an  induction  from 
instances  in  which  the  motion  is  deflected  into  a curve,  by  being  compound- 
ed with  the  effect  of  an  accelerating  force.  Notwithstanding  the  resources 
afforded  in  this  description  of  cases  by  the  Method  of  Concomitant  Varia- 
tions, the  principles  of  a judicious  experimentation  prescribe  that  the  law 
of  each  of  the  tendencies  should  be  studied,  if  possible,  in  cases  in  which 


THE  DEDUCTIVE  METHOD. 


327 


that  tendency  operates  alone,  or  in  combination  with  no  agencies  but  those 
of  which  the  effect  can,  from  previous  knowledge,  be  calculated  and  allow- 
ed for. 

Accordingly,  in  the  cases,  unfortunately  very  numerous  and  important, 
in  which  the  causes  do  not  suffer  themselves  to  be  separated  and  observed 
apart,  there  is  much  difficulty  in  laying  down  with  due  certainty  the  induc- 
tive foundation  necessary  to  support  the  deductive  method.  This  difficulty 
is  most  of  all  conspicuous  in  the  case  of  physiological  phenomena;  it  being 
seldom  possible  to  separate  the  different  agencies  which  collectively  com- 
pose an  organized  body,  without  destroying  the  very  phenomena  which  it 
is  our  object  to  investigate: 

following  life,  in  creatures  we  dissect, 

We  lose  it,  in  the  moment  we  detect. 

And  for  this  reason  I am  inclined  to  the  opinion  that  physiology  (greatly 
and  rapidly  progressive  as  it  now  is)  is  embarrassed  by  greater  natural  dif- 
ficulties, and  is  probably  susceptible  of  a less  degree  of  ultimate  perfec- 
tion, than  even  the  social  science;  inasmuch  as  it  is  possible  to  study  the 
laws  and  operations  of  one  human  mind  apart  from  other  minds,  much  less 
imperfectly  than  we  can  study  the  laws  of  one  organ  or  tissue  of  the  hu- 
man body  apart  from  the  other  organs  or  tissues. 

It  has  been  judiciously  remarked  that  pathological  facts,  or,  to  speak  in 
common  language,  diseases  in  their  different  forms  and  degrees  afford  in 
the  case  of  physiological  investigation  the  most  valuable  equivalent  to  ex- 
perimentation properly  so  called ; inasmuch  as  they  often  exhibit  to  us  a 
definite  disturbance  in  some  one  organ  or  organic  function,  the  remaining 
organs  and  functions  being,  in  the  first  instance  at  least,  unaffected.  It  is 
true  that  from  the  perpetual  actions  and  reactions  which  are  going  on 
among  all  parts  of  the  organic  economy,  there  can  be  no  jmolonged  disturb- 
ance in  any  one  function  without  ultimately  involving  many  of  the  others; 
and  when  once  it-has  done  so,  the  experiment  for  the  most  part  loses  its 
scientific  value.  All  depends  on  observing  the  early  stages  of  the  derange- 
ment; which,  unfortunately,  are  of  necessity  the  least  marked.  If,  how- 
ever, the  organs  and  functions  not  disturbed  in  the  first  instance  become 
affected  in  a fixed  order  of  succession,  some  light  is  thereby  thrown  upon 
the  action  which  one  organ  exercises  over  another : and  we  occasionally 
obtain  a series  of  effects  which  we  can  refer  with  some  confidence  to  the 
original  local  derangement ; but  for  this  it  is  necessary  that  we  should  know 
that  the  original  derangement  was  local.  If  it  was  what  is  termed  consti- 
tutional; that  is,  if  we  do  not  know  in  what  part  of  the  animal  economy  it 
took  its  rise,  or  the  precise  nature  of  the  disturbance  which  took  place  in 
that  part,  we  are  unable  to  determine  which  of  the  various  derangements 
was  cause  and  which  effect  ; which  of  them  were  produced  by  one  another, 
and  which  by  the  direct,  though  perhaps  tardy,  action  of  the  original  cause. 

Besides  natural  pathological  facts,  we  can  produce  pathological  facts  ar- 
tificially : we  can  try  experiments,  even  in  the  popular  sense  of  the  term, 
by  subjecting  the  living  being  to  some  external  agent,  such  as  the  mercury 
of  our  former  example,  or  the  section  of  a nerve  to  ascertain  the  functions 
of  different  parts  of  the  nervous  system.  As  this  experimentation  is  not 
intended  to  obtain  a direct  solution  of  any  practical  question,  but  to  dis- 
cover general  laws,  from  which  afterward  the  conditions  of  any  particular 
effect  may  be  obtained  by  deduction,  the  best  cases  to  select  are  those  of 
which  the  circumstances  can  be  best  ascertained : and  such  are  generally 


328 


INDUCTION. 


not  those  in  which  there  is  any  practical  object  in  view.  The  experiments 
are  best  tried,  not  in  a state  of  disease,  which  is  essentially  a changeable 
state,  but  in  the  condition  of  health,  comparatively  a fixed  state.  In  the 
one,  unusual  agencies  are  at  work,  the  results  of  which  we  have  no  means 
of  predicting:  in  the  other,  the  course  of  the  accustomed  physiological 
phenomena  would,  it  may  generally  be  presumed,  remain  undisturbed,  were 
it  not  for  the  disturbing  cause  which  we  introduce. 

Such,  with  the  occasional  aid  of  the  Method  of  Concomitant  Variations 
(the  latter  not  less  encumbered  than  the  more  elementary  methods  by  the 
peculiar  difficulties  of  the  subject),  are  our  inductive  resources  for  ascer- 
taining the  laws  of  the  causes  considered  separately,  when  we  have  it  not 
in  our  power  to  make  trial  of  them  in  a state  of  actual  separation.  The 
insufficiency  of  these  resources  is  so  glaring,  that  no  one  can  be  surprised 
at  the  backward  state  of  the  science  of  physiology;  in  which  indeed  our 
knowledge  of  causes  is  so  imperfect,  that  we  can  neither  explain,  nor  could 
without  specific  experience  have  predicted,  many  of  the  facts  which  are 
certified  to  us  by  the  most  ordinary  observation.  Fortunately,  we  are 
much  better  informed  as  to  the  empirical  laws  of  the  phenomena,  that  is, 
the  uniformities  respecting  which  we  can  not  yet  decide  whether  they  are 
cases  of  causation,  or  mere  results  of  it.  Not  only  has  the  order  in  which 
the  facts  of  organization  and  life  successively  manifest  themselves,  from 
the  first  germ  of  existence  to  death,  been  found  to  be  uniform,  and  very 
accurately  ascertainable ; but,  by  a great  application  of  the  Method  of 
Concomitant  Variations  to  the  entire  facts  of  comparative  anatomy  and 
physiology,  the  characteristic  organic  structure  corresponding  to  each  class 
of  functions  has  been  determined  with  considerable  precision.  Whether 
these  organic  conditions  are  the  whole  of  the  conditions,  and  in  many  cases 
whether  they  are  conditions  at  all,  or  mere  collateral  effects  of  some  com- 
mon cause,  we  are  quite  ignorant ; nor  are  we  ever  likely  to  know,  unless 
we  could  construct  an  organized  body  and  try  whether  it  would  live. 

Under  such  disadvantages  do  we,  in  cases  of  this  description,  attempt 
the  initial,  or  inductive  step,  in  the  application  of  the  Deductive  Method  to 
complex  phenomena.  But  such,  fortunately,  is  not  the  common  case.  In 
general,  the  laws  of  the  causes  on  which  the  effect  depends  may  be  obtain- 
ed by  an  induction  from  comparatively  simple  instances,  or,  at  the  worst, 
by  deduction  from  the  laws  of  simpler  causes,  so  obtained.  By  simple  in- 
stances are  meant,  of  course,  those  in  which  the  action  of  each  cause  was 
not  intermixed  or  interfered  with,  or  not  to  any  great  extent,  by  other 
causes  whose  laws  were  unknown.  And  only  when  the  induction  which 
furnished  the  premises  to  the  Deductive  method  rested  on  such  instances 
has  the  application  of  such  a method  to  the  ascertainment  of  the  laws  of  a 
complex  effect,  been  attended  with  brilliant  results. 

§ 2.  When  the  laws  of  the  causes  have  been  ascertained,  and  the  first 
stage  of  the  great  logical  operation  now  under  discussion  satisfactorily  ac 
complished,  the  second  part  follows;  that  of  determining  from  the  laws  of 
the  causes  what  effect  any  given  combination  of  those  causes  will  produce. 
This  is  a process  of  calculation,  in  the  wider  sense  of  the  term ; and  very 
often  involves  processes  of  calculation  in  the  narrowest  sense.  It  is  a 
ratiocination  ; and  when  our  knowledge  of  the  causes  is  so  perfect  as  to 
extend  to  the  exact  numerical  laws  which  they  observe  in  producing  their 
effects,  the  ratiocination  may  reckon  among  its  premises  the  theorems  of 
the  science  of  number,  in  the  whole  immense  extent  of  that  science.  Not 


THE  DEDUCTIVE  METHOD. 


329 


only  are  the  most  advanced  truths  of  mathematics  often  required  to  enable 
us  to  compute  an  effect,  the  numerical  law  of  which  we  already  know;  but, 
even  by  the  aid  of  those  most  advanced  truths,  we  can  go  but  a little  way. 
In  so  simple  a case  as  the  common  problem  of  three  bodies  gravitating  to- 
ward one  another,  with  a force  directly  as  their  mass  and  inversely  as  the 
square  of  the  distance,  all  the  resources  of  the  calculus  have  not  hitherto 
sufficed  to  obtain  any  general  solution,  but  an  approximate  one.  In  a case 
a little  more  complex,  but  still  one  of  the  simplest  which  arise  in  practice, 
that  of  the  motion  of  a projectile,  the  causes  which  affect  the  velocity  and 
range  (for  example)  of  a cannon-ball  may  be  all  known  and  estimated : the 
force  of  the  gunpowder,  the  angle  of  elevation,  the  density  of  the  air,  the 
strength  and  direction  of  the  wind ; but  it  is  one  of  the  most  difficult  of 
mathematical  problems  to  combine  all  these,  so  as  to  determine  the  effect 
resulting  from  their  collective  action. 

Besides  the  theorems  of  number,  those  of  geometry  also  come  in  as 
premises,  where  the  effects  take  place  in  space,  and  involve  motion  and  ex- 
tension, as  in  mechanics,  optics,  acoustics,  astronomy.  But  when  the  com- 
plication increases,  and  the  effects  are  under  the  influence  of  so  many  and 
such  shifting  causes  as  to  give  no  room  either  for  fixed  numbers,  or  for 
straight  lines  and  regular  curves  (as  in  the  case  of  physiological,  to  say 
nothing  of  mental  and  social  phenomena),  the  laws  of  number  and  exten- 
sion are  applicable,  if  at  all,  only  on  that  large  scale  on  which  precision  of 
details  becomes  unimportant.  Although  these  laws  play  a conspicuous 
part  in  the  most  striking  examples  of  the  investigation  of  nature  by  the 
Deductive  Method,  as  for  example  in  the  Newtonian  theory  of  the  celestial 
motions,  they  are  by  no  means  an  indispensable  part  of  every  such  process. 
All  that  is  essential  in  it  is  reasoning  from  a general  law  to  a particular 
case,  that  is,  determining  by  means  of  the  particular  circumstances  of  that 
case,  what  result  is  required  in  that  instance  to  fulfill  the  law.  Thus  in 
the  Torricellian  experiment,  if  the  fact  that  air  has  weight  had  been  pre- 
viously known,  it  would  have  been  easy,  without  any  numerical  data,  to 
deduce  from  the  general  law  of  equilibrium,  that  the  mercury  would  stand 
in  the  tube  at  such  a height  that  the  column  of  mercury  would  exactly  bal- 
ance a column  of  the  atmosphere  of  equal  diameter;  because,  otherwise, 
equilibrium  would  not  exist. 

By  such  ratiocinations  from  the  separate  laws  of  the  causes,  we  may,  to 
a certain  extent,  succeed  in  answering  either  of  the  following  questions : 
Given  a certain  combination  of  causes,  what  effect  will  follow  ? and,  What 
combination  of  causes,  if  it  existed,  would  produce  a given  effect  ? In 
the  one  case,  we  determine  the  effect  to  be  expected  in  any  complex  cir- 
cumstances of  which  the  different  elements  are  known : in  the  other  case 
we  learn,  according  to  what  law  — under  what  antecedent  conditions — a 
given  complex  effect  will  occur. 

§ 3.  But  (it  may  here  be  asked)  are  not  the  same  arguments  by  which 
the  methods  of  direct  observation  and  experiment  were  set  aside  as  illuso- 
ry when  applied  to  the  laws  of  complex  phenomena,  applicable  with  equal 
force  against  the  Method  of  Deduction?  When  in  every  single  instance  a 
multitude,  often  an  unknown  multitude,  of  agencies,  are  clashing  and  com- 
bining, what  security  have  we  that  in  our  computation  a priori  we  have 
taken  all  these  into  our  reckoning?  How  many  must  we  not  generally  be 
ignorant  of?  Among  those  which  we  know,  how  probable  that  some  have 
been  overlooked ; and,  even  were  all  included,  how  vain  the  pretense  of 


330 


INDUCTION. 


summing  up  the  effects  of  many  causes,  unless  we  know  accurately  the 
numerical  law  of  each — a condition  in  most  cases  not  to  be  fulfilled;  and 
even  when  it  is  fulfilled,  to  make  the  calculation  transcends,  in  any  but 
very  simple  cases,  the  utmost  power  of  mathematical  science  with  all  its 
most  modern  improvements. 

These  objections  have  real  weight,  and  would  be  altogether  unanswer- 
able, if  there  were  no  test  by  which,  when  we  employ  the  Deductive  Meth- 
od, we  might  judge  whether  an  error  of  any  of  the  above  descriptions  had 
been  committed  or  not.  Such  a test,  however,  there  is  : and  its  application 
forms,  under  the  name  of  Verification,  the  third  essential  component  part 
of  the  Deductive  Method  ; without  which  all  the  results  it  can  give  have 
little  other  value  than  that  of  conjecture.  To  warrant  reliance  on  the  gen- 
eral conclusions  arrived  at  by  deduction,  these  conclusions  must  be  found, 
on  careful  comparison,  to  accord  with  the  results  of  direct  observation 
wherever  it  can  be  had.  If,  when  we  have  experience  to  compare  with 
them,  this  experience  confirms  them,  we  may  safely  trust  to  them  in  other 
cases  of  which  our  specific  experience  is  yet  to  come.  But  if  our  deduc- 
tions have  led  to  the  conclusion  that  from  a particular  combination  of 
causes  a given  effect  would  result,  then  in  all  known  cases  where  that  com- 
bination can  be  shown  to  have  existed,  and  where  the  effect  has  not  follow- 
ed, we  must  be  able  to  show  (or  at  least  to  make  a probable  surmise)  what 
frustrated  it:  if  we  can  not,  the  theory  is  imperfect,  and  not  yet  to  be  re- 
lied upon.  Nor  is  the  verification  complete,  unless  some  of  the  cases  in 
which  the  theory  is  borne  out  by  the  observed  result  are  of  at  least 
equal  complexity  with  any  other  cases  in  which  its  application  could  be 
called  for. 

If  direct  observation  and  collation  of  instances  have  furnished  us  with  any 
empirical  laws  of  the  effect  (whether  true  in  all  observed  cases,  or  only  true 
for  the  most  part),  the  most  effectual  verification  of  which  the  theory  could 
be  susceptible,  would  be,  that  it  led  deductively  to  those  empirical  laws; 
that  the  uniformities,  whether  complete  or  incomplete,  which  were  observed 
to  exist  among  the  phenomena,  were  accounted  for  by  the  laws  of  the  causes 
- — were  such  as  could  not  but  exist  if  those  be  really  the  causes  by  which 
the  phenomena  are  produced.  Thus  it  was  very  reasonably  deemed  an  es- 
sential requisite  of  any  true  theory  of  the  causes  of  the  Celestial  motions, 
that  it  should  lead  by  deduction  to  Kepler’s  laws;  which,  accordingly,  the 
Newtonian  theory  did. 

In  order,  therefore,  to  facilitate  the  verification  of  theories  obtained  by 
deduction,  it  is  important  that  as  many  as  possible  of  the  empirical  laws 
of  the  phenomena  should  be  ascertained,  by  a comparison  of  instances,  con 
formably  to  the  Method  of  Agreement:  as  well  as  (it  must  be  added)  that 
the  phenomena  themselves  should  be  described,  in  the  most  comprehensive 
as  well  as  accurate  manner  possible;  by  collecting  from  the  observation 
of  parts,  the  simplest  possible  correct  expressions  for  the  corresponding 
wholes : as  when  the  series  of  the  observed  places  of  a planet  was  first 
expressed  by  a circle,  then  by  a system  of  epicycles,  and  subsequently  by 
an  ellipse. 

It  is  worth  remarking,  that  complex  instances  which  would  have  been 
of  no  use  for  the  discovery  of  the  simple  laws  into  which  we  ultimately 
analyze  their  phenomena,  nevertheless,  when  they  have  served  to  verify  the 
analysis,  become  additional  evidence  of  the  laws  themselves.  Although 
we  could  not  have  got  at  the  law  from  complex  cases,  still  when  the  law, 
got  at  otherwise,  is  found  to  be  in  accordance  with  the  result  of  a complex 


THE  DEDUCTIVE  METHOD. 


331 


case,  that  case  becomes  a new  experiment  on  the  law,  and  helps  to  confirm 
what  it  did  not  assist  to  discover.  It  is  a new  trial  of  the  principle  in  a 
different  set  of  circumstances;  and  occasionally  serves  to  eliminate  some 
circumstance  not  previously  excluded,  and  the  exclusion  of  which  might 
require  an  experiment  impossible  to  be  executed.  This  was  strikingly 
conspicuous  in  the  example  formerly  quoted,  in  which  the  difference  be- 
tween the  observed  and  the  calculated  velocity  of  sound  was  ascertained  to 
result  from  the  heat  extricated  by  the  condensation  which  takes  place  in 
each  sonorous  vibration.  This  was  a trial,  in  new  circumstances,  of  the 
law  of  the  development  of  heat  by  compression ; and  it  added  materially 
to  the  proof  of  the  universality  of  that  law.  Accordingly,  any  law  of  na- 
ture is  deemed  to  have  gained  in  point  of  certainty,  by  being  found  to 
explain  some  complex  case  which  had  not  previously  been  thought  of  in 
connection  with  it ; and  this  indeed  is  a consideration  to  which  it  is  the 
habit  of  scientific  inquirers  to  attach  rather  too  much  value  than  too  little. 

To  the  Deductive  Method,  thus  characterized  in  its  three  constituent 
parts,  Induction,  Ratiocination,  and  Verification,  the  human  mind  is  in- 
debted for  its  most  conspicuous  triumphs  in  the  investigation  of  nature. 
To  it  we  owe  all  the  theories  by  which  vast  and  complicated  phenomena 
are  embraced  under  a few  simple  laws,  which,  considered  as  the  laws  of 
those  great  phenomena,  could  never  have  been  detected  by  their  direct 
study.  We  may  form  some  conception  of  what  the  method  has  done  for 
us  from  the  case  of  the  celestial  motions  : one  of  the  simplest  among  the 
greater  instances  of  the  Composition  of  Causes,  since  (except  in  a few  cases 
not  of  primary  importance)  each  of  the  heavenly  bodies  may  be  consider- 
ed, without  material  inaccuracy,  to  be  never  at  one  time  infiuenced  by  the 
attraction  of  more  than  two  bodies,  the  sun  and  one  other  planet  or  satel- 
lite ; making,  with  the  reaction  of  the  body  itself,  and  the  force  generated 
by  the  body’s  own  motion  and  acting  in  the  direction  of  the  tangent,  only 
four  different  agents  on  the  concurrence  of  which  the  motions  of  that  body 
depend ; a much  smaller  number,  no  doubt,  than  that  by  which  any  other 
of  the  great  phenomena  of  nature  is  determined  or  modified.  Yet  how 
could  we  ever  have  ascertained  the  combination  of  forces  on  which  the 
motions  of  the  earth  and  planets  are  dependent,  by  merely  comparing  the 
orbits  or  velocities  of  different  planets,  or  the  different  velocities  or  posi- 
tions of  the  same  planet?  Notwithstanding  the  regularity  which  mani- 
fests itself  in  those  motions,  in  a degree  so  rare  among  the  effects  of  con- 
currence of  causes ; and  although  the  periodical  recurrence  of  exactly  the 
same  effect,  affords  positive  proof  that  all  the  combinations  of  causes  which 
occur  at  all, recur  periodically;  we  should  not  have  known  what  the  causes 
were,  if  the  existence  of  agencies  precisely  similar  on  our  own  earth  had 
not,  fortunately,  brought  the  causes  themselves  within  the  reach  of  experi- 
mentation under  simple  circumstances.  As  we  shall  have  occasion  to  an- 
alyze, further  on,  this  great  example  of  the  Method  of  Deduction,  we  shall 
not  occupy  any  time  with  it  here,  but  shall  proceed  to  that  secondary  ap- 
plication of  the  Deductive  Method,  the  result  of  which  is  not  to  prove  laws 
of  phenomena,  but  to  explain  them. 


332 


INDUCTION. 


CHAPTER  XII. 

OP  THE  EXPLANATION  OP  LAWS  OP  NATURE. 

§ 1.  The  deductive  operation  by  which  we  derive  the  law  of  an  effect 
from  the  laws  of  the  causes,  the  concurrence  of  which  gives  rise  to  it,  may 
be  undertaken  either  for  the  purpose  of  discovering  the  law,  or  of  explain- 
ing a law  already  discovered.  The  word  explanation  occurs  so  continual- 
ly, and  holds  so  important  a place  in  philosophy,  that  a little  time  spent  in 
fixing  the  meaning  of  it  will  be  profitably  employed. 

An  individual  fact  is  said  to  be  explained,  by  pointing  out  its  cause,  that 
is,  by  stating  the  law  or  laws  of  causation,  of  which  its  production  is  an 
instance.  Thus,  a conflagration  is  explained,  when  it  is  proved  to  have 
arisen  from  a spark  falling  into  the  midst  of  a heap  of  combustibles.  And 
in  a similar  manner,  a law  or  uniformity  in  nature  is  said  to  be  explained, 
when  another  law  or  laws  are  pointed  out,  of  which  that  law  itself  is  but  a 
case,  and  from  which  it  could  be  deduced. 

§ 2.  There  are  three  distinguishable  sets  of  circumstances  in  which  a law 
of  causation  may  be  explained  from,  or,  as  it  also  is  often  expressed,  re- 
solved into,  other  laws. 

The  first  is  the  case  already  so  fully  considered  ; an  intermixture  of  laws, 
producing  a joint  effect  equal  to  the  sum  of  the  effects  of  the  causes  taken 
separately.  The  law  of  the  complex  effect  is  explained,  by  being  resolved 
into  the  separate  laws  of  the  causes  which  contribute  to  it.  Thus,  the  law 
of  the  motion  of  a planet  is  resolved  into  the  law  of  the  acquired  force, 
which  tends  to  produce  a uniform  motion  in  the  tangent,  and  the  law  of 
the  centripetal  force,  which  tends  to  produce  an  accelerating  motion  toward 
the  sun ; the  real  motion  being  a compound  of  the  two. 

It  is  necessary  here  to  remark,  that  in  this  resolution  of  the  law  of  a 
complex  effect,  the  laws  of  which  it  is  compounded  are  not  the  only  ele- 
ments. It  is  resolved  into  the  laws  of  the  separate  causes,  together  with 
the  fact  of  their  co-existence.  The  one  is  as  essential  an  ingredient  as  the 
other  ; whether  the  object  be  to  discover  the  law  of  the  effect,  or  only  to 
explain  it.  To  deduce  the  laws  of  the  heavenly  motions,  we  require  not 
only  to  know  the  law  of  a rectilineal  and  that  of  a gravitative  force,  but  the 
existence  of  both  these  forces  in  the  celestial  regions,  and  even  their  rela- 
tive amount.  The  complex  laws  of  causation  are  thus  resolved  into  two 
distinct  kinds  of  elements : the  one,  simpler  laws  of  causation,  the  other 
(in  the  aptly  selected  expression  of  Dr.  Chalmers)  collocations;  the  colloca- 
tions consisting  in  the  existence  of  certain  agents  or  powers,  in  certain 
circumstances  of  place  and  time.  We  shall  hereafter  have  occasion  to  re- 
turn to  this  distinction,  and  to  dwell  on  it  at  such  length  as  dispenses  with 
the  necessity  of  further  insisting  on  it  here.  The  first  mode,  then,  of  the 
explanation  of  Laws  of  Causation,  is  when  the  law  of  an  effect  is  resolved 
into  the  various  tendencies  of  which  it  is  the  result,  together  with  the  laws 
of  those  tendencies. 

§ 3.  A second  case  is  when,  between  what  seemed  the  cause  and  what 


EXPLANATION  OF  LAWS. 


333 


was  supposed  to  be  its  effect,  further  observation  detects  an  intermediate 
link ; a fact  caused  by  the  antecedent,  and  in  its  turn  causing  the  conse- 
quent ; so  that  the  cause  at  first  assigned  is  but  the  remote  cause,  operating- 
through  the  intermediate  phenomenon.  A seemed  the  cause  of  C,  but  it 
subsequently  appeared  that  A was  only  the  cause  of  B,  and  that  it  is  B 
which  was  the  cause  of  C.  For  example:  mankind  were  aware  that  the 
act  of  touching  an  outward  object  caused  a sensation.  It  was  subsequent- 
ly discovered  that  after  we  have  touched  the  object,  and  before  we  ex- 
perience the  sensation,  some  change  takes  place  in  a kind  of  thread  called 
a nerve,  which  extends  from  our  outward  organs  to  the  brain.  Touching 
the  object,  therefore,  is  only  the  remote  cause  of  our  sensation ; that  is,  not 
the  cause, properly  speaking,  but  the  cause  of  the  cause;  the  real  cause  of 
the  sensation  is  the  change  in  the  state  of  the  nerve.  Future  experience, 
may  not  only  give  us  more  knowledge  than  we  now  have  of  the  particular 
nature  of  this  change,  but  may  also  interpolate  another  link : between  the 
contact  (for  example)  of  the  object  with  our  outward  organs,  and  the  pro- 
duction of  the  change  of  state  in  the  nerve,  there  may  take  place  some 
electric  phenomenon,  or  some  phenomenon  of  a nature  not  resembling  the 
effects  of  any  known  agency.  Hitherto,  however,  no  such  intermediate 
link  has  been  discovered ; and  the  touch  of  the  object  must  be  considered, 
provisionally,  as  the  proximate  cause  of  the  affection  of  the  nerve.  The 
sequence,  therefore,  of  a sensation  of  touch  on  contact  with  an  object  is 
ascertained  not  to  be  an  ultimate  law  ; it  is  resolved,  as  the  phrase  is,  into 
two  other  laws — the  law  that  contact  with  an  object  produces  an  affection 
of  the  nerve,  and  the  law  that  an  affection  of  the  nerve  produces  sensation. 

To  take  another  example:  the  more  powerful  acids  corrode  or  blacken 
organic  compounds.  This  is  a case  of  causation, but  of  remote  causation; 
and  is  said  to  be  explained  when  it  is  shown  that  there  is  an  intermediate 
link,  namely,  the  separation  of  some  of  the  chemical  elements  of  the  organ- 
ic structure  from  the  rest,  and  their  entering  into  combination  with  the 
acid.  The  acid  causes  this  separation  of  the  elements,  and  the  separation 
of  the  elements  causes  the  disorganization,  and  often  the  charring  of  the 
structure.  So,  again,  chlorine  extracts  coloring  matters  (whence  its  efficacy 
in  bleaching)  and  purifies  the  air  from  infection.  This  law  is  resolved  into 
the  two  following  laws:  Chlorine  has  a powerful  affinity  for  bases  of  all 
kinds,  particularly  metallic  bases  and  hydrogen:  such  bases  are  essential 
elements  of  coloring  matters  and  contagious  compounds,  which  substances, 
therefore,  are  decomposed  and  destroyed  by  chlorine. 

§ 4.  It  is  of  importance  to  remark,  that  when  a sequence  of  phenomena 
is  thus  resolved  into  other  laws,  they  are  always  laws  more  general  than 
itself.  The  law  that  A is  followed  by  C,  is  less  general  than  either  of  the 
laws  which  connect  B with  C and  A with  B.  This  will  appear  from  very 
simple  considerations. 

All  laws  of  causation  are  liable  to  be  counteracted  or  fustrated,  by  the 
non-fulfillment  of  some  negative  condition;  the  tendency,  therefore,  of  B 
to  produce  C may  be  defeated.  Now  the  law  that  A produces  B,  is  equal- 
ly fulfilled  whether  B is  followed  by  C or  not ; but.  the  law  that  A pro- 
duces C by  means  of  B,  is  of  course  only  fulfilled  when  B is  really  followed 
by  C,  and  is,  therefore,  less  general  than  the  law  that  A produces  B.  It  is 
also  less  general  than  the  law  that  B produces  C.  For  B may  have  other 
causes  besides  A;  and  as  A produces  C only  by  means  of  B,  while  B pro- 
duces C,  whether  it  has  itself  been  produced  by  A or  by  any  thing  else,  the 


334 


INDUCTION. 


second  law  embraces  a greater  number  of  instances,  covers  as  it  were  a 
greater  space  of  ground,  than  the  first. 

Thus,  in  our  former  example,  the  law  that  the  contact  of  an  object 
causes  a change  in  the  state  of  the  nerve,  is  more  general  than  the  law 
that  contact  with  an  object  causes  sensation,  since,  for  aught  we  know,  the 
change  in  the  nerve  may  equally  take  place  when,  from  a counteracting 
cause,  as,  for  instance,  strong  mental  excitement,  the  sensation  does  not 
follow  ; as  in  a battle,  where  wounds  are  sometimes  received  without  any 
consciousness  of  receiving  them.  And  again,  the  law  that  change  in  the 
state  of  a nerve  produces  sensation,  is  more  general  than  the  law  that  con- 
tact with  an  object  produces  sensation ; since  the  sensation  equally  follows 
the  change  in  the  nerve  when  not  produced  by  contact  with  an  object,  but 
by  some  other  cause ; as  in  the  well-known  case,  when  a person  who  has 
lost  a limb  feels  the  same  sensation  which  he  has  been  accustomed  to  call 
a pain  in  the  limb. 

Not  only  are  the  laws  of  more  immediate  sequence  into  which  the  law 
of  a remote  sequence  is  resolved,  laws  of  greater  generality  than  that  law 
is,  but  (as  a consequence  of,  or  rather  as  implied  in,  their  greater  general- 
ity) they  are  more  to  be  relied  on  ; there  are  fewer  chances  of  their  being 
ultimately  found  not  to  be  universally  true.  From  the  moment  when  the 
sequence  of  A and  C is  shown  not  to  be  immediate,  but  to  depend  on  an 
intervening  phenomenon,  then,  however  constant  and  invariable  the  se- 
quence of  A and  C has  hitherto  been  found,  possibilities  arise  of  its  failure, 
exceeding  those  which  can  effect  either  of  the  more  immediate  sequences, 
A,  B,  and  B,  C.  The  tendency  of  A to  produce  C may  be  defeated  by 
whatever  is  capable  of  defeating  either  the  tendency  of  A to  produce  B, 
or  the  tendency  of  B to  produce  C ; it  is,  therefore,  twice  as  liable  to  failure 
as  either  of  those  more  elementary  tendencies;  and  the  generalization  that 
A is  always  followed  by  C,  is  twice  as  likely  to  be  found  erroneous.  And 
so  of  the  converse  generalization,  that  C is  always  preceded  and  caused  by 
A ; which  will  be  erroneous  not  only  if  there  should  happen  to  be  a sec- 
ond immediate  mode  of  production  of  C itself,  but  moreover  if  there  be 
a second  mode  of  production  of  B,  the  immediate  antecedent  of  C in  the 
sequence, 

The  resolution  of  the  one  generalization  into  the  other  two,  not  only 
shows  that  there  are  possible  limitations  of  the  former,  from  which  its  two 
elements  are  exempt,  but  shows  also  where  these  are  to  be  looked  for.  As 
soon  as  we  know  that  B intervenes  between  A and  C,  we  also  know  that 
if  there  be  cases  in  which  the  sequence  of  A and  C does  not  hold,  these  are 
most  likely  to  be  found  by  studying  the  effects  or  the  conditions  of  the 
phenomenon  B. 

It  appears,  then,  that  in  the  second  of  the  three  modes  in  which  a law 
may  be  resolved  into  other  laws,  the  latter  are  more  general,  that  is,  extend 
to  more  cases,  and  are  also  less  likely  to  require  limitation  from  subsequent 
experience,  than  the  law  which  they  serve  to  explain.  They  are  more  near- 
ly unconditional;  they  are  defeated  by  fewer  contingencies;  they  are  a 
nearer  approach  to  the  universal  truth  of  nature.  The  same  observations 
are  still  more  evidently  true  with  regard  to  the  first  of  the  three  modes  of 
resolution.  When  the  law  of  an  effect  of  combined  forces  is  resolved  into 
the  separate  laws  of  the  causes,  the  nature  of  the  case  implies  that  the  law 
of  the  effect  is  less  general  than  the  law  of  any  of  the  causes,  since  it  only 
holds  when  they  are  combined ; while  the  law  of  any  one  of  the  causes 
holds  good  both  then,  and  also  when  that  cause  acts  apart  from  the  rest. 


EXPLANATION  OE  LAWS. 


335 


It  is  also  manifest  that  the  complex  law  is  liable  to  be  oftenev  unfulfilled 
than  any  one  of  the  simpler  laws  of  which  it  is  the  result,  since  every  con- 
tingency which  defeats  any  of  the  laws  prevents  so  much  of  the  effect  as 
depends  on  it,  and  thereby  defeats  the  complex  law.  The  mere  rusting,  for 
example,  of  some  small  part  of  a great  machine,  often  suffices  entirely  to 
prevent  the  effect  which  ought  to  result  from  the  joint  action  of  all  the 
parts.  The  law  of  the  effect  of  a combination  of  causes  is  always  subject 
to  the  whole  of  the  negative  conditions  which  attach  to  the  action  of  all 
the  causes  severally. 

There  is  another  and  an  equally  strong  reason  why  the  law  of  a complex 
effect  must  be  less  general  than  the  laws  of  the  causes  which  conspire  to 
produce  it.  The  same  causes,  acting  according  to  the  same  laws,  and  differ- 
ing only  in  the  proportions  in  which  they  are  combined,  often  produce  ef- 
fects which  differ  not  merely  in  quantity,  but  in  kind.  The  combination 
of  a centripetal  with  a projectile  force,  in  the  proportions  which  obtain  in 
all  the  planets  and  satellites  of  our  solar  system,  gives  rise  to  an  elliptical 
motion  ; but  if  the  ratio  of  the  two  forces  to  each  other  were  slightly  al- 
tered, it  is  demonstrated  that  the  motion  produced  would  be  in  a circle,  or 
a parabola,  or  an  hyperbola;  and  it  is  thought  that  in  the  case  of  some 
comets  one  of  these  is  probably  the  fact.  Yet  the  law  of  the  parabolic  mo- 
tion would  be  resolvable  into  the  very  same  simple  laws  into  which  that  of 
the  elliptical  motion  is  resolved,  namely,  the  law  of  the  permanence  of  rec- 
tilineal motion,  and  the  law  of  gravitation.  If,  therefore,  in  the'course  of 
ages,  some  circumstance  were  to  manifest  itself  which,  without  defeating 
the  law  of  either  of  those  forces,  should  merely  alter  their  proportion  to 
one  another  (such  as  the  shock  of  some  solid  body,  or  even  the  accumula- 
ting effect  of  the  resistance  of  the  medium  in  which  astronomers  have  been 
led  to  surmise  that  the  motions  of  the  heavenly  bodies  take  place),  the  el- 
liptical motion  might  be  changed  into  a motion  in  some  other  conic  section  ; 
and  the  complex  law,  that  the  planetary  motions  take  place  in  ellipses,  would 
be  deprived  of  its  universality,  though  the  discovery  would  not  at  all  de- 
tract from  the  universality  of  the  simpler  laws  into  which  that  complex  law 
is  resolved.  The  law,  in  short,  of  each  of  the  concurrent  causes  remains 
the  same,  however  their  collocations  may  vary;  but  the  law  of  their  joint 
effect  varies  with  every  difference  in  the  collocations.  There  needs  no  more 
to  show  how  much  more  general  the  elementary  laws  must  be  than  any  of 
the  complex  laws  which  are  derived  from  them. 

§ 5.  Besides  the  two  modes  which  have  been  treated  of,  there  is  a third 
mode  in  which  laws  are  resolved  into  one  another;  and  in  this  it  is  self-ev- 
ident that  they  are  resolved  into  laws  more  general  than  themselves.  This 
third  mode  is  the  subsumption  (as  it  has  been  called)  of  one  law  under  an- 
other; or  (what  comes  to  the  same  thing)  the  gathering  up  of  several  laws 
into  one  more  general  law  which  includes  them  all.  The  most  splendid  ex- 
ample of  this  operation  was  when  terrestrial  gravity  and  the  central  force 
of  the  solar  system  were  brought  together  under  the  general  law  of  gravi- 
tation. It  had  been  proved  antecedently  that  the  earth  and  the  other  plan- 
ets tend  to  the  sun  ; and  it  had  been  known  from  the  earliest  times  that 
terrestrial  bodies  tend  toward  the  earth.  These  were  similar  phenomena; 
and  to  enable  them  both  to  be  subsumed  under  one  law,  it  was  only  neces- 
sary to  prove  that,  as  the  effects  were  similar  in  quality  so  also  they,  as  to 
quantity,  conform  to  the  same  rules.  This  was  first  shown  to  be  true  of 
the  moon,  which  agreed  with  terrestrial  objects  not  only  in  tending  to  a 


/ 


336 


INDUCTION. 


centre,  but  in  the  fact  that  this  centre  was  the  earth.  The  tendency  of  the 
moon  toward  the  earth  being  ascertained  to  vary  as  the  inverse  square  of 
tlie  distance,  it  was  deduced  from  this,  by  direct  calculation,  that  if  the  moon 
were  as  near  to  the  earth  as  terrestrial  objects  are,  and  the  acquired  force 
in  the  direction  of  the  tangent  were  suspended,  the  moon  would  fall  toward 
the  earth  through  exactly  as  many  feet  in  a second  as  those  objects  do  by 
virtue  of  their  weight.  Hence  the  inference  was  irresistible,  that  the  moon 
also  tends  to  the  earth  by  virtue  of  its  weight : and  that  the  two  phenome- 
na, the  tendency  of  the  moon  to  the  earth  and  the  tendency  of  terrestrial 
objects  to  the  earth,  being  not  only  similar  in  quality,  but,  when  in  the 
same  circumstances,  identical  in  quantity,  are  cases  of  one  and  the  same 
law  of  causation.  But  the  tendency  of  the  moon  to  the  earth,  and  the  tend- 
ency of  the  earth  and  planets  to  the  sun,  were  .already  known  to  be  cases 
of  the  same  law  of  causation ; and  thus  the  law  of  all  these  tendencies,  and 
the  law  of  terrestrial  gravity,  were  recognized  as  identical,  and  were  sub- 
sumed under  one  general  law,  that  of  gravitation. 

In  a similar  manner,  the  laws  of  magnetic  phenomena  have  more  recently 
been  subsumed  under  known  laws  of  electricity.  It  is  thus  that  the  most 
general  laws  of  nature  are  usually  arrived  at : we  mount  to  them  by  suc- 
cessive steps.  For,  to  arrive  by  correct  induction  at  laws  which  hold  un- 
der such  an  immense  variety  of  circumstances,  laws  so  general  as  to  be  in- 
dependent of  any  varieties  of  space  or  time  which  we  are  able  to  observe, 
requires  for  the  most  part  many  distinct  sets  of  experiments  or  observa- 
tions, conducted  at  different  times  and  by  different  people.  One  part  of 
the  law  is  first  ascertained,  afterward  another  part : one  set  of  observations 
teaches  us  that  the  law  holds  good  under  some  conditions,  another  that  it 
holds  good  under  other  conditions,  by  combining  which  observations  we 
find  that  it  holds  good  under  conditions  much  more  general,  or  even  uni- 
versally. The  general  law,  in  this  case,  is  literally  the  sum  of  all  the  partial 
ones  ; it  is  a recognition  of  the  same  sequence  in  different  sets  of  instances  ; 
and  may,  in  fact,  be  regarded  as  merely  one  step  in  the  process  of  elimi- 
nation. The  tendency  of  bodies  toward  one  another,  which  we  now  call 
gravity,  had  at  first  been  observed  only  on  the  earth’s  surface,  where  it 
manifested  itself  only  as  a tendency  of  all  bodies  toward  the  earth,  and 
might,  therefore,  be  ascribed  to  a peculiar  property  of  the  earth  itself : one  of 
the  circumstances,  namely,  the  proximity  of  the  earth,  had  not  been  elimi- 
nated. To  eliminate  this  circumstance  required  a fresh  set  of  instances  in 
other  parts  of  the  universe : these  we  could  not  ourselves  create ; and 
though  nature  had  created  them  for  us,  we  were  placed  in  very  unfavorable 
circumstances  for  observing  them.  To  make  these  observations,  fell  nat- 
urally to  the  lot  of  a different  set  of  persons  from  those  who  studied  ter- 
restrial phenomena ; and  had,  indeed,  been  a matter  of  great  interest  at 
a time  when  the  idea  of  explaining  celestial  facts  by  terrestrial  laws  was 
looked  upon  as  the  confounding  of  an  indefeasible  distinction.  When, 
however,  the  celestial  motions  were  accurately  ascertained,  and  the  deduc- 
tive processes  performed,  from  which  it  appeared  that  their  laws  and 
those  of  terrestrial  gravity  corresponded,  those  celestial  observations  be- 
came a set  of  instances  which  exactly  eliminated  the  circumstance  of  prox- 
imity to  the  earth ; and  proved  that  in  the  original  case,  that  of  terrestrial 
objects,  it  wras  not  the  earth,  as  such,  that  caused  the  motion  or  the  press- 
ure, but  the  circumstance  common  to  that  case  with  the  celestial  instances, 
namely,  the  presence  of  some  great  body  within  certain  limits  of  dis- 
tance. 


EXPLANATION  OF  LAWS. 


337 


§ 6.  There  are,  then,  three  modes  of  explaining  laws  of  causation,  or, 
which  is  the  same  thing,  resolving  them  into  other  laws.  First,  when  the 
law  of  an  effect  of  combined  causes  is  resolved  into  the  separate  laws  of 
the  causes,  together  with  the  fact  of  their  combination.  Secondly,  when 
the  law  which  connects  any  two  links,  not  proximate,  in  a chain  of  causa- 
tion, is  resolved  into  the  laws  which  connect  each  with  the  intermediate 
links.  Both  of  these  are  cases  of  resolving  one  law  into  two  or  more  ; in 
the  third,  two  or  more  are  resolved  into  one  : when,  after  the  law  has  been 
shown  to  hold  good  in  several  different  classes  of  cases,  we  decide  that 
what  is  true  in  each  of  these  classes  of  cases,  is  true  under  some  more  gen- 
eral supposition,  consisting  of  what  all  those  classes  of  cases  have  in  com- 
mon. We  may  here  remark  that  this  last  operation  involves  none  of  the 
uncertainties  attendant  on  induction  by  the  Method  of  Agreement,  since  we 
need  not  suppose  the  result  to  be  extended  by  way  of  inference  to  any  new  class 
of  cases  different  from  those  by  the  comparison  of  which  it  was  engendered. 

In  all  these  three  processes,  laws  are,  as  we  have  seen,  resolved  into  laws 
more  general  than  themselves;  laws  extending  to  all  the  cases  which  the 
former  extended  to,  and  others  besides.  In  the  first  two  modes  they  are 
also  resolved  into  laws  more  certain,  in  other  words,  more  universally  true 
than  themselves  ; they  are,  in  fact,  proved  not  to  be  themselves  laws  of  na- 
ture, the  character  of  which  is  to  be  universally  true,  but  results  of  laws  of 
nature,  which  may  be  only  true  conditionally,  and  for  the  most  part.  No 
difference  of  this  sort  exists  in  the  third  case ; since  here  the  partial  laws 
are,  in  fact,  the  very  same  law  as  the  general  one,  and  any  exception  to 
them  would  be  an  exception  to  it  too. 

By  all  the  three  processes,  the  range  of  deductive  science  is  extended; 
since  the  laws,  thus  resolved,  may  be  thenceforth  deduced  demonstratively 
from  the  laws  into  which  they  are  resolved.  As  already  remarked,  the 
same  deductive  process  which  proves  a law  or  fact  of  causation  if  un- 
known, serves  to  explain  it  when  known. 

The  word  explanation  is  here  used  in  its  philosophical  sense.  What  is 
called  explaining  one  law  of  nature  by  another,  is  but  substituting  one 
mystery  for  another ; and  does  nothing  to  render  the  general  course  of  na- 
ture other  than  mysterious  : we  can  no  more  assign  a why  for  the  more 
extensive  laws  than  for  the  partial  ones.  The  explanation  may  substitute 
a mystery  which  has  become  familiar,  and  has  grown  to  seem  not  mysteri- 
ous, for  one  which  is  still  strange.  And  this  is  the  meaning  of  explanation, 
in  common  parlance.  But  the  process  with  which  we  are  here  concerned 
often  does  the  very  contrary : it  resolves  a phenomenon  with  which  we  are 
familiar  into  one  of  which  we  previously  knew  little  or  nothing;  as  when 
the  common  fact  of  the  fall  of  heavy  bodies  was  resolved  into  the  tendency 
of  all  particles  of  matter  toward  one  another.  It  must  be  kept  constantly 
in  view,  therefore,  that  in  science,  those  who  speak  of  explaining  any  phe- 
nomenon mean  (or  should  mean)  pointing  out  not  some  more  familiar,  but 
merely  some  more  general,  phenomenon,  of  which  it  is  a partial  exemplifica- 
tion ; or  some  laws  of  causation  which  produce  it  by  their  joint  or  succes- 
sive action,  and  from  which,  therefore,  its  conditions  may  be  determined 
deductively.  Every  such  operation  brings  us  a step  nearer  toward  answer- 
ing the  question  which  was  stated  in  a previous  chapter  as  comprehending 
the  whole  problem  of  the  investigation  of  nature,  viz. : what  are  the  fewest 
assumptions,  which  being  granted,  the  order  of  nature  as  it  exists  would 
be  the  result?  What  are  the  fewest  general  propositions  from  which  all 
the  uniformities  existing  in  nature  could  be  deduced  ? 

22 


338 


INDUCTION. 


The  laws,  thus  explained  or  resolved,  are  sometimes  said  to  be  accounted 
for ; but  the  expression  is  incorrect,  if  taken  to  mean  any  thing  more  than 
what  has  been  already  stated.  In  minds  not  habituated  to  accurate  think- 
ing, there  is  often  a confused  notion  that  the  general  laws  are  the  causes  of 
the  partial  ones ; that  the  law  of  general  gravitation,  for  example,  causes 
the  phenomenon  of  the  fall  of  bodies  to  the  earth.  But  to  assert  this 
would  be  a misuse  of  the  word  cause : terrestrial  gravity  is  not  an  effect  of 
general  gravitation,  but  a case  of  it;  that  is,  one  kind  of  the  particular  in- 
stances in  which  that  general  law  obtains.  To  account  for  a law  of  nature 
means,  and  can  mean,  nothing  more  than  to  assign  other  laws  more  general, 
together  with  collocations,  which  laws  and  collocations  being  supposed,  the 
partial  law  follows  without  any  additional  supposition. 


CHAPTER  XIII. 

MISCELLANEOUS  EXAMPLES  OF  THE  EXPLANATION  OF  LAWS  OF  NATURE. 

§ 1.  The  most  striking  example  which  the  history  of  science  presents, 
of  the  explanation  of  laws  of  causation  and  other  uniformities  of  sequence 
among  special  phenomena,  by  resolving  them  into  laws  of  greater  simplic- 
ity and  generality,  is  the  great  Newtonian  generalization ; respecting 
which  typical  instance,  so  much  having  already  been  said,  it  is  sufficient  to 
call  attention  to  the  great  number  and  variety  of  the  special  observed  uni- 
formities, which  are  in  this  case  accounted  for,  either  as  particular  cases,  or 
as  consequences,  of  one  very  simple  law  of  universal  nature.  The  simple 
fact  of  a tendency  of  every  particle  of  matter  toward  every  other  particle, 
varying  inversely  as  the  square  of  the  distance,  explains  the  fall  of  bodies 
to  the  earth,  the  revolutions  of  the  planets  and  satellites,  the  motions  (so 
far  as  known)  of  comets,  and  all  the  various  regularities  which  have  been 
observed  in  these  special  phenomena;  such  as  the  elliptical  orbits,  and  the 
variations  from  exact  ellipses;  the  relation  between  the  solar  distances  of 
the  planets  and  the  duration  of  their  revolutions;  the  precession  of  the 
equinoxes;  the  tides,  and  a vast  number  of  minor  astronomical  truths. 

Mention  has  also  been  made  in  the  preceding  chapter  of  the  explanation 
of  the  phenomena  of  magnetism  from  laws  of  electricity;  the  special  laws 
of  magnetic  agency  having  been  affiliated  by  deduction  to  observed  laws 
of  electric  action,  in  which  they  have  ever  since  been  considered  to  be  in- 
cluded as  special  cases.  An  example  not  so  complete  in  itself,  but  even 
more  fertile  in  consequences,  having  been  the  starting-point  of  the  really 
scientific  study  of  physiology,  is  the  affiliation,  commenced  by  Bichat,  and 
carried  on  by  subsequent  biologists,  of  the  properties  of  the  bodily  organs, 
to  the  elementary  properties  of  the  tissues  into  which  they  are  anatomical- 
ly decomposed. 

Another  striking  instance  is  afforded  by  Dalton’s  generalization,  com- 
monly known  as  the  atomic  theory.  It  had  been  known  from  the  very 
commencement  of  accurate  chemical  observation,  that  any  two  bodies  com- 
bine chemically  with  one  another  in  only  a certain  number  of  proportions  ; 
but  those  proportions  were  in  each  case  expressed  by  a percentage — so 
many  parts  (by  weight)  of  each  ingredient,  in  100  of  the  compound  (say 
35  and  a fraction  of  one  element,  64  and  a fraction  of  the  other) ; in  which 
mode  of  statement  no  relation  was  perceived  between  the  proportion  in 


EXAMPLES  OF  THE  EXPLANATION  OF  LAWS. 


339 


which  a given  element  combines  with  one  substance,  and  that  in  which  it 
combines  with  others.  The  great  step  made  by  Dalton  consisted  in  per- 
ceiving that  a unit  of  wreight  might  be  established  for  each  substance, 
such  that  by  supposing  the  substance  to  enter  into  all  its  combinations  in 
the  ratio  either  of  that  unit,  or  of  some  low  multiple  of  that  unit,  all  the 
different  proportions,  previously  expressed  by  percentages,  were  found  to 
result.  Thus  1 being  assumed  as  the  unit  of  hydrogen,  if  8 were  then 
taken  as  that  of  oxygen,  the  combination  of  one  unit  of  hydrogen  with  one 
unit  of  oxygen  would  produce  the  exact  proportion  of  weight  between  the 
two  substances  which  is  known  to  exist  in  water ; the  combination  of  one 
unit  of  hydrogen  with  two  units  of  oxygen  would  produce  the  proportion 
which  exists  in  the  other  compound  of  the  same  two  elements,  called  perox- 
ide of  hydrogen ; and  the  combinations  of  hydrogen  and  of  oxygen  with 
all  other  substances,  would  correspond  with  the  supposition  that  those  ele- 
ments enter  into  combination  by  single  units,  or  twos,  or  threes,  of  the 
numbers  assigned  to  them,  1 and  8,  and  the  other  substances  by  ones  or 
twos  or  threes  of  other  determinate  numbers  proper  to  each.  The  result 
is  that  a table  of  the  equivalent  numbers,  or,  as  they  are  called,  atomic 
weights,  of  all  the  elementary  substances,  comprises  in  itself,  and  scientific- 
ally explains,  all  the  proportions  in  which  any  substance,  elementary  or 
compound,  is  found  capable  of  entering  into  chemical  combination  with 
any  other  substance  whatever. 

§ 2.  Some  interesting  cases  of  the  explanation  of  old  uniformities  by 
newly  ascertained  laws  are  afforded  by  the  researches  of  Professor  Gra- 
ham. That  eminent  chemist  was  the  first  who  drew  attention  to  the  dis- 
tinction which  may  be  made  of  all  substances  into  two  classes,  termed  by 
him  crystalloids  and  colloids;  or  rather,  of  all  states  of  matter  into  the 
crystalloid  and  the  colloidal  states,  for  many  substances  are  capable  of  ex- 
isting in  either.  When  in  the  colloidal  state,  their  sensible  properties  are 
very  different  from  those  of  the  same  substance  when  crystallized,  or  when 
in  a state  easily  susceptible  of  crystallization.  Colloid  substances  pass  with 
extreme  difficulty  and  slowness  into  the  crystalline  state,  and  are  extreme- 
ly inert  in  all  the  ordinary  chemical  relations.  Substances  in  the  colloid 
state  are  almost  always,  wdien  combined  with  water,  more  or  less  viscous  or 
gelatinous.  The  most  prominent  examples  of  the  state  are  certain  animal 
and  vegetable  substances,  particularly  gelatine,  albumen,  starch,  the  gums, 
caramel,  tannin,  and  some  others.  Among  substances  not  of  organic  origin, 
the  most  notable  instances  are  hydrated  silicic  acid,  and  hydrated  alumina, 
with  other  metallic  peroxides  of  the  aluminous  class. 

Now  it  is  found,  that  while  colloidal  substances  are  easily  penetrated  by 
water,  and  by  the  solutions  of  crystalloid  substances,  they  are  very  little 
penetrable  by  one  another : which  enabled  Professor  Graham  to  introduce 
a highly  effective  process  (termed  dialysis)  for  separating  the  crystalloid 
substances  contained  in  any  liquid  mixture,  by  jjassing  them  through  a 
thin  septum  of  colloidal  matter,  which  does  not  suffer  any  thing  colloidal 
to  pass,  or  suffers  it  only  in  very  minute  quantity.  This  property  of  col- 
loids enabled  Mr.  Graham  to  account  for  a number  of  special  results  of 
observation,  not  previously  explained. 

For  instance,  “ while  soluble  crystalloids  are  always  highly  sapid,  soluble 
colloids  are  singularly  insipid,”  as  might  be  expected ; for,  as  the  sentient 
extremities  of  the  nerves  of  the  palate  “ are  probably  protected  by  a col- 
loidal membrane,”  impermeable  to  other  colloids,  a colloid,  when  tasted, 


340 


INDUCTION. 


probably  never  reaches  those  nerves.  Again,  a it  lias  been  observed  that 
vegetable  gum  is  not  digested  in  the  stomach;  the  coats  of  that  organ 
dialyse  the  soluble  food,  absorbing  crystalloids,  and  rejecting  all  colloids.” 
One  of  the  mysterious  processes  accompanying  digestion,  the  secretion  of 
free  muriatic  acid  by  the  coats  of  the  stomach,  obtains  a probable  hyjio- 
thetical  explanation  through  the  same  law.  Finally,  much  light  is  thrown 
upon  the  observed  phenomena  of  osmose  (the  passage  of  fluids  outward 
and  inward  through  animal  membranes)  by  the  fact  that  the  membranes 
are  colloidal.  In  consequence,  the  water  and  saline  solutions  contained  in 
the  animal  body  pass  easily  and  rapidly  through  the  membranes,  while  the 
substances  directly  applicable  to  nutrition,  which  are  mostly  colloidal,  are 
detained  by  them.* 

The  property  which  salt  possesses  of  preserving  animal  substances  from 
putrefaction  is  resolved  by  Liebig  into  two  more  general  laws,  the  strong 
attraction  of  salt  for  water,  and  the  necessity  of  the  presence  of  water  as  a 
condition  of  putrefaction.  The  intermediate  phenomenon  which  is  inter- 
polated between  the  remote  cause  and  the  effect,  can  here  be  not  merely 
inferred  but  seen;  for  it  is  a familiar  fact,  that  flesh  upon  which  salt  has 
been  thrown  is  speedily  found  swimming  in  brine. 

The  second  of  the  two  factors  (as  they  may  be  termed)  into  which  the 
preceding  law  has  been  resolved,  the  necessity  of  water  to  putrefaction, 
itself  affords  an  additional  example  of  the  Resolution  of  Laws.  The  law 
itself  is  proved  by  the  Method  of  Difference,  since  flesh  completely  dried 
and  kept  in  a dry  atmosphere  does  not  putrefy; 'as  we  see  in  the  case  of 
dried  provisions  and  human  bodies  in  very  dry  climates.  A deductive 
explanation  of  this  same  law  results  from  Liebig’s  speculations.  The 
putrefaction  of  animal  and  other  azotized  bodies  is  a chemical  process,  by 
which  they  are  gradually  dissipated  in  a gaseous  form,  chiefly  in  that  of 
carbonic  acid  and  ammonia;  now  to  convert  the  carbon  of  the  animal  sub 
stance  into  carbonic  acid  requires  oxygen,  and  to  convert  the  azote  into 
ammonia  requires  hydrogen,  which  are  the  elements  of  water.  The  ex- 
treme rapidity  of  the  putrefaction  of  azotized  substances,  compared  with 
the  gradual  decay  of  non-azotized  bodies  (such  as  wood  and  the  like)  by 
the  action  of  oxygen  alone,  he  explains  from  the  general  law  that  sub- 
stances are  much  more  easily  decomposed  by  the  action  of  two  different 
affinities  upon  two  of  their  elements  than  by  the  action  of  only  one. 

§ 3.  Among  the  many  important  properties  of  the  nervous  system  which 
have  either  been  first  discovered  or  strikingly  illustrated  by  Dr.  Brown- 
Sequard,  I select  the  reflex  influence  of  the  nervous  system  on  nutrition 
and  secretion.  By  reflex  nervous  action  is  meant,  action  which  one  part 
of  the  nervous  system  exerts  over  another  part,  without  any  intermediate 
action  on  the  brain,  and  consequently  without  consciousness ; or  which,  if 
it  does  pass  through  the  brain,  at  least  produces  its  effects  independently 
of  the  will.  There  are  many  experiments  which  prove  that  irritation  of  a 
nerve  in  one  part  of  the  body  may  in  this  manner  excite  powerful  action 
in  another  part;  for  example,  food  injected  into  the  stomach  through  a 
divided  oesophagus,  nevertheless  produces  secretion  of  saliva ; warm  water 
injected  into  the  bowels,  and  various  other  irritations  of  the  lower  intes- 
tines,  have  been  found  to  excite  secretion  of  the  gastric  juice,  and  so  forth. 

* Vide  Memoir  by  Thomas  Graham,  F.R.S.,  Master  of  the  Mint,  “On  Liquid  Diffusion 
applied  to  Analysis,”  in  the  Philosophical  Transactions  for  1862,  reprinted  in  the  Journal  of 
the  Chemical  Society , and  also  separately  as  a pamphlet. 


EXAMPLES  OF  THE  EXPLANATION  OF  LAWS. 


341 


The  reality  of  the  power  being  thus  proved,  its  agency  explains  a great 
variety  of  apparently  anomalous  phenomena ; of  which  I select  the  follow- 
ing from  Dr.  Brown-Sequard’s  Lectures  on  the  Nervous  System: 

The  production  of  tears  by  irritation  of  the  eye,  or  of  the  mucous  mem 
brane  of  the  nose  ; 

The  secretions  of  the  eye  and  nose  increased  by  exposure  of  other  parts 
of  the  body  to  cold  ; 

Inflammation  of  the  eye,  especially  when  of  traumatic  origin,  very  fre- 
quently excites  a similar  affection  in  the  other  eye,  which  may  be  cured  by 
section  of  the  intervening  nerve ; 

Loss  of  sight  sometimes  produced  by  neuralgia,  and  has  been  known 
to  be  at  once  cured  bv  the  extirpation  (for  instance)  of  a carious  tooth ; 

Even  cataract  has  been  produced  in  a healthy  eye  by  cataract  in  the 
other  eye,  or  by  neuralgia,  or  by  a wound  of  the  frontal  nerve ; 

The  well-known  phenomenon  of  a sudden  stoppage  of  the  heart’s  action, 
and  consequent  death,  produced  by  irritation  of  some  of  the  nervous  ex- 
tremities ; e.  g.,  by  drinking  very  cold  water,  or  by  a blow  on  the  abdo- 
men, or  other  sudden  excitation  of  the  abdominal  sympathetic  nerve, 
though  this  nerve  may  be  irritated  to  any  extent  without  stopping  the 
heart’s  action,  if  a section  be  made  of  the  communicating  nerves ; 

The  extraordinary  effects  produced  on  the  internal  organs  by  an  exten- 
sive burn  on  the  surface  of  the  body,  consisting  in  violent  inflammation 
of  the  tissues  of  the  abdomen,  chest,  or  head,  which,  when  death  ensues 
from  this  kind  of  injury,  is  one  of  the  most  frequent  causes  of  it; 

Paralysis  and  anaesthesia  of  one  part  of  the  body  from  neuralgia  in  an- 
other part ; and  muscular  atrophy  from  neuralgia,  even  when  there  is  no 
paralysis ; 

Tetanus  produced  by  the  lesion  of  a nerve.  Dr.  Brown-Sequard  thinks 
it  highly  probable  that  hydrophobia  is  a phenomenon  of  a similar  nature; 

Morbid  changes  in  the  nutrition  of  the  brain  and  spinal  cord,  manifest- 
ing themselves  by  epilepsy,  chorea,  hysteria,  and  other  diseases,  occasioned 
by  lesion  of  some  of  the  nervous  extremities  in  remote  places,  as  by  worms, 
calculi,  tumors,  carious  bones,  and  in  some  cases  even  by  very  slight  irri- 
tations of  the  skin. 

§ 4.  From  the  foregoing  and  similar  instances,  we  may  see  the  impor- 
tance, when  a law  of  nature  previously  unknown  has  been  brought  to  light, 
or  when  new  light  has  been  thrown  upon  a known  law  by  experiment,  of 
examining  all  cases  which  present  the  conditions  necessary  for  bringing 
that  law  into  action  ; a process  fertile  in  demonstrations  of  special  laws 
previously  unsuspected,  and  explanations  of  others  already  emjnrically 
known. 

For  instance,  Faraday  discovered  by  experiment,  that  voltaic  electricity 
could  be  evolved  from  a natural  magnet,  provided  a conducting  body  were 
set  in  motion  at  right  angles  to  the  direction  of  the  magnet;  and  this  he 
found  to  hold  not  only  of  small  magnets,  but  of  that  great -magnet,  the 
earth.  The  law  being  thus  established  experimentally,  that  electricity  is 
evolved,  by  a magnet,  and  a conductor  moving  at  right  angles  to  the  direc- 
tion of  its  poles,  we  may  now  look  out  for  fresh  instances  in  which  these 
conditions  meet.  Wherever  a conductor  moves  or  revolves  at  right  angles 
to  the  direction  of  the  earth’s  magnetic  poles,  there  we  may  expect  an  evo- 
lution of  electricity.  In  the  northern  regions,  where  the  polar  direction  is 
nearly  perpendicular  to  the  horizon,  all  horizontal  motions  of  conductors 


342 


INDUCTION. 


will  produce  electricity;  horizontal  wheels,  for  example,  made  of  metal; 
likewise  all  running  streams  will  evolve  a current  of  electricity,  which  will 
circulate  round  them ; and  the  air  thus  charged  with  electricity  may  be 
one  of  the  causes  of  the  Aurora  Borealis.  In  the  equatorial  regions,  on 
the  contrary,  upright  wheels  placed  parallel  to  the  equator  will  originate  a 
voltaic  circuit,  and  water-falls  will  naturally  become  electric. 

For  a second  example,  it  has  been  proved,  chiefly  by  the  researches  of 
Professor  Graham,  that  gases  have  a strong  tendency  to  permeate  animal 
membranes,  and  diffuse  themselves  through  the  spaces  which  such  mem- 
branes inclose,  notwithstanding  the  presence  of  other  gases  in  those  spaces. 
Proceeding  from  this  general  law,  and  reviewing  a variety  of  cases  in  which 
gases  lie  contiguous  to  membranes,  we  are  enabled  to  demonstrate  or  to 
explain  the  following  more  special  laws:  1st.  The  human  or  animal  body, 
when  surrounded  with  any  gas  not  already  contained  within  the  body, 
absorbs  it  rapidly;  such,  for  instance,  as  the  gases  of  putrefying  matters: 
which  helps  to  explain  malaria.  2d.  The  carbonic  acid  gas  of  effervescing 
drinks, evolved  in  the  stomach, permeates  its  membranes, and  rapidly  spreads 
through  the  system.  3d.  Alcohol  taken  into  the  stomach  passes  into  vapor, 
and  spreads  through  the  system  with  great  rapidity  (which,  combined  with 
the  high  combustibility  of  alcohol,  or  in  other  words  its  ready  combination 
with  oxygen,  may  perhaps  help  to  explain  the  bodily  warmth  immediately 
consequent  on  drinking  spirituous  liquors).  4th.  In  any  state  of  the  body 
in  which  peculiar  gases  are  formed  within  it,  these  will  rapidly  exhale 
through  all  parts  of  the  body ; and  hence  the  rapidity  with  which,  in  certain 
states  of  disease,  the  surrounding  atmosphere  becomes  tainted.  5th.  The 
putrefaction  of  the  interior  parts  of  a carcass  will  proceed  as  rapidly  as 
that  of  the  exterior,  from  the  ready  passage  outward  of  the  gaseous  prod- 
ucts. 6th.  The  exchange  of  oxygen  and  carbonic  acid  in  the  lungs  is  not 
prevented,  but  rather  promoted,  by  the  intervention  of  the  membrane  of 
the  lungs  and  the  coats  of  the  blood-vessels  between  the  blood  and  the  air. 
It  is  necessary,  however,  that  there  should  be  a substance  in  the  blood  with 
which  the  oxygen  of  the  air  may  immediately  combine;  otherwise,  instead 
of  passing  into  the  blood,  it  would  permeate  the  whole  organism:  and  it  is 
necessary  that  the  carbonic  acid,  as  it  is  formed  in  the  capillaries,  should 
also  find  a substance  in  the  bloorf  with  which  it  can  combine;  otherwise  it 
would  leave  the  body  at  all  points,  instead  of  being  discharged  through 
the  lungs. 

§ 5.  The  following  is  a deduction  which  confirms,  by  explaining,  the  em- 
pirical generalization,  that  soda  powders  weaken  the  human  system.  These 
powders,  consisting  of  a mixture  of  tartaric  acid  with  bicarbonate  of  soda, 
from  which  the  carbonic  acid  is  set  free,  must  pass  into  the  stomach  as 
tartrate  of  soda.  Now,  neutral  tartrates,  citrates,  and  acetates  of  the  al- 
kalis are  found,  in  their  passage  through  the  system,  to  be  changed  into 
carbonates;  and  to  convert  a tartrate  into  a carbonate  requires  an  addi- 
tional quantity  of  oxygen,  the  abstraction  of  which  must  lessen  the  oxygen 
destined  for  assimilation  with  the  blood,  on  the  quantity  of  which  the 
vigorous  action  of  the  human  system  partly  depends. 

The  instances  of  new  theories  agreeing  with  and  explaining  old  empiri- 
cisms, are  innumerable.  All  the  just  remarks  made  by  experienced  per- 
sons on  human  character  and  conduct,  are  so  many  special  laws,  which 
the  general  laws  of  the  human  mind  explain  and  resolve.  The  empirical 
generalizations  on  which  the  operations  of  the  arts  have  usually  been 


EXAMPLES  OF  THE  EXPLANATION  OF  LAWS. 


343 


founded,  are  continually  justified  and  confirmed  on  the  one  hand,  or  cor- 
rected and  improved  on  the  other,  by  the  discovery  of  the  simpler  scientific 
laws  on  which  the  efficacy  of  those  operations  depends.  The  effects  of  the 
rotation  of  crops,  of  the  various  manures,  and  other  processes  of  improved 
agriculture,  have  been  for  the  first  time  resolved  in  our  own  day  into  known 
laws  of  chemical  and  organic  action,  by  Davy,  Liebig,  and  others.  The 
processes  of  the  medical  art  are  even  now  mostly  empirical:  their  efficacy 
is  concluded,  in  each  instance,  from  a special  and  most  precarious  experi- 
mental generalization:  but  as  science  advances  in  discovering  the  simple 
laws  of  chemistry  and  physiology,  progress  is  made  in  ascertaining  the  in- 
termediate links  in  the  series  of  phenomena,  and  the  more  general  laws  on 
which  they  depend;  and  thus,  while  the  old  processes  are  either  exploded, 
or  their  efficacy,  in  so  far  as  real,  explained,  better  processes,  founded  on 
the  knowledge  of  proximate  causes,  are  continually  suggested  and  brought 
into  use.*  Many  even  of  the  truths  of  geometry  were  generalizations  from 
experience  before  they  were  deduced  from  first  principles.  The  quadra- 
ture of  the  cycloid  is  said  to  have  been  first  effected  by  measurement,  or 
rather  by  weighing  a cycloidal  card,  and  comparing  its  weight  with  that 
of  a piece  of  similar  card  of  known  dimensions. 

§ 6.  To  the  foregoing  examples  from  physical  science,  let  us  add  another 
from  mental.  The  following  is  one  of  the  simple  laws  of  mind:  Ideas  of 
a pleasurable  or  painful  character  form  associations  more  easily  and  strong- 
ly than  other  ideas,  that  is,  they  become  associated  after  fewer  repetitions, 
and  the  association  is  more  durable.  This  is  an  experimental  law,  ground- 
ed on  the  Method  of  Difference.  By  deduction  from  this  law,  many  of  the 
more  special  laws  which  experience  shows  to  exist  among  particular  men- 
tal phenomena  may  be  demonstrated  and  explained : the  ease  and  rapid- 
ity, for  instance,  with  which  thoughts  connected  with  our  passions  or  our 
more  cherished  interests  are  excited,  and  the  firm  hold  which  the  facts  re- 
lating to  them  have  on  our  memory;  the  vivid  recollection  we  retain  of 
minute  circumstances  which  accompanied  any  object  or  event  that  deeply 
interested  us,  and  of  the  times  and  places  in  which  we  have  been  very 
happy  or  very  miserable ; the  horror  with  which  we  view  the  accidental 
instrument  of  any  occurrence  which  shocked  us,  or  the  locality  where  it 
took  place  and  the  pleasure  we  derive  from  any  memorial  of  past  enjoy- 
ment ; all  these  effects  being  proportional  to  the  sensibility  of  the  individ- 
ual mind,  and  to  the  consequent  intensity  of  the  pain  or  pleasure  from 
which  the  association  originated.  It  has  been  suggested  by  the  able  writer 
of  a biographical  sketch  of  Dr.  Priestley  in  a monthly  periodical, f that  the 
same  elementary  law  of  our  mental  constitution,  suitably  followed  out, 
would  explain  a variety  of  mental  phenomena  previously  inexplicable,  and 
in  particular  some  of  the  fundamental  diversities  of  human  character  and 
genius.  Associations  being  of  two  sorts,  either  between  synchronous,  or 

* It  was  an  old  generalization  in  surgery,  that  fight  bandaging  had  a tendency  to  prevent 
or  dissipate  local  inflammation.  This  sequence,  being,  in  the  progress  of  physiological  knowl- 
edge, resolved  into  more  general  laws,  led  to  the  important  surgical  invention  made  by  Dr. 
Arnott,  the  treatment  of  local  inflammation  and  tumors  by  means  of  an  equable  pressure, 
produced  by  a bladder  partially  filled  with  air.  The  pressure,  by  keeping  back  the  blood 
from  the  part,  prevents  the  inflammation,  or  the  tumor,  from  being  nourished:  in  the  case  of 
inflammation,  it  removes  the  stimulus,  which  the  organ  is  unfit  to  receive ; in  the  case  of  tu- 
mors, by  keeping  back  the  nutritive  fluid,  it  causes  the  absorption  of  matter  to  exceed  the 
supply,  and  the  diseased  mass  is  gradually  absorbed  and  disappears. 

f Since  acknowledged  and  reprinted  in  Mr.  Martineau's  Miscellanies. 


344 


INDUCTION. 


between  successive  impressions ; and  the  influence  of  the  law  which  renders 
associations  stronger  in  proportion  to  the  pleasurable  or  painful  character 
of  the  impressions,  being  felt  with  peculiar  force  in  the  synchronous  class 
of  associations;  it  is  remarked  by  the  writer  referred  to,  that  in  minds  of 
strong  organic  sensibility  synchronous  associations  will  be  likely  to  pre- 
dominate, producing  a tendency  to  conceive  things  in  pictures  and  in  the 
concrete,  richly  clothed  in  attributes  and  circumstances,  a mental  habit 
which  is  commonly  called  Imagination,  and  is  one  of  the  peculiarities  of 
the  painter  and  the  poet;  while  persons  of  more  moderate  susceptibility 
to  pleasure  and  pain  will  have  a tendency  to  associate  facts  chiefly  in  the 
order  of  their  succession,  and  such  persons,  if  they  possess  mental  superior- 
ity, will  addict  themselves  to  history  or  science  rather  than  to  creative  art. 
This  interesting  speculation  the  author  of  the  present  work  has  endeavored, 
on  another  occasion,  to  pursue  further,  and  to  examine  how  far  it  will  avail 
toward  explaining  the  peculiarities  of  the  poetical  temperament.*  It  is 
at  least  an  example  which  may  serve,  instead  of  many  others,  to  show  the 
extensive  scope  which  exists  for  deductive  investigation  in  the  important 
and  hitherto  so  imperfect  Science  of  Mind. 

§ V.  The  copiousness  with  which  the  discovery  and  explanation  of  special 
laws  of  phenomena  by  deduction  from  simpler  and  more  general  ones  has 
here  been  exemplified,  was  prompted  by  a desire  to  characterize  clearly,  and 
place  in  its  due  position  of  importance,  the  Deductive  Method ; which,  in  the 
present  state  of  knowledge,  is  destined  henceforth  irrevocably  to  predom- 
inate in  the  course  of  scientific  investigation.  A revolution  is  peaceably 
and  progressively  effecting  itself  in  philosophy,  the  reverse  of  that  to  which 
Bacon  has  attached  his  name.  That  great  man  changed  the  method  of 
the  sciences  from  deductive  to  experimental,  and  it  is  now  rapidly  revert- 
ing from  experimental  to  deductive.  But  the  deductions  which  Bacon 
abolished  were  from  premises  hastily  snatched  up,  or  arbitrarily  assumed. 
The  principles  were  neither  established  by  legitimate  canons  of  experi- 
mental inquiry,  nor  the  results  tested  by  that  indispensable  element  of  a 
rational  Deductive  Method,  verification  by  specific  experience.  Between 
the  primitive  method  of  Deduction  and  that  which  I have  attempted  to 
characterize,  there  is  all  the  difference  which  exists  between  the  Aristotelian 
physics  and  the  Newtonian  theory  of  the  heavens. 

It  would,  however,  be  a mistake  to  expect  that  those  great  generaliza- 
tions, from  which  the  subordinate  truths  of  the  more  backward  sciences 
will  probably  at  some  future  period  be  deduced  by  reasoning  (as  the 
truths  of  astronomy  are  deduced  from  the  generalities  of  the  Newtonian 
theory),  will  be  found  in  all,  or  even  in  most  cases,  among  truths  now 
known  and  admitted.  We  may  rest  assured,  that  many  of  the  most  gen- 
eral laws  of  nature  are  as  yet  entirely  unthought  of ; and  that  many  others, 
destined  hereafter  to  assume  the  same  character,  are  known,  if  at  all,  only 
as  laws  or  properties  of  some  limited  class  of  phenomena;  just  as  electric- 
ity, now  recognized  as  one  of  the  most  universal  of  natural  agencies,  was 
once  known  only  as  a curious  property  which  certain  substances  acquired 
by  friction,  of  first  attracting  and  then  repelling  light  bodies.  If  the  theo- 
ries of  heat,  cohesion,  crystallization,  and  chemical  action  are  destined,  as 
there  can  be  little  doubt  that  they  are,  to  become  deductive,  the  truths 
which  will  then  be  regarded  as  th eprincipia  of  those  sciences  would  prob- 


* Dissertations  and  Discussions,  vol.  i.,  fourth  paper. 


HYPOTHESES. 


345 


ably,  if  now  announced,  appear  quite  as  novel*  as  the  law  of  gravitation 
appeared  to  the  contemporaries  of  Newton;  possibly  even  more  so,  since 
Newton’s  law,  after  all,  was  but  an  extension  of  the  law  of  weight — that  is, 
of  a generalization  familiar  from  of  old,  and  which  already  comprehended 
a not  inconsiderable  body  of  natural  phenomena.  The  general  laws  of  a 
similarly  commanding  character,  which  we  still  look  forward  to  the  dis- 
covery of,  may  not  always  find  so  much  of  their  foundations  already  laid. 

These  general  truths  will  doubtless  make  their  first  appearance  in  tire 
character  of  hypotheses ; not  proved,  nor  even  admitting  of  proof,  in  the 
first  instance,  but  assumed  as  premises  for  the  purpose  of  deducing  from 
them  the  known  laws  of  concrete  phenomena.  But  this,  though  their  ini- 
tial, can  not  be  their  final  state.  To  entitle  an  hypothesis  to  be  received 
as  one  of  the  truths  of  nature,  and  not  as  a mere  technical  help  to  the  hu- 
man faculties,  it  must  be  capable  of  being  tested  by  the  canons  of  legiti- 
mate induction,  and  must  actually  have  been  submitted  to  that  test.  When 
this  shall  have  been  done,  and  clone  successfully,  premises  will  have  been 
obtained  from  which  all  the  other  propositions  of  the  science  will  thence- 
forth be  presented  as  conclusions,  and  the  science  will,  by  means  of  a new 
and  unexpected  Induction,  be  rendered  Deductive. 


CHAPTER  XIV. 

OP  THE  LIMITS  TO  THE  EXPLANATION  OP  LAWS  OP  NATURE ; AND  OP 

HYPOTHESES. 

§ 1.  The  preceding  considerations  have  led  us  to  recognize  a distinc- 
tion between  two  kinds  of  laws,  or  observed  uniformities  in  nature : ulti- 
mate laws,  and  what  may  be  termed  derivative  laws.  Derivative  laws  are 
such  as  are  deducible  from,  and  may,  in  any  of  the  modes  which  we  have 
pointed  out,  be  resolved  into,  other  and  more  general  ones.  Ultimate  law's 
are  those  which  can  not.  We  are  not  sure  that  any  of  the  uniformities 
with  which  we  are  yet  acquainted  are  ultimate  laws;  but  we  know  that 
there  must  be  ultimate  laws;  and  that  every  resolution  of  a derivative  law 
into  more  general  laws  brings  us  nearer  to  them. 

Since  we  are  continually  discovering  that  uniformities,  not  previously 
known  to  be  other  than  ultimate,  are  derivative,  and  resolvable  into  more 
general  law's ; since  (in  other  words)  wTe  are  continually  discovering  the 
explanation  of  some  sequence  v'hich  was  previously  known  only  as  a fact ; 
it  becomes  an  interesting  question  whether  there  are  any  necessary  limits 
to  this  philosophical  operation,  or  whether  it  may  proceed  until  all  the  uni- 
form sequences  in  nature  are  resolved'  into  some  one  universal  law.  For 
this  seems,  at  first  sight,  to  be  the  ultimatum  toward  which  the  progress 
of  induction  by  the  Deductive  Method,  resting  on  a basis  of  observation 
and  experiment,  is  tending.  Projects  of  this  kind  were  universal  in  the 
infancy  of  philosophy;  any  speculations  which  held  out  a less  brilliant 
prospect  being  in  these  early  times  deemed  not  worth  pursuing.  And  the 
idea  receives  so  much  apparent  countenance  from  the  nature  of  the  most 
remarkable  achievements  of  modern  science,  that  speculators  are  even  now 
frequently  appearing,  who  profess  either  to  have  solved  the  problem,  or  to 
suggest  modes  in  which  it  may  one  day  be  solved.  Even  where  pretensions 

* Written  before  the  rise  of  the  new  views  respecting  the  relation  of  heat  to  mechanical 
force ; but  confirmed  rather  than  contradicted  by  them. 


346 


INDUCTION. 


of  this  magnitude  are  not  made,  the  character  of  the  solutions  Avhich  are 
given  or  sought  of  particular  classes  of  phenomena,  often  involves  such 
conceptions  of  what  constitutes  explanation,  as  would  render  the  notion  of 
explaining  all  phenomena  whatever  by  means  of  some  one  cause  or  law, 
perfectly  admissible. 

§ 2.  It  is,  therefore,  useful  to  remark  that  the  ultimate  Laws  of  Nature 
can  not  possibly  be  less  numerous  than  the  distinguishable  sensations  or 
other  feelings  of  our  nature;  those,  I mean,  which  are  distinguishable 
from  one  another  in  quality,  and  not  merely  in  quantity  or  degree.  For 
example : since  there  is  a phenomenon  sui  generis,  called  color,  which  our 
consciousness  testifies  to  be  not  a particular  degree  of  some  other  phenom- 
enon, as  heat  or  odor  or  motion,  but  intrinsically  unlike  all  others,  it  fol- 
lows that  there  are  ultimate  laws  of  color;  that  though  the  facts  of  color 
may  admit  of  explanation,  they  never  can  be  explained  from  laws  of  heat 
or  odor  alone,  or  of  motion  alone,  but  that,  however  far  the  explanation  may 
be  carried,  there  will  always  remain  in  it  a law  of  color.  I do  not  mean 
that  it  might  not  possibly  be  shown  that  some  other  phenomenon,  some 
chemical  or  mechanical  action,  for  example,  invariably  precedes,  and  is  the 
cause  of,  every  phenomenon  of  color.  But  though  this,  if  proved,  would 
be  an  important  extension  of  our  knowledge  of  nature,  it  would  not  explain 
how  or  why  a motion,  or  a chemical  action,  can  produce  a sensation  of 
color;  and,  however  diligent  might  be  our  scrutiny  of  the  phenomena, 
whatever  number  of  hidden  links  we  might  detect  in  the  chain  of  causa- 
tion terminating  in  the  color,  the  last  link  would  still  be  a law  of  color,  not 
a law  of  motion,  nor  of  any  other  phenomenon  whatever.  Nor  does  this 
observation  apply  only  to  color,  as  compared  with  any  other  of  the  great 
classes  of  sensations ; it  applies  to  every  particular  color,  as  compared  with 
others.  White  color  can  in  no  manner  be  explained  exclusively  by  the 
laws  of  the  production  of  red  color.  In  any  attempt  to  explain  it,  we  can 
not  but  introduce,  as  one  element  of  the  explanation,  the  proposition  that 
some  antecedent  or  other  produces  the  sensation  of  white. 

The  ideal  limit,  therefore,  of  the  explanation  of  natural  phenomena  (to- 
ward which  as  toward  other  ideal  limits  we  are  constantly  tending,  with- 
out the  prospect  of  ever  completely  attaining  it)  would  be  to  show  that 
each  distinguishable  variety  of  our  sensations,  or  other  states  of  conscious- 
ness, has  only  one  sort  of  cause;  that,  for  example,  whenever  we  perceive 
a white  color,  there  is  some  one  condition  or  set  of  conditions  which  is  al- 
ways present,  and  the  presence  of  which  always  produces  in  us  that  sensa- 
tion. As  long  as  there  are  several  known  modes  of  production  of  a phe- 
nomenon (several  different  substances,  for  instance,  which  have  the  property 
of  whiteness,  and  between  which  we  can  not  trace  any  other  resemblance) 
so  long  it  is  not  impossible  that  one  of  these  modes  of  production  may 
be  resolved  into  another,  or  that  all  of  them  may  be  resolved  into  some 
more  general  mode  of  production  not  hitherto  recognized.  But  when  the 
modes  of  production  are  reduced  to  one,  we  can  not,  in  point  of  simplifica- 
tion, go  any  further.  This  one  may  not,  after  all,  be  the  ultimate  mode; 
there  may  be  other  links  to  be  discovered  between  the  supposed  cause  and 
the  effect;  but  we  can  only  further  resolve  the  known  law,  by  introducing 
some  other  law  hitherto  unknown,  which  will  not  diminish  the  number  of 
ultimate  laws. 

In  what  cases,  accordingly,  has  science  been  most  successful  in  explaining 
phenomena,  by  resolving  their  complex  laws  into  laws  of  greater  simplicity 


HYPOTHESES 


34V 


and  generality?  Hitherto  chiefly  in  cases  of  the  propagation  of  various 
phenomena  through  space;  and,  first  and  principally,  the  most  extensive 
and  important  of  all  facts  of  that  description,  mechanical  motion.  Now 
this  is  exactly  what  might  be  expected  from  the  principles  here  laid  down. 
Not  only  is  motion  one  of  the  most  universal  of  all  phenomena,  it  is  also 
(as  might  be  expected  from  that  circumstance)  one  of  those  which,  appar- 
ently at  least,  are  produced  in  the  greatest  number  of  ways ; but  the  phe- 
nomenon itself  is  always,  to  our  sensations,  the  same  in  every  respect  but 
degree.  Differences  of  duration  or  of  velocity,  are  evidently  differences  in 
degree  only;  and  differences  of  direction  in  space,  which  alone  has  any 
semblance  of  being  a distinction  in  kind,  entirely  disappear  (so  far  as  our 
sensations  are  concerned)  by  a change  in  our  own  position ; indeed,  the 
very  same  motion  appears  to  us,  according  to  our  position,  to  take  place  in 
every  variety  of  direction,  and  motions  in  every  different  direction  to  take 
place  in  the  same.  And  again,  motion  in  a straight  line  and  in  a curve  are 
no  otherwise  distinct  than  that  the  one  is  motion  continuing  in  the  same 
direction,  the  other  is  motion  which  at  each  instant  changes  its  direction. 
There  is,  therefore,  according  to  the  principles  I have  stated,  no  absurdity 
in  supposing  that  all  motion  may  be  produced  in  one  and  the  same  way, 
by  the  same  kind  of  cause.  Accordingly,  the  greatest  achievements  in  phys- 
ical science  have  consisted  in  resolving  one  observed  law  of  the  production 
of  motion  into  the  laws  of  other  known  modes  of  production,  or  the  laws 
of  several  such  modes  into  one  more  general  mode ; as  when  the  fall  of 
bodies  to  the  earth,  and  the  motions  of  the  planets,  were  brought  under 
the  one  law  of  the  mutual  attraction  of  all  particles  of  matter;  when  the 
motions  said  to  be  produced  by  magnetism  were  shown  to  be  produced  by 
electricity ; when  the  motions  of  fluids  in  a lateral  direction,  or  even  con- 
trary to  the  direction  of  gravity,  were  shown  to  be  produced  by  gravity; 
and  the  like.  There  is  an  abundance  of  distinct  causes  of  motion  still  un- 
resolved into  one  another  : gravitation,  heat,  electricity,  chemical  action, 
nervous  action,  and  so  forth ; but  whether  the  efforts  of  the  present  gener- 
ation of  savants  to  resolve  all  these  different  modes  of  production  into  one 
are  ultimately  successful  or  not,  the  attempt  so  to  resolve  them  is  perfect- 
ly legitimate.  For,  though  these  various  causes  produce,  in  other  respects, 
sensations  intrinsically  different,  and  are  not,  therefore,  capable  of  being- 
resolved  into  one  another,  yet,  in  so  far  as  they  all  produce  motion,  it  is 
quite  possible  that  the  immediate  antecedent  of  the  motion  may  in  all  these 
different  cases  be  the  same;  nor  is  it  impossible  that  these  various  agencies 
themselves  may,  as  the  new  doctrines  assert,  all  of  them  have  for  their  own 
immediate  antecedent  modes  of  molecular  motion. 

We  need  not  extend  our  illustration  to  other  cases,  as,  for  instance,  to  the 
propagation  of  light,  sound,  heat,  electricity,  etc.,  through  space,  or  any  of 
the  other  phenomena  which  have  been  found  susceptible  of  explanation  by 
the  resolution  of  their  observed  laws  into  more  general  laws.  Enough  has 
been  said  to  display  the  difference  between  the  kind  of  explanation  and 
resolution  of  laws  which  is  chimerical,  and  that  of  which  the  accomplish- 
ment is  the  great  aim  of  science;  and  to  show  into  what  sort  of  elements 
the  resolution  must  be  effected,  if  at  all.* 

* As  is  well  remarked  by  Professor  Bain,  in  the  very  valuable  chapter  of  his  Logic  which 
treats  of  this  subject  (ii. , 121),  “scientific  explanation  and  inductive  generalization  being  the 
same  thing,  the  limits  of  Explanation  are  the  limits  of  Induction,”  and  “the  limits  to  induct- 
ive generalization  are  the  limits  to  the  agreement  or  community  of  facts.  Induction  sup- 
poses similarity  among  phenomena ; and  when  such  similarity  is  discovered,  it  reduces  the 


348 


INDUCTION. 


§ 3.  As,  however,  there  is  scarcely  any  one  of  the  principles  of  a true 
method  of  philosophizing  which  does  not  require  to  be  guarded  against 
errors  on  both  sides,  I must  enter  a caveat  against  another  misapprehen- 
sion, of  a kind  directly  contrary  to  the  preceding.  M.  Comte,  among  other 
occasions  on  which  he  has  condemned,  with  some  asperity,  any  attempt  to 
explain  phenomena  which  are  “evidently  primordial”  (meaning,  apparent- 
ly, no  more  than  that  every  peculiar  phenomenon  must  have  at  least  one 
peculiar  and  therefore  inexplicable  law),  has  spoken  of  the  attempt  to  fur- 
nish any  explanation  of  the  color  belonging  to  each  substance,  “ la  couleur 
elementaire  propre  a chaque  substance,”  as  essentially  illusory.  “No  one,” 
says  he,  “ in  our  time  attempts  to  explain  the  particular  specific  gravity  of 
each  substance  or  of  each  structure.  Why  should  it  be  otherwise  as  to 
the  specific  color,  the  notion  of  which  is  undoubtedly  no  less  primordial?”* 
Now  although,  as  he  elsewhere  observes,  a color  must  always  remain  a 
different  thing  from  a weight  or  a sound,  varieties  of  color  might  neverthe- 
less follow,  or  correspond  to,  given  varieties  of  weight,  or  sound,  or  some 
other  phenomenon  as  different  as  these  are  from  color  itself.  It  is  one 
question  what  a thing  is,  and  another  what  it  depends  on;  and  though  to 
ascertain  the  conditions  of  an  elementary  phenomenon  is  not  to  obtain  any 
new  insight  into  the  nature  of  the  phenomenon  itself,  that  is  no  reason 
against  attempting  to  discover  the  conditions.  The  interdict  against  en- 
deavoring to  reduce  distinctions  of  color  to  any  common  principle,  would 
have  held  equally  good  against  a like  attempt  on  the  subject  of  distinctions 
of  sound  ; which  nevertheless  have  been  found  to  be  immediately  preceded 
and  caused  by  distinguishable  varieties  in  the  vibrations  of  elastic  bodies; 
though  a sound,  no  doubt,  is  quite  as  different  as  a color  is  from  any  mo- 
tion of  particles,  vibratory  or  otherwise.  We  might  add,  that,  in  the  case 
of  colors,  there  are  strong  positive  indications  that  they  are  not  ultimate 

phenomena  under  a common  statement.  The  similarity  of  terrestrial  gravity  to  celestial  at- 
traction enables  the  two  to  be  expressed  as  one  phenomenon.  The  similarity  between  cap- 
illary attraction,  solution,  the  operation  of  cements,  etc.,  leads  to  their  being  regarded  not  as 

a plurality,  but  as  a unity,  a single  causative  link,  the  operation  of  a single  agency If 

it  be  asked  whether  we  can  merge  gravity  itself  in  some  still  higher  law,  the  answer  must  de- 
pend upon  the  facts.  Are  there  any  other  forces,  at  present  held  distinct  from  gravity,  that 
we  may  hope  to  make  fraternize  with  it,  so  as  to  join  in  constituting  a higher  unity?  Gravity 
is  an  attractive  force ; and  another  great  attractive  force  is  cohesion,  or  the  force  that  binds 
together  the  atoms  of  solid  matter.  Might  we,  then,  join  these  two  in  a still  higher  unity,  ex- 
pressed under  a more  comprehensive  law  ? Certainly  we  might,  but  not  to  any  advantage. 
The  two  kinds  of  force  agree  in  the  one  point,  attraction,  but  they  agree  in  no  other ; indeed, 
in  the  manner  of  the  attraction,  they  differ  widely ; so  widely  that  we  should  have  to  state 
totally  distinct  laws  for  each.  Gravity  is  common  to  all  matter,  and  equal  in  amount  in  equal 
masses  of  matter,  whatever  be  the  kind  ; it  follows  the  law  of  the  diffusion  of  space  from  a 
point  (the  inverse  square  of  the  distance);  it  extends  to  distances  unlimited;  it  is  indestructi- 
ble and  invariable.  Cohesion  is  special  for  each  separate  substance;  it  decreases  according 
to  distance  much  more  rapidly  than  the  inverse  square,  vanishing  entirely  at  very  small  dis- 
tances. Two  such  forces  have  not  sufficient  kindred  to  he  generalized  into  one  force;  the 
generalization  is  only  illusory ; the  statement  of  the  difference  would  still  make  two  forces ; 
while  the  consideration  of  one  would  not  in  any  way  simplify  the  phenomena  of  the  other,  as 
happened  in  the  generalization  of  gravity  itself.” 

To  the  impassable  limit  of  the  explanation  of  laws  of  nature,  set  forth  in  the  text,  must 
therefore  be  added  a further  limitation.  Although,  when  the  phenomena  to  be  explained  are 
not,  in  their  own  nature,  generically  distinct,  the  attempt  to  refer  them  to  the  same  cause  is 
scientifically  legitimate ; yet  to  the  success  of  the  attempt  it  is  indispensable  that  the  cause 
should  be  shown  to  be  capable  of  producing  them  according  to  the  same  law.  Otherwise  the 
unity  of  cause  is  a mere  guess,  and  the  generalization  only  a nominal  one,  which,  even  if  ad- 
mitted, would  not  diminish  the  number  of  ultimate  laws  of  nature. 

* Corns  de  Philosophie  Positive,  ii. , 656. 


HYPOTHESES. 


349 


properties  of  the  different  kinds  of  substances,  but  depend  on  conditions 
capable  of  being  superinduced  upon  all  substances;  since  there  is  no  sub- 
stance which  can  not,  according  to  the  kind  of  light  thrown  upon  it,  be 
made  to  assume  almost  any  color;  and  since  almost  every  change  in  the 
mode  of  aggregation  of  the  particles  of  the  same  substance  is  attended 
with  alterations  in  its  color,  and  in  its  optical  properties  generally. 

The  really  weak  point  in  the  attempts  which  have  been  made  to  account 
for  colors  by  the  vibrations  of  a fluid,  is  not  that  the  attempt  itself  is  un- 
philosophical,  but  that  the  existence  of  the  fluid,  and  the  fact  of  its  vibra- 
tory motion,  are  not  proved,  but  are  assumed,  on  no  other  ground  than 
the  facility  they  are  supposed  to  afford  of  explaining  the  phenomena.  And 
this  consideration  leads  to  the  important  question  of  the  proper  use  of 
scientific  hypotheses,  the  connection  of  which  with  the  subject  of  the  ex- 
planation of  the  phenomena  of  nature,  and  of  the  necessary  limits  to  that 
explanation,  need  not  be  pointed  out. 

§ 4.  An  hypothesis  is  any  supposition  which  we  make  (either  without 
actual  evidence,  or  on  evidence  avowedly  insufficient)  in  order  to  endeavor 
to  deduce  from  it  conclusions  in  accordance  with  facts  which  are  known  to 
be  real ; under  the  idea  that  if  the  conclusions  to  which  the  hypothesis 
leads  are  known  truths,  the  hypothesis  itself  either  must  be,  or  at  least  is 
likely  to  be,  true.  If  the  hypothesis  relates  to  the  cause  or  mode  of  pro- 
duction of  a phenomenon,  it  will  serve,  if  admitted,  to  explain  such  facts  as 
are  found  capable  of  being  deduced  from  it.  And  this  explanation  is  the 
purpose  of  many,  if  not  most  hypotheses.  Since  explaining,  in  the  scien- 
tific sense,  means  resolving  a uniformity  which  is  not  a law  of  causation, 
into  the  laws  of  causation  from  which  it  results,  or  a complex  law  of  causa- 
tion into  simpler  and  more  general  ones  from  which  it  is  capable  of  being 
deductively  inferred,  if  there  do  not  exist  any  known  laws  which  fulfill 
this  requirement,  we  may  feign  or  imagine  some  which  would  fulfill  it; 
and  this  is  making  an  hypothesis. 

An  hypothesis  being  a mere  supposition,  there  are  no  other  limits  to 
hypotheses  than  those  of  the  human  imagination;  we  may,  if  we  please, 
imagine,  by  way  of  accounting  for  an  effect,  some  cause  of  a kind  utterly 
unknown,  and  acting  according  to  a lawr  altogether  fictitious.  But  as  hy- 
potheses of  this  sort  would  not  have  any  of  the  plausibility  belonging  to 
those  which  ally  themselves  by  analogy  with  known  laws  of  nature,  and  be- 
sides would  not  supply  the  want  which  arbitrary  hypotheses  are  generally 
invented  to  satisfy,  by  enabling  the  imagination  to  represent  to  itself  an 
obscure  phenomenon  in  a familiar  light,  there  is  probably  no  hypothesis 
in  the  history  of  science  in  which  both  the  agent  itself  and  the  law  of  its 
operation  were  fictitious.  Either  the  phenomenon  assigned  as  the  cause  is 
real,  but  the  law  according  to  which  it  acts  merely  supposed ; or  the  cause 
is  fictitious,  but  is  supposed  to  produce  its  effects  according  to  laws  similar 
to  those  of  some  known  class  of  phenomena.  An  instance  of  the  first  kind 
is  afforded  by  the  different  suppositions  made  respecting  the  law  of  the 
planetary  central  force,  anterior  to  the  discovery  of  the  true  law,  that  the 
force  varies  as  the  inverse  square  of  the  distance ; which  also  suggested 
itself  to  Newton,  in  the  first  instance,  as  an  hypothesis,  and  was  verified 
by  proving  that  it  led  deductively  to  Kepler’s  laws.  Hypotheses  of  the 
second  kind  are  such. as  the  vortices  of  Descartes,  which  were  fictitious, 
but  were  supposed  to  obey  the  known  lawrs  of  rotatory  motion ; or  the 
two  rival  hypotheses  respecting  the  nature  of  light,  the  one  ascribing 


350 


INDUCTION. 


the  phenomena  to  a fluid  emitted  from  all  luminous  bodies,  the  other  (now 
generally  received)  attributing  them  to  vibratory  motions  among  the  par- 
ticles of  an  ether  pervading  all  space.  Of  the  existence  of  either  fluid 
there  is  no  evidence,  save  the  explanation  they  are  calculated  to  afford  of 
some  of  the  phenomena;  but  they  are  supposed  to  produce  their  effects 
according  to  known  laws:  the  ordinary  laws  of  continued  locomotion  in 
the  one  case,  and  in  the  other  those  of  the  propagation  of  undulatory 
movements  among  the  particles  of  an  elastic  fluid. 

According  to  the  foregoing  remarks,  hypotheses  are  invented  to  enable 
the  Deductive  Method  to  be  earlier  applied  to  phenomena.  But*  in  order  to 
discover  the  cause  of  any  phenomenon  by  the  Deductive  Method,  the  proc- 
ess must  consist  of  three  parts:  induction,  ratiocination,  and  verification. 
Induction  (the  place  of  which,  however,  may  be  supplied  by  a prior  deduc- 
tion), to  ascertain  the  laws  of  the  causes;  ratiocination,  to  compute  from 
those  laws  how  the  causes  will  operate  in  the  particular  combination  known 
to  exist  in  the  case  in  hand ; verification,  by  comparing  this  calculated  ef- 
fect with  the  actual  phenomenon.  No  one  of  these  three  parts  of  the 
process  can  be  dispensed  with.  In  the  deduction  which  proves  the  iden- 
tity of  gravity  with  the  central  force  of  the  solar  system,  all  the  three  are 
found.  First,  it  is  proved  from  the  moon’s  motions,  that  the  earth  at- 
tracts her  with  a force  varying  as  the  inverse  square  of  the  distance.  This 
(though  partly  dependent  on  prior  deductions)  corresponds  to  the  first,  or 
purely  inductive,  step:  the  ascertainment  of  the  law  of  the  cause.  Second- 
ly, from  this  law,  and  from  the  knowledge  previously  obtained  of  the 
moon’s  mean  distance  from  the  earth,  and  of  the  actual  amount  of  her  de- 
flection from  the  tangent,  it  is  ascertained  with  what  rapidity  the  earth’s 
attraction  would  cause  the  moon  to  fall,  if  she  were  no  further  off,  and  no 
more  acted  upon  by  extraneous  forces,  than  terrestrial  bodies  are:  that  is 
the  second  step,  the  ratiocination.  Finally,  this  calculated  velocity  being 
compared  with  the  observed  velocity  with  which  all  heavy  bodies  fall, 
by  mere  gravity,  toward  the  surface  of  the  earth  (sixteen  feet  in  the  first 
second,  forty-eight  in  the  second,  and  so  forth,  in  the  ratio  of  the  odd  num- 
bers, 1,  3,  5,  etc.),  the  two  quantities  are  found  to  agree.  The  order  in 
which  the  steps  are  here  presented  was  not  that  of  their  discovery ; but  it  is 
their  correct  logical  order,  as  portions  of  the  proof  that  the  same  attraction 
of  the  earth  which  causes  the  moon’s  motion  causes  also  the  fall  of  heavy 
bodies  to  the  earth  : a proof  which  is  thus  complete  in  all  its  parts. 

Now,  the  Hypothetical  Method  suppresses  the  first  of  the  three  steps, 
the  induction  to  ascertain  the  law;  and  contents  itself  with  the  other  two 
operations,  ratiocination  and  verification ; the  law  which  is  reasoned  from 
being  assumed  instead  of  proved. 

This  process  may  evidently  be  legitimate  on  one  supposition,  namely,  if 
the  nature  of  the  case  be  such  that  the  final  step,  the  verification,  shall 
amount  to,  and  fulfill  the  conditions  of,  a complete  induction.  We  want 
to  be  assured  that  the  law  we  have  hypothetically  assumed  is  a true  one ; 
and  its  leading  deductively  to  true  results  will  afford  this  assurance,  pro- 
vided the  case  be  such  that  a false  law  can  not  lead  to  a true  result;  pro- 
vided no  law,  except  the  very  one  which  we  have  assumed,  can  lead  deduct- 
ively to  the  same  conclusions  which  that  leads  to.  And  this  proviso  is 
often  realized.  For  example,  in  the  very  complete  specimen  of  deduction 
which  we  just  cited,  the  original  major  premise  of  the  ratiocination,  the 


Vide  supra,  bookiii.,  chap.  xi. 


HYPOTHESES. 


351 


law  of  the  attractive  force,  was  ascertained  in  this  mode;  by  this  legitimate 
employment  of  the  Hypothetical  Method.  Newton  began  by  an  assump- 
tion that  the  force  which  at  each  instant  deflects  a planet  from  its  rectilin- 
eal course,  and  makes  it  describe  a curve  round  the  sun,  is  a force  tending 
directly  toward  the  sun.  He  then  proved  that  if  this  be  so,  the  planet  will 
describe,  as  we  know  by  Kepler’s  first  law  that  it  does  describe,  equal  areas 
in  equal  times;  and,  lastly,  he  proved  that  if  the  force  acted  in  any  other 
direction  whatever,  the  planet  would  not  describe  equal  areas  in  equal 
times.  It  being  thus  shown  that  no  other  hypothesis  would  accord  with 
the  facts,  the  assumption  was  proved  ; the  hypothesis  became  an  inductive 
truth.  Not  only  did  Newton  ascertain  by  this  hypothetical  process  the 
direction  of  the  deflecting  force;  he  proceeded  in  exactly  the  same  manner 
to  ascertain  the  law  of  variation  of  the  quantity  of  that  force.  He  assumed 
that  the  force  varied  inversely  as  the  square  of  the  distance;  showed  that 
from  this  assumption  the  remaining  two  of  Kepler’s  laws  might  be  de- 
duced ; and,  finally,  that  any  other  law  of  variation  would  give  results  in- 
consistent with  those  laws,  and  inconsistent,  therefore,  with  the  real  mo- 
tions of  the  planets,  of  which  Kepler’s  laws  were  known  to  be  a correct 
expression. 

I have  said  that  in  this  case  the  verification  fulfills  the  conditions  of  an 
induction;  but  an  induction  of  what  sort?  On  examination  we  find  that 
it  conforms  to  the  canon  of  the  Method  of  Difference.  It  affords  the  two 
instances,  ABC,  a be,  and  B C,  be.  A represents  central  force;  ABC, 
the  planets  plus  a central  force ; B C,  the  planets  apart  from  a central 
force.  The  planets  with  a central  force  give  a,  areas  proportional  to  the 
times;  the  planets  without  a central  force  give  be  (a  set  of  motions)  with- 
out a,  or  with  something  else  instead  of  a.  This  is  the  Method  of  Differ- 
ence in  all  its  strictness.  It  is  true,  the  two  instances  which  the  method 
requires  are  obtained  in  this  case,  not  by  experiment,  but  by  a prior  de- 
duction. But  that  is  of  no  consequence.  It  is  immaterial  what  is  the 
nature  of  the  evidence  from  which  we  derive  the  assurance  that  ABC 
will  produce  a be,  and  BC  only  be;  it  is  enough  that  we  have  that  as- 
surance. In  the  present  case,  a process  of  reasoning  furnished  Newton 
with  the  very  instances  which,  if  the  nature  of  the  case  had  admitted  of  it, 
he  would  have  sought  by  experiment. 

It  is  thus  perfectly  possible,  and  indeed  is  a very  common  occurrence, 
that  what  was  an  hypothesis  at  the  beginning  of  the  inquiry  becomes  a 
proved  law  of  nature  before  its  close.  But  in  order  that  this  should  hap- 
pen, we  must  be  able,  either  by  deduction  or  experiment,  to  obtain  both  the 
instances  which  the  Method  of  Difference  requires.  That  we  are  able  from 
the  hypothesis  to  deduce  the  known  facts,  gives  only  the  affirmative  in- 
stance, ABC,  a be.  It  is  equally  necessary  that  we  should  be  able  to  ob- 
tain, as  Newton  did,  the  negative  instance  B C,  be;  by  showing  that  no 
antecedent,  except  the  one  assumed  in  the  hypothesis,  would  in  conjunc- 
tion with  B C produce  a. 

Now  it  appears  to  me  that  this  assurance  can  not  be  obtained,  when  the 
cause  assumed  in  the  hypothesis  is  an  unknown  cause  imagined  solely  to 
account  for  a.  When  we  are  only  seeking  to  determine  the  precise  law  of 
a cause  already  ascertained,  or  to  distinguish  the  particular  agent  which  is 
in  fact  the  cause,  among  several  agents  of  the  same  kind,  one  or  other  of 
which  it  is  already  known  to  be,  we  may  then  obtain  the  negative  instance. 
An  inquiry  which  of  the  bodies  of  the  solar  system  causes  by  its  attraction 
some  particular  irregularity  in  the  orbit  or  periodic  time  of  some  satellite 


352 


INDUCTION. 


or  comet,  would  be  a case  of  the  second  description.  Newton’s  was  a case 
of  the  first.  If  it  had  not  been  previously  known  that  the  planets  were 
hindered  from  moving  in  straight  lines  by  some  force  tending  toward  the 
interior  of  their  orbit,  though  the  exact  direction  was  doubtful;  or  if  it 
had  not  been  known  that  the  force  increased  in  some  proportion  or  other 
as  the  distance  diminished,  and  diminished  as  it  increased,  Newton’s  ar- 
gument would  not  have  proved  his  conclusion.  These  facts,  however,  be- 
ing already  certain,  the  range  of  admissible  suppositions  was  limited  to 
the  various  possible  directions  of  a line,  and  the  various  possible  numerical 
relations  between  the  variations  of  the  distance,  and  the  variations  of  the 
attractive  force.  Now  among  these  it  was  easily  shown  that  different  sup- 
positions could  not  lead  to  identical  consequences. 

Accordingly,  Newton  could  not  have  performed  his  second  great  scien- 
tific operation  : that  of  identifying  terrestrial  gravity  with  the  central  force 
of  the  solar  system  by  the  same  hypothetical  method.  When  the  law  of 
the  moon’s  attraction  had  been  proved  from  the  data  of  the  moon  itself, 
then,  on  finding  the  same  law  to  accord  with  the  phenomena  of  terrestrial 
gravity,  he  was  warranted  in  adopting  it  as  the  law  of  those  phenomena 
likewise;  but  it  would  not  have  been  allowable  for  him,  without  any  lunar 
data,  to  assume  that  the  moon  was  attracted  toward  the  earth  with  a force 
as  the  inverse  square  of  the  distance,  merely  because  that  ratio  would 
enable  him  to  account  for  terrestrial  gravity;  for  it  would  have  been  im- 
possible for  him  to  prove  that  the  observed  law  of  the  fall  of  heavy  bodies 
to  the  earth  could  not  result  from  any  force,  save  one  extending  to  the 
moon,  and  proportional  to  the  inverse  square. 

It  appears,  then,  to  be  a condition  of  the  most  genuinely  scientific  hy- 
pothesis, that  it  be  not  destined  always  to  remain  an  hypothesis,  but  be  of 
such  a nature  as  to  be  either  proved  or  disproved  by  comparison  with  ob- 
served facts.  This  condition  is  fulfilled  when  the  effect  is  already  known  to 
depend  on  the  very  cause  supposed,  and  the  hypothesis  relates  only  to  the 
precise  mode  of  dependence  ; the  law  of  the  variation  of  the  effect  according 
to  the  variations  in  the  quantity  or  in  the  relations  of  the  cause.  With  these 
maybe  classed  the  hypotheses  which  do  not  make  any  supposition  with  re- 
gard to  causation,  but  only  with  regard  to  the  law  of  correspondence  between 
facts  which  accompany  each  other  in  their  variations,  though  there  may  be 
no  relation  of  cause  and  effect  between  them.  Such  were  the  different 
false  hypotheses  which  Kepler  made  respecting  the  law  of  the  refraction 
of  light.  It  was  known  that  the  direction  of  the  line  of  refraction  varied 
with  every  variation  in  the  direction  of  the  line  of  incidence,  but  it  was 
not  known  how ; that  is,  what  changes  of  the  one  corresponded  to  the  dif- 
ferent changes  of  the  other.  In  this  case  any  law  different  from  the  true 
one  must  have  led  to  false  results.  And,  lastly,  we  must  add  to  these  all 
hypothetical  modes  of  merely  representing  or  describing  phenomena;  such 
as  the  hypothesis  of  the  ancient  astronomers  that  the  heavenly  bodies 
moved  in  circles;  the  various  hypotheses  of  eccentrics,  deferents,  and  epi- 
cycles, which  were  added  to  that  original  hypothesis;  the  nineteen  false 
hypotheses  which  Kepler  made  and  abandoned  respecting  the  form  of  the 
planetary  orbits;  and  even  the  doctrine  in  which  he  finally  rested,  that 
those  orbits  are  ellipses,  which  was  but  an  hypothesis  like  the  rest  until 
verified  by  facts. 

In  all  these  cases,  verification  is  proof ; if  the  supposition  accords  with 
the  phenomena  there  needs  no  other  evidence  of  it.  But  in  order  that  this 
may  be  the  case,  I conceive  it  to  be  necessary,  when  the  hypothesis  relates 


HYPOTHESES. 


353 


to  causation,  that  the  supposed  cause  should  not  only  be  a real  phenomenon, 
something  actually  existing  in  nature,  but  should  be  already  known  to  ex- 
ercise, or  at  least  to  be  capable  of  exercising,  an  influence  of  some  sort  over 
the  effect.  In  any  other  case,  it  is  no  sufficient  evidence  of  the  truth  of  the 
hypothesis  that  we  are  able  to  deduce  the  real  phenomena  from  it. 

Is  it,  then,  never  allowable,  in  a scientific  hypothesis,  to  assume  a cause, 
but  only  to  ascribe  an  assumed  law  to  a known  cause  ? Ido  not  assert 
this.  I only  say,  that  in  the  latter  case  alone  can  the  hypothesis  be  received 
as  true  merely  because  it  explains  the  phenomena.  In  the  former  case  it 
may  be  very  useful  by  suggesting  a line  of  investigation  which  may  possi- 
bly terminate  in  obtaining  real  proof.  But  for  this  purpose,  as  is  justly 
remarked  by  M.  Comte,  it  is  indispensable  that  the  cause  suggested  by  the 
hypothesis  should  be  in  its  own  nature  susceptible  of  being  proved  by  other 
evidence.  This  seems  to  be  the  philosophical  import  of  Newton’s  maxim, 
(so  often  cited  with  approbation  by  subsequent  writers),  that  the  cause  as- 
signed for  any  phenomenon  must  not  only  be  such  as  if  admitted  would 
explain  the  phenomenon,  but  must  also  be  a vera  causa.  What  he  meant 
by  a vera  causa  Newton  did  not  indeed  very  explicitly  define;  and  Dr. 
Whewell,  who  dissents  from  the  propriety  of  any- such  restriction  upon  the 
latitude  of  framing  hypotheses,  has  had  little  difficulty  in  showing*  that  his 
conception  of  it  was  neither  precise  nor  consistent  with  itself;  according- 
ly his  optical  theory  was  a signal  instance  of  the  violation  of  his  own  rule. 
It  is  certainly  not  necessary  that  the  cause  assigned  should  be  a cause  al- 
ready known  ; otherwise  we  should  sacrifice  our  best  opportunities  of  be- 
coming acquainted  with  new  causes.  But  what  is  true  in  the  maxim  is, 
that  the  cause,  though  not  known  previously,  should  be  capable  of  being 
known  thereafter ; that  its  existence  should  be  capable  of  being  detected, 
and  its  connection  with  the  effect  ascribed  to  it  should  be  susceptible  of 
being  proved,  by  independent  evidence.  The  hypothesis,  by  suggesting 
observations  and  experiments,  puts  us  on  the  roacl  to  that  independent  ev- 
idence, if  it  be  really  attainable ; and  till  it  be  attained,  the  hypothesis 
ought  only  to  count  for  a more  or  less  plausible  conjecture. 

§ 5.  This  function,  however,  of  hypotheses,  is  one  which  must  be  reckon- 
ed absolutely  indispensable  in  science.  When  Newton  said,  “ Hypotheses 
non  fingo,”  he  did  not  mean  that  he  deprived  himself  of  the  facilities  of 
investigation  afforded  by  assuming  in  the  first  instance  what  he  hoped  ul- 
timately to  be  able  to  prove.  Without  such  assumptions,  science  could 
never  have  attained  its  present  state  ; they  are  necessary  steps  in  the  prog- 
ress to  something  more  certain  ; and  nearly  every  thing  which  is  now  theo- 
ry was  once  hypothesis.  Even  in  purely  experimental  science,  some  in- 
ducement is  necessary  for  trying  one  experiment  rather  than  another;  and 
though  it  is  abstractedly  possible  that  all  the  experiments  which  have  been 
tried,  might  have  been  produced  by  the  mere  desire  to  ascertain  what 
would  happen  in  certain  circumstances,  without  any  previous  conjecture 
as  to  the  result ; yet,  in  point  of  fact,  those  unobvious,  delicate,  and  often 
cumbrous  and  tedious  processes  of  experiment,  which  have  thrown  most 
light  upon  the  general  constitution  of  nature,  would  hardly  ever  have  been 
undertaken  by  the  persons  or  at  the  time  they  were,  unless  it  had  seemed 
to  depend  on  them  whether  some  general  doctrine  or  theory  which  had 
been  suggested,  but  not  yet  proved,  should  be  admitted  or  not.  If  this  be 


Philosophy  of  Discovery , p.  185  et  seq. 
23 


354 


INDUCTION. 


true  even  of  merely  experimental  inquiry,  the  conversion  of  experimental 
into  deductive  truths  could  still  less  have  been  effected  without  large 
temporary  assistance  from  hypotheses.  The  process  of  tracing  regularity 
in  any  complicated,  and  at  first  sight  confused,  set  of  appearances,  is  neces- 
sarily tentative;  we  begin  by  making  any  supposition,  even  a false  one,  to 
see  what  consequences  will  follow  from  it;  and  by  observing  how  these 
differ  from  the  real  phenomena,  we  learn  what  corrections  to  make  in  our 
assumption.  The  simplest  supposition  which  accords  with  the  more  obvi- 
ous facts  is  the  best  to  begin  with ; because  its  consequences  are  the  most 
easily  traced.  This  rude  hypothesis  is  then  rudely  corrected,  and  the  op- 
eration repeated ; and  the  comparison  of  the  consequences  deducible  from 
the  corrected  hypothesis,  with  the  observed  facts,  suggests  still  further 
correction,  until  the  deductive  results  are  at  last  made  to  tally  with  the  phe- 
nomena. “ Some  fact  is  as  yet  little  understood,  or  some  law  is  unknown  ; 
we  frame  on  the  subject  an  hypothesis  as  accordant  as  possible  with  the 
whole  of  the  data  already  possessed ; and  the  science,  being  thus  enabled 
to  move  forward  freely,  always  ends  by  leading  to  new  consequences  ca- 
pable of  observation,  which  either  confirm  or  refute,  unequivocally,  the 
first  supposition.”  Neither  induction  nor  deduction  would  enable  us  to 
understand  even  the  simplest  phenomena,  “ if  we  did  not  often  commence 
by  anticipating  on  the  results ; by  making  a provisional  supposition,  at  first 
essentially  conjectural,  as  to  some  of  the  very  notions  which  constitute  the 
final  object  of  the  inquiry.”*  Let  any  one  watch  the  manner  in  which  he 
himself  unravels  a complicated  mass  of  evidence;  let  him  observe  how, for 
instance,  he  elicits  the  true  history  of  any  occurrence  from  the  involved 
statements  of  one  or  of  many  witnesses ; he  will  find  that  he  does  not  take 
all  the  items  of  evidence  into  his  mind  at  once,  and  attempt  to  weave  them 
together;  he  extemporizes, from  a few  of  the  particulars,  a first  rude  the- 
ory of  the  mode  in  which  the  facts  took  place,  and  then  looks  at  the  other 
statements  one  by  one,  to  try  whether  they  can  be  reconciled  with  that 
provisional  theory,  or  what  alterations  or  additions  it  requires  to  make  it 
square  with  them.  In  this  way,  which  has  been  justly  compared  to  the 
Methods  of  Approximation  of  mathematicians,  we  arrive,  by  means  of  hy- 
potheses, at  conclusions  not  hypothetical. f 


* Comte,  Philosophic  Positive , ii. , 434-437. 

f As  an  example  of  legitimate  hypothesis  according  to  the  test  here  laid  down,  has  been 
justly  cited  that  of  Broussais,  who,  proceeding  on  the  very  rational  principle  that  every  dis- 
ease must  originate  in  some  definite  part  or  other  of  the  organism,  boldly  assumed  that  cer- 
tain fevers,  which  not  being  known  to  be  local  were  called  constitutional,  had  their  origin  in 
the  mucous  membrane  of  the  alimentary  canal.  The  supposition  was,  indeed,  as  is  now  gen- 
erally admitted,  erroneous ; but  he  was  justified  in  making  it,  since  by  deducing  the  conse- 
quences of  the  supposition,  and  comparing  them  with  the  facts  of  those  maladies,  he  might  be 
certain  of  disproving  his  hypothesis  if  it  was  ill  founded,  and  might  expect  that  the  compari- 
son woidd  materially  aid  him  in  framing  another  more  conformable  to  the  phenomena. 

The  doctrine  now  universally  received  that  the  earth  is  a natural  magnet,  was  originally  an 
hypothesis  of  the  celebrated  Gilbert. 

Another  hypothesis,  to  the  legitimacy  of  which  no  objection  can  lie,  and  which  is  well  cal- 
culated to  light  the  path  of  scientific  inquiry,  is  that  suggested  by  several  recent  writers,  that 
the  brain  is  a voltaic  pile,  and  that  each  of  its  pulsations  is  a discharge  of  electricity  through 
the  system.  It  has  been  remarked  that  the  sensation  felt  by  the  hand  from  the  beating  of  a 
brain,  bears  a strong  resemblance  to  a voltaic  shock.  And  the  hypothesis,  if  followed  to  its 
consequences,  might  afford  a plausible  explanation  of  many  physiological  facts,  while  there  is 
nothing  to  discourage  the  hope  that  we  may  in  time  sufficiently  understand  the  conditions  of 
voltaic  phenomena  to  render  the  truth  of  the  hypothesis  amenable  to  observation  and  experi- 
ment. 

The  attempt  to  localize,  in  different  regions  of  the  brain,  the  physical  organs  of  our  different 


HYPOTHESES. 


355 


§ 6.  It  is  perfectly  consistent  with  the  spirit  of  the  method,  to  assume  in 
this  provisional  manner  not  only  an  hypothesis  respecting  the  law  of  what 
we  already  know  to  be  the  cause,  but  an  hypothesis  respecting  the  cause 
itself.  It  is  allowable,  useful,  and  often  even  necessary,  to  begin  by  asking 
ourselves  what  cause  may  have  produced  the  effect,  in  order  that  we  may 
know  in  what  direction  to  look  out  for  evidence  to  determine  whether  it 
actually  did.  The  vortices  of  Descartes  would  have  been  a perfectly  legit- 
imate hypothesis,  if  it  had  been  possible,  by  any  mode  of  exploration  which 
we  could  entertain  the  hope  of  ever  possessing,  to  bring  the  reality  of  the 
vortices,  as  a fact  in  nature,  conclusively  to  the  test  of  observation.  The 
vice  of  the  hypothesis  was  that  it  could  not  lead  to  any  course  of  inves- 
tigation capable  of  converting  it  from  an  hypothesis  into  a proved  fact. 
It  might  chance  to  be  disproved,  either  by  some  want  of  correspondence 
with  the  phenomena  it  purported  to  explain,  or  (as  actually  happened)  by 
some  extraneous  fact.  “ The  free  passage  of  comets  through  the  spaces  in 
which  these  vortices  should  have  been,  convinced  men  that  these  vortices 
did  not  exist.”*  But  the  hypothesis  would  have  been  false,  though  no  such 
direct  evidence  of  its  falsity  had  been  procurable.  Direct  evidence  of  its 
truth  there  could  not  be. 

The  prevailing  hypothesis  of  a luminiferous  ether,  in  other  respects  not 
without  analogy  to  that  of  Descartes,  is  not  in  its  own  nature  entirely  cut 
off  from  the  possibility  of  direct  evidence  in  its  favor.  It  is  well  known 
that  the  difference  between  the  calculated  and  the  observed  times  of  the 
periodical  return  of  Encke’s  comet,  has  led  to  a conjecture  that  a medium 
capable  of  opposing  resistance  to  motion  is  diffused  through  space.  If 
this  surmise  should  be  confirmed,  in  the  course  of  ages,  by  the  gradual  ac- 
cumulation of  a similar  variance  in  the  case  of  the  other  bodies  of  the  solar 
system,  the  luminiferous  ether  would  have  made  a considerable  advance 
toward  the  character  of  a vera  causa,  since  the  existence  would  have  been 
ascertained  of  a great  cosmical  agent,  possessing  some  of  the  attributes 
which  the  hypothesis  assumes ; though  there  would  still  remain  many  dif- 
ficulties, and  the  identification  of  the  ether  with  the  resisting  medium 
would  even,  I imagine,  give  rise  to  new  ones.  At  present,  however,  this 

mental  faculties  and  propensities,  was,  on  the  part  of  its  original  author,  a legitimate  example 
of  a scientific  hypothesis  ; and  we  ought  not,  therefore,  to  blame  him  for  the  extremely  slight 
grounds  on  which  he  often  proceeded,  in  an  operation  which  could  only  be  tentative,  though  we 
may  regret  that  materials  barely  sufficient  for  a first  rude  hypothesis  should  have  been  hastily- 
worked  up  into  the  vain  semblance  of  a science.  If  there  be  really  a connection  between  the 
scale  of  mental  endowments  and  the  various  degrees  of  complication  in  the  cerebral  system,  the 
nature  of  that  connection  was  in  no  other  way  so  likely  to  be  brought  to  light  as  by  framing, 
in  the  first  instance,  an  hypothesis  similar  to  that  of  Gall.  But  the  verification  of  any  such 
hypothesis  is  attended,  from  the  peculiar  nature  of  the  phenomena,  with  difficulties  which 
phrenologists  have  not  shown  themselves  even  competent  to  appreciate,  much  less  to  overcome. 

Mr.  Darwin’s  remarkable  speculation  on  the  Origin  of  Species  is  another  unimpeachable 
example  of  a legitimate  hypothesis.  What  he  terms  “natural  selection”  is  not  only  a vera 
causa,  but  one  proved  to  lje  capable  of  producing  effects  of  the  same  kind  with  those  which 
the  hypothesis  ascribes  to  it ; the  question  of  possibility  is  entirely  one  of  degree.  It  is  un- 
reasonable to  accuse  Mr.  Darwin  (as  has  been  done)  of  violating  the  rules  of  Induction.  The 
rules  of  Induction  are  concerned  with  the  conditions  of  Proof.  Mr.  Darwin  has  never  pre- 
tended that  his  doctrine  was  proved.  He  was  not  bound  by  the  rules  of  Induction,  but  by 
those  of  Hypothesis.  And  these  last  have  seldom  been  more  completely  fulfilled.  He  has 
opened  a path  of  inquiry  full  of  promise,  the  results  of  which  none  can  foresee.  And  is  it 
not  a wonderful  feat  of  scientific  knowledge  and  ingenuity  to  have  rendered  so  bold  a sugges- 
tion, which  the  first  impulse  of  every  one  was  to  reject  at  once,  admissible  and  discussible, 
even  as  a conjecture  ? 

* Whewell's  Phil,  of  Discovery , pp.  275,  276. 


356 


INDUCTION. 


supposition  cun  not  be  looked  upon  as  more  than  a conjecture ; the  exist- 
ence of  the  ether  still  rests  on  the  possibility  of  deducing  from  its  as- 
sumed laws  a considerable  number  of  actual  phenomena;  and  this  evidence 
I can  not  regard  as  conclusive,  because  we  can  not  have,  in  the  case  of  such 
an  hypothesis,  the  assurance  that  if  the  hypothesis  be  false  it  must  lead  to 
results  at  variance  with  the  true  facts. 

Accordingly,  most  thinkers  of  any  degree  of  sobriety  allow  that  an  hy- 
pothesis of  this  kind  is  not  to  be  received  as  probably  true  because  it  ac- 
counts for  all  the  known  phenomena;  since  this  is  a condition  sometimes 
fulfilled  tolerably  well  by  two  conflicting  hypotheses;  while  there  are  prob- 
ably many  others  which  are  equally  possible,  but  which,  for  want  of  any 
thing  analogous  in  our  experience,  our  minds  are  unfitted  to  conceive.  But 
it  seems  to  be  thought  that  an  hypothesis  of  the  sort  in  question  is  entitled 
to  a more  favorable  reception,  if,  besides  accounting  for  all  the  facts  previ- 
ously known,  it  has  led  to  the  anticipation  and  prediction  of  others  which 
experience  afterward  verified ; as  the  undulatory  theory  of  light  led  to  the 
prediction,  subsequently  realized  by  experiment,  that  two  luminous  rays 
might  meet  each  other  in  such"  a manner  as  to  produce  darkness.  Such 
predictions  and  their  fulfillment  are,  indeed,  well  calculated  to  impress  the 
uninformed,  whose  faith  in  science  rests  solely  on  similar  coincidences  be- 
tween its  prophecies  and  what  comes  to  pass.  But  it  is  strange  that  any 
considerable  stress  should  be  laid  upon  such  a coincidence  by  persons  of 
scientific  attainments.  If  the  laws  of  the  propagation  of  light  accord  with 
those  of  the  vibrations  of  an  elastic  fluid  in  as  many  respects  as  is  necessa- 
ry to  make  the  hypothesis  afford  a correct  expression  of  all  or  most  of  the 
phenomena  known  at  the  time,  it  is  nothing  strange  that  they  should  ac- 
cord with  each  other  in  one  respect  more.  Though  twenty  such  coinci- 
dences should  occur,  they  would  not  prove  the  reality  of  the  undulatory 
ether;  it  would  not  follow  that  the  phenomena  of  light  were  results  of  the 
laws  of  elastic  fluids,  but  at  most  that  they  are  governed  by  laws  partially 
identical  with  these ; which,  we  may  observe,  is  already  certain,  from  the 
fact  that  the  hypothesis  in  question  could  be  for  a moment  tenable,* 
Cases  may  be  cited,  even  in  our  imperfect  acquaintance  with  nature,  where 
agencies  that  we  have  good  reason  to  consider  as  radically  distinct  produce 
their  effects,  or  some  of  their  effects,  according  to  laws  which  are  identical. 
The  law,  for  example,  of  the  inverse  square  of  the  distance,  is  the  measure 
of  the  intensity  not  only  of  gravitation,  but  (it  is  believed)  of  illumination, 
and  of  heat  diffused  from  a centre.  Yet  no  one  looks  upon  this  identity 
as  proving  similarity  in  the  mechanism  by  which  the  three  kinds  of  phe- 
nomena are  produced. 

According  to  Dr.  Whewell,  the  coincidence  of  results  predicted  from  an 
hypothesis  with  facts  afterward  observed,  amounts  to  a conclusive  proof 
of  the  truth  of  the  theory.  “ If  I copy  a long  series  of  letters,  of  which 
the  last  half-dozen  are  concealed,  and  if  I guess  these  aright,  as  is  found 
to  be  the  case  when  they  are  afterward  uncovered,  thjs  must  be  because  I 
have  made  out  the  import  of  the  inscription.  To  say  that  because  I have 

* What  has  most  contributed  to  accredit  the  hypothesis  of  a physical  medium  for  the  con- 
veyance of  light,  is  the  certain  fact  that  light  travels  (which  can  not  be  proved  of  gravita- 
tion) ; that  its  communication  is  not  instantaneous,  but  requires  time ; and  that  it  is  intercepted 
(which  gravitation  is  not)  by  intervening  objects.  These  are  analogies  between  its  phenome- 
na and  those  of  the  mechanical  motion  of  a solid  or  fluid  substance.  But  we  are  not  entitled 
to  assume  that  mechanical  motion  is  the  only  power  in  nature  capable  of  exhibiting  those  at- 
tributes. 


HYPOTHESES. 


357 


copied  all  that  I could  see,  it  is  nothing  strange  that  I should  guess  those 
which  I can  not  see,  would  be  absurd,  without  supposing  such  a ground  for 
guessing.”*  If  any  one,  from  examining  the  greater  part  of  a long  inscrip- 
tion, can  interpret  the  characters  so  that  the  inscription  gives  a rational 
meaning  in  a known  language,  there  is  a strong  presumption  that  his  inter- 
pretation is  correct ; but  I do  not  think  the  presumption  much  increased 
by  his  being  able  to  guess  the  few  remaining  letters  without  seeing  them ; 
for  we  should  naturally  expect  (when  the  nature  of  the  case  excludes 
chance)  that  even  an  erroneous  interpretation  which  accorded  with  all  the 
visible  parts  of  the  inscription  would  accord  also  with  the  small  remain- 
der ; as  would  be  the  case,  for  example,  if  the  inscription  had  been  design- 
edly so  contrived  as  to  admit  of  a double  sense.  I assume  that  the  uncov- 
ered characters  afford  an  amount  of  coincidence  too  great  to  be  merely 
casual;  otherwise  the  illustration  is  not  a fair  one.  No  one  supposes 
the  agreement  of  the  phenomena  of  light  with  the  theory  of  undulations 
to  be  merely  fortuitous.  It  must  arise  from  the  actual  identity  of  some 
of  the  laws  of  undulations  with  some  of  those  of  light;  and  if  there  be 
that  identity,  it  is  reasonable  to  suppose  that  its  consequences  would  not 
end  with  the  phenomena  which  first  suggested  the  identification,  nor  be 
even  confined  to  such  phenomena  as  were  known  at  the  time.  But  it  does 
not  follow,  because  some  of  the  laws  agree  with  those  of  undulations,  that 
there  are  any  actual  undulations ; no  more  than  it  followed  because  some 
(though  not  so  many)  of  the  same  laws  agreed  with  those  of  the  projection 
of  particles,  that  there  was  actual  emission  of  particles.  Even  the  undula- 
tory  hypothesis  does  not  account  for  all  the  phenomena  of  light.  The  nat- 
ural colors  of  objects,  the  compound  nature  of  the  solar  ray,  the  absorption 
of  light,  and  its  chemical  and  vital  action,  the  hypothesis  leaves  as  myste- 
rious as  it  found  them  ; and  some  of  these  facts  are,  at  least  apparently, 
more  reconcilable  with  the  emission  theory  than  with  that  of  Young  and 
Fresnel.  Who  knows  but  that  some  third  hypothesis,  including  all  these 
phenomena,  may  in  time  leave  the  undulatory  theory  as  far  behind  as  that 
has  left  the  theory  of  Newton  and  his  successors? 

To  the  statement,  that  the  condition  of  accounting  for  all  the  known 
phenomena  is  often  fulfilled  equally  well  by  two  conflicting  hypotheses, 
Dr.  Whewell  makes  answer  that  he  knows  “of  no  such  case  in  the  history 
of  science,  where  the  phenomena  are  at  all  numerous  and  complicated.”f 
Such  an  atfirmation,  by  a writer  of  Dr.  Whewell’s  minute  acquaintance  with 
the  history  of  science,  would  carry  great  authority,  if  he  had  not,  a few 
pages  before,  taken  pains  to  refute  it, J by  maintaining  that  even  the  ex- 
ploded scientific  hypotheses  might  always,  or  almost  always,  have  been  so 
modified  as  to  make  them  correct  representations  of  the  phenomena.  The 
hypothesis  of  vortices,  he  tells  us,  was,  by  successive  modifications,  brought 
to  coincide  in  its  results  with  the  Newtonian  theory  and  with  the  facts. 
The  vortices  did  not,  indeed,  explain  all  the  phenomena  which  the  Newto- 
nian theory  was  ultimately  found  to  account  for,  such  as  the  precession  of 
the  equinoxes;  but  this  phenomenon  was  not,  at  the  time,  in  the  contem- 
plation of  either  party,  as  one  of  the  facts  to  be  accounted  for.  All  the 
facts  which  they  did  contemplate,  we  may  believe  on  Dr.  Whewell’s  au- 
thority to  have  accorded  as  accurately  with  the  Cartesian  hypothesis,  in  its 
finally  improved  state,  as  with  Newton’s. 

But  it  is  not,  I conceive,  a valid  reason  for  accepting  any  given  hypothe- 


Phil.  of  Discovery , p.  274. 


tP.  271. 


t P.  251  and  the  whole  of  Appendix  G. 


358 


INDUCTION. 


sis,  that  we  are  unable  to  imagine  any  other  which  will  account  for  the 
facts.  There  is  no  necessity  for  supposing  that  the  true  explanation  must 
be  one  which,  with  only  our  present  experience,  we  could  imagine.  Among 
the  natural  agents  with  which  we  are  acquainted,  the  vibrations  of  an  elas- 
tic fluid  may  be  the  only  one  whose  laws  bear  a close  resemblance  to  those 
of  light;  but  we  can  not  tell  that  there  does  not  exist  an  unknown  cause, 
other  than  an  elastic  ether  diffused  through  space,  yet  producing  effects 
identical  in  some  respects  with  those  which  would  result  from  the  undula- 
tions of  such  an  ether.  To  assume  that  no  such  cause  can  exist,  appears  to 
me  an  extreme  case  of  assumption  without  evidence.  And  at  the  risk  of 
being  charged  with  want  of  modesty,  I can  not  help  expressing  astonish- 
ment that  a philosopher  of  Dr.  Whewell’s  abilities  and  attainments  should 
have  written  an  elaborate  treatise  on  the  philosophy  of  induction,  in  which 
he  recognizes  absolutely  no  mode  of  induction  except  that  of  trying  hy- 
pothesis after  hypothesis  until  one  is  found  which  fits  the  phenomena; 
which  one,  when  found,  is  to  be  assumed  as  true,  with  no  other  reservation 
than  that  if,  on  re-examination,  it  should  appear  to  assume  more  than  is 
needful  for  explaining  the  phenomena,  the  superfluous  part  of  the  assump- 
tion should  be  cut  off.  And  this  without  the  slightest  distinction  between 
the  cases  in  which  it  may  be  known  beforehand  that  two  different  hypoth- 
eses can  not  lead  to  the  same  result,  and  those  in  which,  for  aught  we  can 
ever  know,  the  range  of  suppositions,  all  equally  consistent  with  the  phe- 
nomena, may  be  infinite.* 

Nevertheless,  I do  not  agree  with  M.  Comte  in  condemning  those  who 
employ  themselves  in  working  out  into  detail  the  application  of  these  hy- 
potheses to  the  explanation  of  ascertained  facts,  provided  they  bear  in 
mind  that  the  utmost  they  can  prove  is,  not  that  the  hypothesis  is,  but  that 
it  may  be  true.  The  ether  hypothesis  has  a very  strong  claim  to  be  so  fol- 
lowed out,  a claim  greatly  strengthened  since  it  has  been  shown  to  afford 
a mechanism  which  would  explain  the  mode  of  production,  not  of  light 
only,  but  also  of  heat.  Indeed,  the  speculation  has  a smaller  element  of 
hypothesis  in  its  application  to  heat,  than  in  the  case  for  which  it  was 
originally  framed.  We  have  proof  by  our  senses  of  the  existence  of  molec- 
ular movement  among  the  particles  of  all  heated  bodies;  while  we  have  no 
similar  experience  in  the  case  of  light.  When,  therefore,  heat  is  communi- 
cated from  the  sun  to  the  earth  across  apparently  empty  space,  the  chain 

* In  Dr.  Whewell’s  latest  version  of  his  theory  ( Philosophy  of  Discovery , p.  331)  he  makes 
a concession  respecting  the  medium  of  the  transmission  of  light,  which,  taken  in  conjunction 
with  the  rest  of  his  doctrine  on  the  subject,  is  not,  I confess,  very  intelligible  to  me,  but  which 
goes  far  toward  removing,  if  it  does  not  actually  remove,  the  whole  of  the  difference  between 
us.  He  is  contending,  against  Sir  William  Hamilton,  that  all  matter  lias  weight.  Sir  Wil- 
liam, in  proof  of  the  contrary,  cited  the  luminiferous  ether,  and  the  calorific  and  electric  fluids, 
“which,”  he  said,  “we  can  neither  denude  of  their  character  of  substance,  nor  clothe  with 
the  attribute  of  weight.”  “To  which,”  continues  Dr.  Whewell,  “my  reply  is,  that  precisely 
because  I can  not  clothe  these  agents  with  the  attribute  of  Weight,  I do  denude  them  of  the 
character  of  Substance.  They  at;e  not  substances,  but  agencies.  These  Imponderable  Agents 
are  not  properly  called  Imponderable  Fluids.  This  I conceive  that  I have  proved.”  Noth- 
ing can  be  more  philosophical.  But  if  the  luminiferous  ether  is  not  matter,  and  fluid  matter, 
too,  what  is  the  meaning  of  its  undulations?  Can  an  agency  undulate?  Can  there  be  al- 
ternate motion  forward  and  backward  of  the  particles  of  an  agency  ? And  does  not  the  whole 
mathematical  theory  of  the  undulations  imply  them  to  be  material  ? Is  it  not  a series  of  de- 
ductions from  the  known  properties  of  elastic  fluids  ? This  opinion  of  Dr.  Whewell  reduces 
the  undulations  to  a figure  of  speech,  and  the  undulatory  theory  to  the  proposition  which  all 
must  admit,  that  the  transmission  of  light  takes  place  according  to  laws  which  present  a very 
striking  and  remarkable  agreement  with  those  of  undulations.  If  Dr.  Whewell  is  prepared 
to  stand  by  this  doctrine,  I have  no  difference  with  him  on  the  subject. 


HYPOTHESES. 


359 


of  causation  has  molecular  motion  both  at  the  beginning  and  end.  The 
hypothesis  only  makes  the  motion  continuous  by  extending  it  to  the  mid- 
dle. Now,  motion  in  a body  is  known  to  be  capable  of  being  imparted  tc 
another  body  contiguous  to  it ; and  the  intervention  of  a hypothetical  elas- 
tic fluid  occupying  the  space  between  the  sun  and  the  earth,  supplies  the 
contiguity  which  is  the  only  condition  wanting,  and  which  can  be  supplied 
by  no  supposition  but  that  of  an  intervening  medium.  The  supposition, 
notwithstanding,  is  at  best  a probable  conjecture,  not  a proved  truth.  For 
there  is  no  proof  that  contiguity  is  absolutely  required  for  the  communica- 
tion of  motion  from  one  body  to  another.  Contiguity  does  not  always  ex- 
ist, to  our  senses  at  least,  in  the  cases  in  which  motion  produces  motion. 
The  forces  which  go  under  the  name  of  attraction,  especially  the  greatest 
of  all,  gravitation,  are  examples  of  motion  producing  motion  without  ap- 
parent contiguity.  When  a planet  moves,  its  distant  satellites  accompany 
its  motion.  The  sun  carries  the  whole  solar  system  along  with  it  in  the 
progress  which  it  is  ascertained  to  be  executing  through  space.  And  even 
if  we  were  to  accept  as  conclusive  the  geometrical  reasonings  (strikingly 
similar  to  those  by  which  the  Cartesians  defended  their  vortices)  by  which 
it  has  been  attempted  to  show  that  the  motions  of  the  ether  may  account 
for  gravitation  itself,  even  then  it  would  only  have  been  proved  that  the 
supposed  mode  of  production  may  be,  but  not  that  no  other  mode  can  be, 
the  true  one. 

§ 7.  It  is  necessary,  before  quitting  the  subject  of  hypotheses,  to  guard 
against  the  appearance  of  reflecting  upon  the  scientific  value  of  several 
branches  of  physical  inquiry,  which,  though  only  in  their  infancy,  I hold  to 
be  strictly  inductive.  There  is  a great  difference  between  inventing  agen- 
cies to  account  for  classes  of  phenomena,  and  endeavoring,  in  conformity 
with  known  laws,  to  conjecture  what  former  collocations  of  known  agents 
may  have  given  birth  to  individual  facts  still  in  existence.  The  latter  is 
the  legitimate  operation  of  inferring  from  an  observed  effect  the  existence, 
in  time  past,  of  a cause  similar  to  that  by  which  we  know  it  to  be  produced 
in  all  cases  in  which  we  have  actual  experience  of  its  origin.  This,  for  ex- 
ample, is  the  scope  of  the  inquiries  of  geology  ; and  they  are  no  more  illogic- 
al or  visionary  than  judicial  inquiries,  which  also  aim  at  discovering  a past 
event  by  inference  from  those  of  its  effects  which  still  subsist.  As  we  can 
ascertain  whether  a man  was  murdered  or  died  a natural  death,  from  the 
indications  exhibited  by  the  corpse,  the  presence  or  absence  of  signs  of 
struggling  on  the  ground  or  on  the  adjacent  objects,  the  marks  of  blood, 
the  footsteps  of  the  supposed  murderers,  and  so  on,  proceeding  throughout 
on  uniformities  ascertained  by  a perfect  induction  without  any  mixture  of 
hypothesis  ; so  if  we  find,  on  and  beneath  the  surface  of  our  planet,  masses 
exactly  similar  to  deposits  from  water,  or  to  results  of  the  cooling  of  mat- 
ter melted  by  fire,  we  may  justly  conclude  that  such  has  been  their  origin  ; 
and  if  the  effects,  though  similar  in  kind,  are  on  a far  larger  scale  than  any 
which  are  now  produced,  we  may  rationally,  and  without  hypothesis,  con- 
clude either  that  the  causes  existed  formerly  with  greater  intensity,  or  that 
they  have  operated  during  an  enormous  length  of  time.  Further  than  this 
no  geologist  of  authority  has,  since  the  rise  of  the  present  enlightened 
school  of  geological  speculation,  attempted  to  go. 

In  many  geological  inquiries  it  doubtless  happens  that  though  the  laws 
to  which  the  phenomena  are  ascribed  are  known  laws,  and  the  agents 
known  agents,  those  agents  are  not  known  to  have  been  present  in  the  par- 


360 


INDUCTION. 


ticulav  case.  In  the  speculation  respecting  the  igneous  origin  of  trap  or 
granite,  the  fact  does  not  admit  of  direct  proof  that  those  substances  have 
been  actually  subjected  to  intense  heat.  But  the  same  thing  might  be  said 
of  all  judicial  inquiries  which  proceed  on  circumstantial  evidence.  We  can 
conclude  that  a man  was  murdered,  though  it  is  not  proved  by  the  testimony 
of  eye-witnesses  that  some  person  who  had  the  intention  of  murdering  him 
was  present  on  the  spot.  It  is  enough  for  most  purposes,  if  no  other  known 
cause  could  have  generated  the  effects  shown  to  have  been  produced. 

The  celebrated  speculation  of  Laplace  concerning  the  origin  of  the  earth 
and  planets,  participates  essentially  in  the  inductive  character  of  modern 
geological  theory.  The  speculation  is,  that  the  atmosphere  of  the  sun 
originally  extended  to  the  present  limits  of  the  solar  system;  from  which, 
by  the  process  of  cooling,  it  has  contracted  to  its  present  dimensions ; and 
since,  by  the  general  principles  of  mechanics  the  rotation  of  the  sun  and 
of  its  accompanying  atmosphere  must  increase  in  rapidity  as  its  volume 
diminishes,  the  increased  centrifugal  force  generated  by  the  more  rapid 
rotation,  overbalancing  the  action  of  gravitation,  has  caused  the  sun  to 
abandon  successive  rings  of  vaporous  matter,  which  are  supposed  to  have 
condensed  by  cooling,  and  to  have  become  the  planets.  There  is  in  this 
theory  no  unknown  substance  introduced  on  supposition,  nor  any  unknown 
property  or  law  ascribed  to  a known  substance.  The  known  laws  of  mat- 
ter authorize  us  to  suppose  that  a body  which  is  constantly  giving  out  so 
large  an  amount  of  heat  as  the  sun  is,  must  be  progressively  cooling,  and 
that,  by  the  process  of  cooling  it  must  contract;  if,  therefore,  we  endeavor, 
from  the  present  state  of  that  luminary,  to  infer  its  state  in  a time  long- 
past,  we  must  necessarily  suppose  that  its  atmosphere  extended  much  far- 
ther than  at  present,  and  we  are  entitled  to  suppose  that  it  extended  as  far 
as  we  can  trace  effects  such  as  it  might  naturally  leave  behind  it  on  retir- 
ing; and  such  the  planets  are.  These  suppositions  being  made,  it  follows 
from  known  laws  that  successive  zones  of  the  solar  atmosphere  might  be 
abandoned;  that  these  would  continue  to  revolve  round  the  sun  with  the 
same  velocity  as  when  they  formed  part  of  its  substance  ; and  that  they 
would  cool  down,  long  befoie  the  sun  itself,  to  any  given  temperature,  and 
consequently  to  that  at  which  the  greater  part  of  the  vaporous  matter  of 
which  they  consisted  would  become  liquid  or  solid.  The  known  law  of 
gravitation  would  then  cause  them  to  agglomerate  in  masses,  which  would 
assume  the  shape  our  planets  actually  exhibit;  would  acquire,  each  about 
its  own  axis, a rotatory  movement;  and  would  in  that  state  revolve,  as  the 
planets  actually  do,  about  the  sun,  in  the  same  direction  with  the  sun’s  ro- 
tation, but  with  less  velocity,  because  in  the  same  periodic  time  which  the 
sun’s  rotation  occupied  when  his  atmosphere  extended  to  that  point.  There 
is  thus,  in  Laplace’s  theory,  nothing,  strictly  speaking,  hypothetical ; it  is 
an  example  of  legitimate  reasoning  from  a present  effect  to  a possible  past 
cause,  according  to  the  known  laws  of  that  cause.  The  theory,  therefore, 
is,  as  I have  said,  of  a similar  character  to  the  theories  of  geologists  ; but 
considerably  inferior  to  them  in  point  of  evidence.  Even  if  it  were  proved 
(which  it  is  not)  that  the  conditions  necessary  for  determining  the  break- 
ing off  of  successive  rings  would  certainly  occur,  there  would  still  be  a 
much  greater  chance  of  error  in  assuming  that  the  existing  laws  of  nature 
are  the  same  which  existed  at  the  origin  of  the  solar  system,  than  in  mere- 
ly presuming  (with  geologists)  that  those  laws  have  lasted  through  a few 
revolutions  and  transformations  of  a single  one  among  the  bodies  of  which 
that  system  is  composed. 


PEOGEESSIVE  EEEECTS. 


361 


CHAPTER  XY. 

OP  PROGRESSIVE  EFFECTS  ; AND  OF  THE  CONTINUED  ACTION  OF  CAUSES. 

§ 1.  In  the  last  four  chapters  we  have  traced  the  general  outlines  of  the 
theory  of  the  generation  of  derivative  laws  from  ultimate  ones.  In  the 
present  chapter  our  attention  will  be  directed  to  a particular  case  of  the 
derivation  of  laws  from  other  laws,  but  a case  so  general,  and  so  important 
as  not  only  to  repay,  but  to  require,  a separate  examination.  This  is  the 
case  of  a complex  phenomenon  resulting  from  one  simple  law,  by  the  con- 
tinual addition  of  an  effect  to  itself. 

There  are  some  phenomena,  some  bodily  sensations,  for  example,  which 
are  essentially  instantaneous,  and  whose  existence  can  only  be  prolonged 
by  the  prolongation  of  the  existence  of  the  cause  by  which  they  are  pro- 
duced. But  most  phenomena  are  in  their  own  nature  permanent;  having 
begun  to  exist,  they  would  exist  forever  unless  some  cause  intervened  hav- 
ing a tendency  to  alter  or  destroy  them.  Such,  for  example,  are  all  the 
facts  of  phenomena  which  we  call  bodies.  Water,  once  produced,  will  not 
of  itself  relapse  into  a state  of  hydrogen  and  oxygen ; such  a change  re- 
quires some  agent  having  the  power  of  decomposing  the  compound.  Such, 
again,  are  the  positions  in  space  and  the  movements  of  bodies.  No  object 
at  rest  alters  its  position  without  the  intervention  of  some  conditions  ex- 
traneous to  itself;  and  when  once  in  motion,  no  object  returns  to  a state 
of  rest,  or  alters  either  its  direction  or  its  velocity,  unless  some  new  exter- 
nal conditions  are  superinduced.  It,  therefore,  perpetually  happens  that  a 
temporary  cause  gives  rise  to  a permanent  effect.  The  contact  of  iron 
with  moist  air  for  a few  hours,  produces  a rust  which  may  endure  for  cen- 
turies; or  a projectile  force  which  launches  a cannon-ball  into  space,  pro- 
duces a motion  which  would  continue  forever  unless  some  other  force 
counteracted  it. 

Between  the  two  examples  which  we  have  here  given,  there  is  a differ- 
ence worth  pointing  out.  In  the  former  (in  which  the  phenomenon  pro- 
duced is  a substance,  and  not  a motion  of  a substance),  since  the  rust  re- 
mains forever  and  unaltered  unless  some  new  cause  supervenes,  we  may 
speak  of  the  contact  of  air  a hundred  years  ago  as  even  the  proximate 
cause  of  the  rust  which  has  existed  from  that  time  until  now.  But  when 
the  effect  is  motion,  which  is  itself  a change,  we  must  use  a different  lan- 
guage. The  permanency  of  the  effect  is  now  only  the  permanency  of  a 
series  of  changes.  The  second  foot,  or  inch,  or  mile  of  motion  is  not  the 
mere  prolonged  duration  of  the  first  foot,  or  inch,  or  mile,  but  another  fact 
which  succeeds,  and  which  may  in  some  respects  be  very  unlike  the  former, 
since  it  carries  the  body  through  a different  region  of  space.  Now,  the 
original  projectile  force  which  set  the  body  moving  is  the  remote  cause  of 
all  its  motion,  however  long  continued,  but  the  proximate  cause  of  no  mo- 
tion except  that  which  took  place  at  the  first  instant.  The  motion  at  any 
subsequent  instant  is  proximately  caused  by  the  motion  which  took  place 
at  the  instant  preceding.  It  is  on  that,  and  not  on  the  original  moving 
cause,  that  the  motion  at  any  given  moment  depends.  For,  suppose  that 
the  body  passes  through  some  resisting  medium,  which  partially  counter- 


362 


INDUCTION. 


acts  the  effect  of  the  original  impulse,  and  retards  the  motion ; this  coun- 
teraction  (it  need  scarcely  here  be  repeated)  is  as  strict  an  example  of  obe- 
dience to  the  law  of  the  impulse,  as  if  the  body  had  gone  on  moving  with 
its  original  velocity;  but  the  motion  which  results  is  different,  being  now 
a compound  of  the  effects  of  two  causes  acting  in  contrary  directions,  in- 
stead of  the  single  effect  of  one  cause.  Now,  what  cause  does  the  body 
obey  in  its  subsequent  motion?  The  original  cause  of  motion,  or  the  act- 
ual motion  at  the  preceding  instant?  The  latter;  for  when  the  object 
issues  from  the  resisting  medium,  it  continues  moving,  not  with  its  orig- 
inal, but  with  its  retarded  velocity.  The  motion  having  once  been  dimin- 
ished, all  that  which  follows  is  diminished.  The  effect  changes,  because 
the  cause  which  it  really  obeys,  the  proximate  cause,  the  real  cause  in  fact, 
has  changed.  This  principle  is  recognized  by  mathematicians  when  they 
enumerate  among  the  causes  by  which  the  motion  of  a body  is  at  any  in- 
stant determined  the  force  generated  by  the  previous  motion ; an  expres- 
sion which  would  be  absurd  if  taken  to  imply  that  this  “ force  ” was  an  in- 
termediate link  between  the  cause  and  the  effect,  but  which  really  means 
only  the  previous  motion  itself,  considered  as  a cause  of  further  motion. 
We  must,  therefore,  if  we  would  speak  with  perfect  precision,  consider 
each  link  in  the  succession  of  motions  as  the  effect  of  the  link  preceding  it. 
But  if,  for  the  convenience  of  discourse,  we  speak  of  the  whole  series  as 
one  effect,  it  must  be  as  an  effect  produced  by  the  original  impelling  force ; 
a permanent  effect  produced  by  an  instantaneous  cause,  and  possessing  the 
property  of  self-perpetuation. 

Let  us  now  suppose  that  the  original  agent  or  cause,  instead  of  being  in- 
stantaneous, is  permanent.  Whatever  effect  has  been  produced  up  to  a 
given  time,  would  (unless  prevented  by  the  intervention  of  some  new  cause) 
subsist  permanently,  even  if  the  cause  were  to  perish.  Since,  however,  the 
cause  does  not  perish,  but  continues  to  exist  and  to  operate,  it  must  go  on 
producing  more  and  more  of  the  effect;  and  instead  of  a uniform  effect, 
we  have  a progressive  series  of  effects,  arising  from  the  accumulated  influ- 
ence  of  a permanent  cause.  Thus,  the  contact  of  iron  with  the  atmosphere 
causes  a portion  of  it  to  rust ; and  if  the  cause  ceased,  the  effect  already 
produced  would  be  permanent,  but  no  further  effect  would  be  added.  If, 
however,  the  cause,  namely,  exposure  to  moist  air,  continues,  more  and 
more  of  the  iron  becomes  rusted,  until  all  which  is  exposed  is  converted 
into  a red  powder,  when  one  of  the  conditions  of  the  production  of  rust, 
namely,  the  presence  of  unoxidized  iron,  has  ceased,  and  the  effect  can  not 
any  longer  be  produced.  Again,  the  earth  causes  bodies  to  fall  toward  it; 
that  is,  the  existence  of  the  earth  at  a given  instant  causes  an  unsupported 
body  to  move  toward  it  at  the  succeeding  instant ; and  if  the  earth  were 
annihilated,  as  much  of  the  effect  as  is  already  produced  would  continue; 
the  object  would  go  on  moving  in  the  same  direction,  with  its  acquired 
velocity,  until  intercepted  by  some  body  or  deflected  by  some  other  force. 
The  earth,  however,  not  being  annihilated,  goes  on  producing  in  the  sec- 
ond instant  an  effect  similar  and  of  equal  amount  with  the  first,  which  two 
effects  being  added  together,  there  results  an  accelerated  velocity ; and 
this  operation  being  repeated  at  each  successive  instant,  the  mere  perma- 
nence of  the  cause,  though  without  increase,  gives  rise  to  a constant  pro- 
gressive increase  of  the  effect,  so  long  as  all  the  conditions,  negative  and 
positive,  of  the  production  of  that  effect  continue  to  be  realized. 

It  is  obvious  that  this  state  of  things  is  merely  a case  of  the  Composi- 
tion of  Causes.  A cause  which  continues  in  action  must  on  a strict  analy- 


PROGRESSIVE  EFFECTS. 


363 


sis  be  considered  as  a number  of  causes  exactly  similar,  successively  intro- 
duced, and  producing  by  their  combination  the  sum  of  the  effects  which 
they  would  severally  produce  if  they  acted  singly.  The  progressive  rust- 
ing of  the  iron  is  in  strictness  the  sum  of  the  effects  of  many  particles  of 
air  acting  in  succession  upon  corresponding  particles  of  iron.  The  con- 
tinued action  of  the  earth  upon  a falling  body  is  equivalent  to  a series  of 
forces,  applied  in  successive  instants,  each  tending  to  produce  a certain  con- 
stant quantity  of  motion ; and  the  motion  at  each  instant  is  the  sum  of  the 
effects  of  the  new  force  applied  at  the  preceding  instant,  and  the  motion 
already  acquired.  In  each  instant  a fresh  effect,  of  which  gravity  is  the 
proximate  cause,  is  added  to  the  effect  of  which  it  was  the  remote  cause; 
or  (to  express  the  same  thing  in  another  manner),  the  effect  produced  by 
the  earth’s  influence  at  the  instant  last  elapsed  is  added  to  the  sum  of  the 
effects  of  which  the  remote  causes  were  the  influences  exerted  by  the  earth 
at  all  the  previous  instants  since  the  motion  began.  The  case,  therefore, 
comes  under  the  principle  of  a concurrence  of  causes  producing  an  effect 
equal  to  the  sum  of  their  separate  effects.  But  as  the  causes  come  into 
play  not  all  at  once,  but  successively,  and  as  the  effect  at  each  instant  is  the 
sum  of  the  effects  of  those  causes  only  which  have  come  into  action  up  to 
that  instant,  the  result  assumes  the  form  of  an  ascending  series;  a succes- 
sion of  sums,  each  greater  than  that  which  preceded  it;  and  we  have  thus 
a progressive  effect  from  the  continued  action  of  a cause. 

Since  the  continuance  of  the  cause  influences  the  effect  only  by  adding 
to  its  quantity,  and  since  the  addition  takes  place  according  to  a fixed  law 
(equal  quantities  in  equal  times),  the  result  is  capable  of  being  computed 
on  mathematical  principles.  In  fact,  this  case,  being  that  of  infinitesimal 
increments,  is  precisely  the  case  which  the  differential  calculus  was  invent- 
ed to  meet.  The  questions,  what  effect  will  result  from  the  continual  ad- 
dition of  a given  cause  to  itself,  and  what  amount  of  the  cause,  being  con- 
tinually added  to  itself,  will  produce  a given  amount  of  the  effect,  are  evi- 
dently mathematical  questions,  and  to  be  treated,  therefore,  deductively. 
If,  as  we  have  seen,  cases  of  the  Composition  of  Causes  are  seldom  adapt- 
ed for  any  other  than  deductive  investigation,  this  is  especially  true  in  the 
case  now  examined,  the  continual  composition  of  a cause  with  its  own  pre- 
vious effects;  since  such  a case  is  peculiarly  amenable  to  the  deductive 
method,  while  the  undistinguishable  manner  in  which  the  effects  are  blend- 
ed with  one  another  and  with  the  causes,  must  make  the  treatment  of  such 
an  instance  experimentally  still  more  chimerical  than  in  any  other  case. 

§ 2.  We  shall  next  advert  to  a rather  more  intricate  operation  of  the 
same  principle,  namely,  when  the  cause  does  not  merely  continue  in  action, 
but  undergoes,  during  the  same  time,  a progressive  change  in  those  of  its 
circumstances  which  contribute  to  determine  the  effect.  In  this  case,  as 
in  the  former,  the  total  effect  goes  on  accumulating  by  the  continual  addi- 
tion of  a fresh  effect  to  that  already  produced,  but  it  is  no  longer  by  the 
addition  of  equal  quantities  in  equal  times;  the  quantities  added  are  un- 
equal, and  even  the  quality  may  now  be  different.  If  the  change  in  the 
state  of  the  permanent  cause  be  progressive,  the  effect  will  go  through  a 
double  series  of  changes,  arising  partly  from  the  accumulated  action  of  the 
cause,  and  partly  from  t he  changes  in  its  action.  The  effect  is  still  a pro- 
gressive effect,  produced,  however,  not  by  the  mere  continuance  of  a cause, 
but  by  its  continuance  and  its  progressiveness  combined. 

A familiar  example  is  afforded  by  the  increase  of  the  temperature  as 


364 


INDUCTION. 


summer  advances,  that  is,  as  the  sun  draws  nearer  to  a vertical  position,  and 
remains  a greater  number  of  hours  above  the  horizon.  This  instance  ex- 
emplifies in  a very  interesting  manner  the  twofold  operation  on  the  effect, 
arising  from  the  continuance  of  the  cause,  and  from  its  progressive  change. 
When  once  the  sun  has  come  near  enough  to  the  zenith,  and  remains  above 
the  horizon  long  enough,  to  give  more  warmth  during  one  diurnal  rotation 
than  the  counteracting  cause,  the  earth’s  radiation,  can  carry  off,  the  mere 
continuance  of  the  cause  would  progressively  increase  the  effect,  even  if  the 
sun  came  no  nearer  and  the  days  grew  no  longer;  but  in  addition  to  this, 
a change  takes  place  in  the  accidents  of  the  cause  (its  series  of  diurnal  po- 
sitions), tending  to  increase  the  quantity  of  the  effect.  When  the  summer 
solstice  has  passed,  the  progressive  change  in  the  cause  begins  to  take  place 
the  reverse  way,  but,  for  some  time,  the  accumulating  effect  of  the  mere 
continuance  of  the  cause  exceeds  the  effect  of  the  changes  in  it,  and  the 
temperature  continues  to  increase. 

Again,  the  motion  of  a planet  is  a progressive  effect,  produced  by  causes 
at  once  permanent  and  progressive.  The  orbit  of  a planet  is  determined 
(omitting  perturbations)  by  two  causes : first,  the  action  of  the  central  body, 
a permanent  cause,  which  alternately  increases  and  diminishes  as  the  planet 
draws  nearer  to  or  goes  farther  from  its  perihelion,  and  which  acts  at  every 
point  in  a different  direction  ; and,  secondly,  the  tendency  of  the  planet  to 
continue  moving  in  the  direction  and  with  the  velocity  which  it  has  already 
acquired.  This  force  also  grows  greater  as  the  planet  draws  nearer  to  its 
perihelion,  because  as  it  does  so  its  velocity  increases,  and  less,  as  it  recedes 
from  its  perihelion ; and  this  force  as  well  as  the  other  acts  at  each  point  in 
a different  direction,  because  at  every  point  the  action  of  the  central  force, 
by  deflecting  the  planet  from  its  previous  direction,  alters  the  line  in  which 
it  tends  to  continue  moving.  The  motion  at  each  instant  is  determined  by 
the  amount  and  direction  of  the  motion,  and  the  amount  and  direction  of 
the  sun’s  action,  at  the  previous  instant;  and  if  we  speak  of  the  entire  rev- 
olution of  the  planet  as  one  phenomenon  (which,  as  it  is  periodical  and 
similar  to  itself,  we  often  find  it  convenient  to  do),  that  phenomenon  is  the 
progressive  effect  of  two  permanent  and  progressive  causes,  the  central 
force  and  the  acquired  motion.  Those  causes  happening  to  be  progressive 
in  the  particular  way  which  is  called  periodical,  the  effect  necessarily  is  so 
too ; because  the  quantities  to  be  added  together  returning  in  a regular 
order,  the  same  sums  must  also  regularly  return. 

This  example  is  worthy  of  consideration  also  in  another  respect.  Though 
the  causes  themselves  are  permanent,  and  independent  of  all  conditions 
known  to  us,  the  changes  which  take  place  in  the  quantities  and  relations 
of  the  causes  are  actually  caused  by  the  periodical  changes  in  the  effects. 
The  causes,  as  they  exist  at  any  moment,  having  produced  a certain  motion, 
that  motion,  becoming  itself  a cause,  reacts  upon  the  causes,  and  produces 
a change  in  them.  By  altering  the  distance  and  direction  of  the  central 
body  relatively  to  the  planet,  and  the  direction  and  quantity  of  the  force  in 
the  direction  of  the  tangent,  it  alters  the  elements  which  determine  the  mo- 
tion at  the  next  succeeding  instant.  This  change  renders  the  next  motion 
somewhat  different;  and  this  difference, by  afresh  reaction  upon  the  causes, 
renders  the  next  motion  again  different,  and  so  on.  The  original  state  of 
the  causes  might  have  been  such  that  this  series  of  actions  modified  by 
reactions  would  not  have  been  periodical.  The  sun’s  action,  and  the  origi- 
nal impelling  force,  might  have  been  in  such  a ratio  to  one  another,  that  the 
reaction  of  the  effect  would  have  been  such  as  to  alter  the  causes  more  and 


PROGRESSIVE  EFFECTS, 


365 


more,  without  ever  bringing  them  back  to  what  they  were  at  any  former 
time.  The  planet  would  then  have  moved  in  a parabola,  or  an  hyperbola, 
curves  not  returning  into  themselves.  The  quantities  of  the  two  forces  were, 
however,  originally  such,  that  the  successive  reactions  of  the  effect  bring  back 
the  causes,  after  a certain  time,  to  what  they  were  before;  and  from  that  time 
all  the  variations  continued  to  recur  again  and  again  in  the  same  periodical 
order,  and  must  so  continue  while  the  causes  subsist  and  are  not  counteracted. 

§ 3.  In  all  cases  of  progressive  effects,  whether  arising  from  the  accumu- 
lation of  unchanging  or  of  changing  elements,  there  is  a uniformity  of  suc- 
cession not  merely  between  the  cause  and  the  effect,  but  between  the  first 
stages  of  the  effect  and  its  subsequent  stages.  That  a body  in  vacuo  falls 
sixteen  feet  in  the  first  second,  forty-eight  in  the  second,  and  so  on  in  the 
ratio  of  the  odd  numbers,  is  as  much  a uniform  sequence  as  that  when  the 
supports  are  removed  the  body  falls.  The  sequence  of  spring  and  summer 
is  as  regular  and  invariable  as  that  of  the  approach  of  the>  sun  and  spring; 
but  we  do  not  consider  spring  to  be  the  cause  of  summer;  it  is  evident 
that  both  are  successive  effects  of  the  heat  received  from  the  sun,  and  that, 
considered  merely  in  itself,  spring  might  continue  forever  without  having  the 
slightest  tendency  to  produce  summer.  As  we  have  so  often  remarked,  not 
the  conditional,  but  the  unconditional  invariable  antecedent  is  termed  the 
cause.  That  which  would  not  be  followed  by  the  effect  unless  something 
else  had  preceded,  and  which  if  that  somethng  else  had  preceded,  would 
not  have  been  required,  is  not  the  cause,  however  invariable  the  sequence 
may  in  fact  be. 

It  is  in  this  way  that  most  of  those  uniformities  of  succession  are  gen- 
erated, which  are  not  cases  of  causation.  When  a phenomenon  goes  on 
increasing,  or  periodically  increases  and  diminishes,  or  goes  through  any 
continued  and  unceasing  process  of  variation  reducible  to  a uniform  rule 
or  law  of  succession,  we  do  not  on  this  account  presume  that  any  two  suc- 
cessive terms  of  the  series  are  cause  and  effect.  We  presume  the  contrary; 
we  expect  to  find  that  the  whole  series  originates  either  from  the  continued 
action  of  fixed  causes  or  from  causes  which  go  through  a corresponding  proc- 
ess of  continuous  change.  A tree  grows  from  half  an  inch  high  to  a hun- 
dred feet;  and  some  trees  will  generally  grow  to  that  height  unless  pre- 
vented  by  some  counteracting  cause.  But  we  do  not  call  the  seedling  the 
cause  of  the  full-grown  tree;  the  invariable  antecedent  it  certainly  is,  and 
we  know  very  imperfectly  on  what  other  antecedents  the  sequence  is  contin- 
gent, but  we  are  convinced  that  it  is  contingent  on  something ; because  the 
homogeneousness  of  the  antecedent  with  the  consequent,  the  close  resem- 
blance of  the  seedling  to  the  tree  in  all  respects  except  magnitude,  and  the 
graduality  of  the  growth,  so  exactly  resembling  the  progressively  accumu- 
lating effect  produced  by  the  long  action  of  some  one  cause,  leave  no  possi- 
bility of  doubting  that  the  seedling  and  the  tree  are  two  terms  in  a series 
of  that  description,  the  first  term  of  which  is  yet  to  seek.  The  conclusion 
is  further  confirmed  by  this,  that  we  are  able  to  prove  by  strict  induction 
the  dependence  of  the  growth  of  the  tree,  and  even  of  the  continuance  of 
its  existence,  upon  the  continued  repetition  of  certain  processes  of  nutri- 
tion, the  rise  of  the  sap,  the  absorptions  and  exhalations  by  the  leaves,  etc. ; 
and  the  same  experiments  would  probably  prove  to  us  that  the  growth  of 
the  tree  is  the  accumulated  sum  of  the  effects  of  these  continued  processes, 
were  we  not,  for  want  of  sufficiently  microscopic  eyes,  unable  to  observe 
correctly  and  in  detail  what  those  effects  are„ 


366 


INDUCTION. 


This  supposition  by  no  means  requires  that  the  effect  should  not,  during 
its  progress,  undergo  many  modifications  besides  those  of  quantity,  or  that 
it  should  not  sometimes  appear  to  undergo  a very  marked  change  of  char- 
acter. This  may  be  either  because  the  unknown  cause  consists  of  several 
component  elements  or  agents,  whose  effects,  accumulating  according  to 
different  laws,  are  compounded  in  different  proportions  at  different  periods 
in  the  existence  of  the  organized  being;  or  because,  at  certain  points  in  its 
progress,  fresh  causes  or  agencies  come  in,  or  are  evolved,  which  intermix 
their  laws  with  those  of  the  prime  agent. 


CHAPTER  XYI. 

OF  EMPIRICAL  L A AV  S . 

§ 1.  Scientific  inquirers  give  the  name  of  Empirical  Laivs  to  those 
uniformities  which  observation  or  experiment  has  shown  to  exist,  but  on 
which  they  hesitate  to  rely  in  cases  varying  much  from  those  which  have 
been  actually  observed,  for  want  of  seeing  any  reason  why  such  a law 
should  exist.  It  is  implied,  therefore,  in  the  notion  of  an  empirical  law, 
that  it  is  not  an  ultimate  law;  that  if  true  at  all,  its  truth  is  capable  of 
being,  and  requires  to  be,  accounted  for.  It  is  a derivative  law,  the  deriva- 
tion of  which  is  not  yet  known.  To  state  the  explanation,  the  why,  of  the 
empirical  latv,  would  be  to  state  the  laws  from  which  it  is  derived— -the 
ultimate  causes  on  which  it  is  contingent.  And  if  we  knew  these,  we 
should  also  know  what  are  its  limits ; under  what  conditions  it  would  cease 
to  be  fulfilled. 

The  periodical  return  of  eclipses,  as  originally  ascertained  by  the  perse- 
vering observation  of  the  early  Eastern  astronomers,  was  an  empirical  law, 
until  the  general  laws  of  the  celestial  motions  had  accounted  for  it.  The 
following  are  empirical  laws  still  Avaiting  to  be  resolved  into  the  simpler 
laws  from  which  they  are  derived:  the  local  laws  of  the  flux  and  reflux 
of  the  tides  in  different  places;  the  succession  of  certain  kinds  of  weather 
to  certain  appearances  of  sky ; the  apparent  exceptions  to  the  almost  uni- 
versal truth  that  bodies  expand  by  increase  of  temperature;  the  law  that 
breeds,  both  animal  and  vegetable,  are  improved  by  crossing;  that  gases 
have  a strong  tendency  to  permeate  animal  membranes ; that  substances 
containing  a very  high  proportion  of  nitrogen  (such  as  hydrocyanic  acid 
and  morphia)  are  powerful  poisons;  that  when  different  metals  are  fused 
together  the  alloy  is  harder  than  the  various  elements;  that  the  number  of 
atoms  of  acid  required  to  neutralize  one  atom  of  any  base  is  equal  to  the 
number  of  atoms  of  oxygen  in  the  base;  that  the  solubility  of  substances 
in  one  another  depends,*  at  least  in  some  degree,  on  the  similarity  of 
their  elements. 

An  empirical  law,  then,  is  an  observed  uniformity,  presumed  to  be  re- 

* Thus  water,  of  which  eight-ninths  in  weight  are  oxygen,  dissolves  most  bodies  which 
contain  a high  proportion  of  oxygen,  such  as  all  the  nitrates  (which  have  more  oxygen  than 
any  others  of  the  common  salts),  most  of  the  sulphates,  many  of  the  carbonates,  etc.  Again, 
bodies  largely  composed  of  combustible  elements,  like  hydrogen  and  carbon,  are  soluble  in 
bodies  of  similar  composition  ; resin,  for  instance,  will  dissolve  in  alcohol,  tar  in  oil  of  turpen- 
tine. This  empirical  generalization  is  far  from  being  universally  true ; no  doubt  because  it  is 
a remote,  and  therefore  easily  defeated,  result  of  general  laws  too  deep  for  us  at  present  to 
penetrate ; but  it  will  probably  in  time  suggest  processes  of  inquiry,  leading  to  the  discovery 
of  those  laws. 


EMPIRICAL  LAWS. 


367 


solvable  into  simpler  laws,  but  not  yet  resolved  into  them.  The  ascertain- 
ment of  the  empirical  laws  of  phenomena  often  precedes  by  a long  interval 
the  explanation  of  those  laws  by  the  Deductive  Method ; and  the  verifica- 
tion of  a deduction  usually  consists  in  the  comparison  of  its  results  with 
empirical  laws  previously  ascertained. 

§ 2.  From  a limited  number  of  ultimate  laws  of  causation,  there  are 
necessarily  generated  a vast  number  of  derivative  uniformities,  both  of 
succession  and  co-existence.  Some  are  laws  of  succession  or  of  co-existence 
between  different  effects  of  the  same  cause;  of  these  we  had  examples  in 
the  last  chapter.  Some  are  laws  of  succession  between  effects  and  their 
remote  causes,  resolvable  into  the  laws  which  connect  each  with  the  in- 
termediate link.  Thirdly,  when  causes  act  together  and  compound  their 
effects,  the  laws  of  those  causes  generate  the  fundamental  law  of  the  effect, 
namely,  that  it  depends  on  the  co-existence  of  those  causes.  And,  finally, 
the  order  of  succession  or  of  co-existence  which  obtains  among  effects 
necessarily  depends  on  their  causes.  If  they  are  effects  of  the  same  cause, 
it  depends  on  the  laws  of  that  cause;  if  on  different  causes,  it  depends  on 
the  laws  of  those  causes  severally,  and  on  the  circumstances  which  deter- 
mine their  co-existence.  If  we  inquire  further  when  and  how  the  causes 
will  co-exist,  that,  again,  depends  on  their  causes ; and  we  may  thus  trace 
back  the  phenomena  higher  and  higher,  until  the  different  series  of  effects 
meet  in  a point,  and  the  whole  is  shown  to  have  depended  ultimately  on 
some  common  cause;  or  until,  instead  of  converging  to  one  point,  they  ter- 
minate in  different  points,  and  the  order  of  the  effects  is  proved  to  have 
arisen  from  the  collocation  of  some  of  the  primeval  causes,  or  natural 
agents.  For  example,  the  order  of  succession  and  of  co-existence  among 
the  heavenly  motions,  which  is  expressed  by  Kepler’s  laws,  is  derived  from 
the  co-existence  of  two  primeval  causes,  the  sun,  and  the  original  impulse 
or  projectile  force  belonging  to  each  planet.*  Kepler’s  laws  are  resolved 
into  the  laws  of  these  causes  and  the  fact  of  their  co  existence. 

Derivative  laws,  therefore,  do  not  depend  solely  on  the  ultimate  laws  into 
which  they  are  resolvable ; they  mostly  depend  on  those  ultimate  laws,  and 
an  ultimate  fact ; namely,  the  mode  of  co-existence  of  some  of  the  component 
elements  of  the  universe.  The  ultimate  laws  of  causation  might  be  the 
same  as  at  present,  and  yet  the  derivative  laws  completely  different,  if  the 
causes  co-existed  in  different  proportions,  or  with  any  difference  in  those 
of  their  relations  by  which  the  effects  are  influenced.  If,  for  example,  the 
sun’s  attraction,  and  the  original  projectile  force,  had  existed  in  some  oth- 
er ratio  to  one  another  than  they  did  (and  we  know  of  no  reason  why  this 
should  not  have  been  the  case),  the  derivative  laws  of  the  heavenly  motions 
might  have  been  quite  different  from  what  they  are.  The  proportions 
which  exist  happen  to  be  such  as  to  produce  regular  elliptical  motions ; 
any  other  proportions  would  have  produced  different  ellipses,  or  circular, 
or  parabolic,  or  hyperbolic  motions,  but  still  regular  ones ; because  the  ef- 
fects of  each  of  the  agents  accumulate  according  to  a uniform  law ; and  two 
regular  series  of  quantities,  when  their  corresponding  terms  are  added,  must 
produce  a regular  series  of  some  sort,  whatever  the  quantities  themselves  are. 

§ 3.  Kow  this  last  - mentioned  element  in  the  resolution  of  a derivative 
law,  the  element  which  is  not  a law  of  causation,  but  a collocation  of  causes, 

* Or,  according  to  Laplace's  theory,  the  sun  and  the  sun's  rotation. 


368 


INDUCTION. 


can  not  itself  be  reduced  to  any  law.  There  is,  as  formerly  remarked,*  no 
uniformity,  no  norma,  principle,  or  rule,  perceivable  in  the  distribution  of 
the  primeval  natural  agents  through  the  universe.  The  different  substances 
composing  the  earth,  the  powers  that  pervade  the  universe,  stand  in  no  con- 
stant relation  to  one  another.  One  substance  is  more  abundant  than  oth- 
ers, one  power  acts  through  a larger  extent  of  space  than  others,  with- 
out any  pervading  analogy  that  we  can  discover.  We  not  only  do  not 
know  of  any  reason  why  the  sun’s  attraction  and  the  force  in  the  direc- 
tion of  the  tangent  co-exist  in  the  exact  proportion  they  do,  but  we  can  trace 
no  coincidence  between  it  and  the  proportions  in  which  any  other  element- 
ary powers  in  the  universe  are  intermingled.  The  utmost  disorder  is  ap- 
parent in  the  combination  of  the  causes,  which  is  consistent  with  the  most 
regular  order  in  their  effects ; for  when  each  agent  carries  on  its  own  op- 
erations according  to  a uniform  law,  even  the  most  capricious  combination 
of  agencies  will  generate  a regularity  of  some  sort ; as  we  see  in  the  kalei- 
doscope, where  any  casual  arrangement  of  colored  bits  of  glass  produces 
by  the  laws  of  reflection  a beautiful  regularity  in  the  effect. 

§ 4.  In  the  above  considerations  lies  the  justification  of  the  limited  degree  of 
reliance  which  scientific  inquirers  are  accustomed  to  place  in  empirical  laws. 

A derivative  law  which  results  wholly  from  the  operation  of  some  one 
cause,  will  be  as  universally  true  as  the  laws  of  the  cause  itself;  that  is, 
it  will  always  be  true  except  where  some  one  of  those  effects  of  the  cause, 
on  which  the  derivative  law  depends,  is  defeated  by  a counteracting  cause. 
But  when  the  derivative  law  results  not  from  different  effects  of  one  cause, 
but  from  effects  of  several  causes,  we  can  not  be  certain  that  it  will  be  true 
under  any  variation  in  the  mode  of  co-existence  of  those  causes,  or  of  the 
primitive  natural  agents  on  which  the  causes  ultimately  depend.  The 
proposition  that  coal-beds  rest  on  certain  descriptions  of  strata  exclusively, 
though  true  on  the  earth,  so  far  as  our  observation  has  reached,  can  not  be 
extended  to  the  moon  or  the  other  planets,  supposing  coal  to  exist  there ; 
because  we  can  not  be  assured  that  the  original  constitution  of  any  other 
planet  was  such  as  to  produce  the  different  depositions  in  the  same  order 
as  in  our  globe.  The  derivative  law  in  this  case  depends  not  solely  on 
laws,  but  on  a collocation;  and  collocations  can  not  be  reduced  to  any  law. 

Now  it  is  the  very  nature  of  a derivative  law  which  has  not  yet  been  re- 
solved into  its  elements,  in  other  words,  an  empirical  law,  that  we  do  not 
know  whether  it  results  from  the  different  effects  of  one  cause,  or  from  ef- 
fects of  different  causes.  We  can  not  tell  whether  it  depends  wholly  on 
laws,  or  partly  on  laws  and  partly  on  a collocation.  If  it  depends  on  a 
collocation,  it  will  be  true  in  all  the  cases  in  which  that  particular  colloca- 
tion exists.  But,  since  we  are  entirely  ignorant,  in  case  of  its  depending 
on  a collocation,  what  the  collocation  is,  we  are  not  safe  in  extending  the 
law  beyond  the  limits  of  time  and  place  in  which  we  have  actual  experience 
of  its  truth.  Since  within  those  limits  the  law  has  always  been  found 
true,  we  have  evidence  that  the  collocations,  whatever  they  are,  on  which 
it  depends,  do  really  exist  within  those  limits.  But,  knowing  of  no  rule  or 
principle  to  which  the  collocations  themselves  conform,  we  can  not  con- 
clude that  because  a collocation  is  proved  to  exist  within  certain  limits  of 
place  or  time,  it  will  exist  beyond  those  limits.  Empirical  laws,  therefore, 
can  only  be  received  as  true  within  the  limits  of  time  and  place  in  which 


Supra,  book  iii.,  chap,  v.,  § 7. 


EMPIRICAL  LAWS. 


369 


they  have  been  found  true  by  observation ; and  not  merely  the  limits  of 
time  and  place,  but  of  time,  place,  and  circumstance  ; for,  since  it  is  the  very 
meaning  of  an  empirical  law  that  we  do  not  know  the  ultimate  laws  of  cau- 
sation on  which  it  is  dependent,  we  can  not  foresee,  without  actual  trial,  in 
what  manner  or  to  what  extent  the  introduction  of  any  new  circumstance 
may  affect  it. 

§ 5.  But  how  are  we  to  know  that  a uniformity  ascertained  by  experi- 
ence is  only  an  empirical  law  ? Since,  by  the  supposition,  we  have  not  been 
able  to  resolve  it  into  any  other  laws,  how  do  we  know  that  it  is  not  an 
ultimate  law  of  causation  ? 

I answer  that  no  generalization  amounts  to  more  than  an  empirical  law 
when  the  only  proof  on  which  it  rests  is  that  of  the  Method  of  Agreement. 
For  it  has  been  seen  that  by  that  method  alone  we  never  can  arrive  at 
causes.  The  utmost  that  the  Method  of  Agreement  can  do  is,  to  ascertain 
the  whole  of  the  circumstances  common  to  all  cases  in  which  a phenome- 
non is  produced  ; and  this  aggregate  includes  not  only  the  cause  of  the 
phenomenon,  but  all  phenomena  with  which  it  is  connected  by  any  deriva- 
tive uniformity,  whether  as  being  collateral  effects  of  the  same  cause,  or 
effects  of  any  other  cause  which,  in  all  the  instances  we  have  been  able  to 
observe,  co-existed  with  it.  The  method  affords  no  means  of  determining 
which  of  these  uniformities  are  laws  of  causation,  and  which  are  merely 
derivative  laws,  resulting  from  those  laws  of  causation  and  from  the  collo- 
cation of  the  causes.  None  of  them,  therefore,  can  be  received  in  any  oth- 
er character  than  that  of  derivative  laws,  the  derivation  of  which  has  not 
been  traced;  in  other  words,  empirical  laws:  in  which  light  all  results  ob- 
tained by  the  Method  of  Agreement  (and  therefore  almost  all  truths  obtain- 
ed by  simple  observation  without  experiment)  must  be  considered,  until 
either  confirmed  by  the  Method  of  Difference,  or  explained  deductively;  in 
other  words,  accounted  for  a priori. 

These  empirical  laws  may  be  of  greater  or  less  authority,  according  as 
there  is  reason  to  presume  that  they  are  resolvable  into  laws  only,  or  into 
laws  and  collocations  together.  The  sequences  which  we  observe  in  the 
production  and  subsequent  life  of  an  animal  or  a vegetable,  resting  on  the 
Method  of  Agreement  only,  are  mere  empirical  laws ; but  though  the  ante- 
cedents in  those  sequences  may  not  be  the  causes  of  the  consequents,  both 
the  one  and  the  other  are  doubtless,  in  the  main,  successive  stages  of  a pro- 
gressive effect  originating  in  a common  cause,  and  therefore  independent 
of  collocations.  The  uniformities,  on  the  other  hand,  in  the  order  of  super- 
position of  strata  on  the  earth,  are  empirical  laws  of  a much  weaker  kind, 
since  they  not  only  are  not  laws  of  causation,  but  there  is  no  reason  to  be- 
lieve that  they  depend  on  any  common  cause  ; all  appearances  are  in  favor 
of  their  depending  on  the  particular  collocation  of  natural  agents  which  at 
some  time  or  other  existed  on  our  globe,  and  from  which  no  inference  can 
be  drawn  as  to  the  collocation  which  exists  or  has  existed  in  any  other  por- 
tion of  the  universe. 

§ 6.  Our  definition  of  an  empirical  law,  including  not  only  those  uniform- 
ities which  are  not  known  to  be  laws  of  causation,  but  also  those  which  are, 
provided  there  be  reason  to  presume  that  they  are  not  ultimate  laws ; this 
is  the  proper  place  to  consider  by  what  signs  we  may  judge  that  even  if  an 
observed  uniformity  be  a law  of  causation,  it  is  not  an  ultimate,  but  a deriv- 
ative law. 


24 


370 


INDUCTION. 


The  first  sign  is,  if  between  the  antecedent  a and  the  consequent  b there 
be  evidence  of  some  intermediate  link ; some  phenomenon  of  which  we  can 
surmise  the  existence,  though  from  the  imperfection  of  our  senses  or  of  our 
instruments  we  are  unable  to  ascertain  its  precise  nature  and  laws.  If  there 
be  such  a phenomenon  (which  may  be  denoted  by  the  letter  x),  it  follows 
that  even  if  a be  the  cause  of  b,  it  is  but  the  remote  cause,  and  that  the 
law,  a causes  b,  is  resolvable  into  at  least  two  laws,  a causes  x,  and  x causes 
b.  This  is  a very  frequent  case,  since  the  operations  of  nature  mostly  take 
place  on  so  minute  a scale,  that  many  of  the  successive  steps  are  either  im- 
perceptible, or  very  indistinctly  perceived. 

Take,  for  example,  the  laws  of  the  chemical  composition  of  substances; 
as  that.hydrogen  and  oxygen  being  combined,  water  is  produced.  All  we 
see  of  the  process  is,  that  the  two  gases  being  mixed  in  certain  proportions, 
and  heat  or  electricity  being  applied,  an  explosion  takes  place,  the  gases 
disappear,  and  water  remains.  There  is  no  doubt  about  the  law,  or  about 
its  being  a law  of  causation.  But  between  the  antecedent  (the  gases  in  a 
state  of  mechanical  mixture,  heated  or  electrified),  and  the  consequent  (the 
production  of  water),  there  must  be  an  intermediate  process  which  we  do 
not  see.  For  if  we  take  any  portion  whatever  of  the  water,  and  subject  it 
to  analysis,  we  find  that  it  always  contains  hydrogen  and  oxygen;  nay,  the 
very  same  proportions  of  them,  namely,  two-thirds,  in  volume,  of  hydrogen, 
and  one-third  oxygen.  This  is  true  of  a single  drop;  it  is  true  of  the  mi- 
nutest portion  which  our  instruments  are  capable  of  appreciating.  Since, 
then,  the  smallest  perceptible  portion  of  the  water  contains  both  those  sub- 
stances, portions  of  hydrogen  and  oxygen  smaller  than  the  smallest  percep- 
tible must  have  come  together  in  every  such  minute  portion  of  space;  must 
have  come  closer  together  than  when  the  gases  were  in  a state  of  mechan- 
ical mixture,  since  (to  mention  no  other  reasons)  the  water  occupies  far  less 
space  than  the  gases.  Now,  as  we  can  not  see  this  contact  or  close  ap- 
proach of  the  minute  particles,  we  can  not  observe  with  what  circumstances 
it  is  attended,  or  according  to  what  laws  it  produces  its  effects.  The  pro- 
duction of  water,  that  is,  of  the  sensible  phenomena  which  characterize  the 
compound,  may  be  a very  remote  effect  of  those  laws.  There  may  be  in- 
numerable intervening  links;  and  we  are  sure  that  there  must  be  some. 
Having  full  proof  that  corpuscular  action  of  some  kind  takes  place  pre- 
vious to  any  of  the  great  transformations  in  the  sensible  properties  of  sub- 
stances, we  can  have  no  doubt  that  the  laws  of  chemical  action,  as  at  pres- 
ent known,  are  not  ultimate,  but  derivative  laws;  however  ignorant  we  may 
be,  and  even  though  we  should  forever  remain  ignorant,  of  the  nature  of 
the  laws  of  corpuscular  action  from  which  they  are  derived. 

In  like  manner,  all  the  processes  of  vegetative  life,  whether  in  the  vege- 
table properly  so  called  or  in  the  animal  body,  are  corpuscular  processes. 
Nutrition  is  the  addition  of  particles  to  one  another,  sometimes  merely 
replacing  other  particles  separated  and  excreted,  sometimes  occasioning 
an  increase  of  bulk  or  weight  so  gradual  that  only  after  a long  contin- 
uance does  it  become  perceptible.  Various  organs,  by  means  of  peculiar 
vessels,  secrete  from  the  blood  fluids,  the  component  particles  of  which 
must  have  been  in  the  blood,  but  which  differ  from  it  most  widely  both  in 
mechanical  properties  and  in  chemical  composition.  Here,  then,  are  abun- 
dance of  unknown  links  to  be  filled  up;  and  there  can  be  no  doubt  that  the 
laws  of  the  phenomena  of  vegetative  or  organic  life  are  derivative  laws,  de- 
pendent on  properties  of  the  corpuscles,  and  of  those  elementary  tissues 
which  are  comparatively  simple  combinations  of  corpuscles. 


EMPIRICAL  LAWS. 


371 


The  first  sign,  then,  from  which  a law  of  causation,  though  hitherto  un- 
resolved, may  be  inferred  to  be  a derivative  law,  is  any  indication  of  the 
existence  of  an  intermediate  link  or  links  between  the  antecedent  and  the 
consequent.  The  second  is,  when  the  antecedent  is  an  extremely  complex 
phenomenon,  and  its  effects,  therefore,  probably  in  part  at  least,  compound- 
ed of  the  effects  of  its  different  elements ; since  we  know  that  the  case  in 
which  the  effect  of  the  whole  is  not  made  up  of  the  effects  of  its  parts  is 
exceptional,  the  Composition  of  Causes  being  by  far  the  more  ordinary 
case. 

We  will  illustrate  this  by  two  examples,  in  one  of  which  the  antecedent  is 
the  sum  of  many  homogeneous,  in  the  other  of  heterogeneous,  parts.  The 
weight  of  a body  is  made  up  of  the  weights  of  its  minute  particles ; a truth 
which  astronomers  express  in  its  most  general  terms  when  they  say  that 
bodies,  at  equal  distances,  gravitate  to  one  another  in  proportion  to  their 
quantity  of  matter.  All  true  propositions,  therefore,  which  can  be  made 
concerning  gravity,  are  derivative  laws ; the  ultimate  law  into  which  they 
are  all  resolvable  being,  that  every  particle  of  matter  attracts  every  other. 
As  our  second  < xample,  we  may  take  any  of  the  sequences  observed  in 
meteorology  ; for  instance,  a diminution  of  the  pressure  of  the  atmosphere 
(indicated  by  a fall  of  the  barometer)  is  followed  by  rain.  The  antecedent 
is  here  a complex  phenomenon,  made  up  of  heterogeneous  elements ; the 
column  of  the  atmosphere  over  any  particular  place  consisting  of  two  parts, 
a column  of  air,  and  a column  of  aqueous  vapor  mixed  with  it;  and  the 
change  in  the  two  together  manifested  by  a fall  of  the  barometer,  and  fol- 
lowed by  rain,  must  be  either  a change  in  one  of  these,  or  in  the  other,  or 
in  both.  We  might,  then,  even  in  the  absence  of  any  other  evidence,  form 
a reasonable  presumption,  from  the  invariable  presence  of  both  these  ele- 
ments in  the  antecedent,  that  the  sequence  is  probably  not  an  ultimate  law, 
but  a result  of  the  laws  of  the  two  different  agents  ; a presumption  only 
to  be  destroyed  when  we  had  made  ourselves  so  well  acquainted  with  the 
laws  of  both,  as  to  be  able  to  affirm  that  those  laws  could  not  by  them- 
selves produce  the  observed  result. 

There  are  but  few  known  cases  of  succession  from  very  complex  ante- 
cedents which  have  not  either  been  actually  accounted  for  from  simpler 
laws,  or  inferred  with  great  probability  (from  the  ascertained  existence  of 
intermediate  links  of  causation  not  yet  understood)  to  be  'capable  of  being 
so  accounted  for.  It  is,  therefore,  highly  probable  that  all  sequences  from 
complex  antecedents  are  thus  resolvable,  and  that  ultimate  laws  are  in  all 
cases  comparatively  simple.  If  there  were  not  the  other  reasons  already 
mentioned  for  believing  that  the  laws  of  organized  nature  are  resolvable 
into  simpler  laws,  it  would  be  almost  a sufficient  reason  that  the  ante- 
cedents in  most  of  the  sequences  are  so  very  complex. 

§ 7.  In  the  preceding  discussion  we  have  recognized  two  kinds  of  em- 
pirical laws : those  known  to  be  laws  of  causation,  but  presumed  to  be  re- 
solvable into  simpler  laws ; and  those  not  known  to  be  laws  of  causation 
at  all.  Both  these  kinds  of  laws  agree  in  the  demand  which  they  make  for 
being  explained  by  deduction,  and  agree  in  being  the  appropriate  means 
of  verifying  such  deduction,  since  they  represent  the  experience  with  which 
the  result  of  the  deduction  must  be  compared.  They  agree,  further,  in 
this,  that  until  explained,  and  connected  with  the  ultimate  laws  from  which 
they  result,  they  have  not  attained  the  highest  degree  of  certainty  of  which 
laws  are  susceptible.  It  has  been  shown  on  a former  occasion  that  laws 


372 


INDUCTION. 


of  causation  which  arc  derivative,  and  compounded  of  simpler  laws,  are 
not  only,  as  the  nature  of  the  case  implies,  less  general,  but  even  less  cer- 
tain, than  the  simpler  laws  from  which  they  result;  not  in  the  same  de- 
gree to  be  relied  on  as  universally  true.  The  inferiority  of  evidence,  how- 
ever, which  attaches  to  this  class  of  laws,  is  trifling,  compared  with  that 
which  is  inherent  in  uniformities  not  known  to  be  laws  of  causation  at 
all.  So  long  as  these  are  unresolved,  we  can  not  tell  on  how  many  collo- 
cations, as  well  as  laws,  their  truth  may  be  dependent ; we  can  never,  there- 
fore, extend  them  with  any  confidence  to  cases  in  which  we  have  not  as- 
sured ourselves,  by  trial,  that  the  necessary  collocation  of  causes,  whatever 
it  may  be,  exists.  It  is  to  this  class  of  laws  alone  that  the  property,  which 
philosophers  usually  consider  as  characteristic  of  empirical  laws,  belongs  in 
all  its  strictness — the  property  of  being  unfit  to  be  relied  on  beyond  the 
limits  of  time,  place,  and  circumstance  in  which  the  observations  have  been 
made.  These  are  empirical  laws  in  a more  emphatic  sense ; and  when  I 
employ  that  term  (except  where  the  context  manifestly  indicates  the  re- 
verse) I shall  generally  mean  to  designate  those  uniformities  only,  whether 
of  succession  or  of  co-existence,  which  are  not  known  to  be  laws  of  causa- 
tion. 


CHAPTER  XVII. 

OF  CHANCE  AND  ITS  ELIMINATION. 

§ 1.  Considering,  then,  as  empirical  laws  only  those  observed  uniform- 
ities respecting  which  the  question  whether  they  are  laws  of  causation 
must  remain  undecided  until  they  can  be  explained  deductively,  or  until 
some  means  are  found  of  applying  the  Method  of  Difference  to  the  case, 
it  has  been  shown  in  the  preceding  chapter  that  until  a uniformity  can, 
in  one  or  the  other  of  these  modes,  be  taken  out  of  the  class  of  empirical 
laws,  and  brought  either  into  that  of  laws  of  causation  or  of  the  demon- 
strated results  of  laws  of  causation,  it  can  not  with  any  assurance  be  pro- 
nounced true  beyond  the  local  and  other  limits  within  which  it  has  been 
found  so  by  actual  observation.  It  remains  to  consider  how  we  are  to 
assure  ourselves  of  its  truth  even  within  those  limits ; after  what  quantity 
of  experience  a generalization  which  rests  solely  on  the  Method  of  Agree- 
ment can  be  considered  sufficiently  established,  even  as  an  empirical  law. 
In  a former  chapter,  when  treating  of  the  Methods  of  Direct  Induction,  we 
expressly  reserved  this  question,*  and  the  time  is  now  come  for  endeavor- 
ing to  solve  it. 

We  found  that  the  Method  of  Agreement  has  the  defect  of  not  proving 
causation,  and  can,  therefore,  only  be  employed  for  the  ascertainment  of 
empirical  laws.  But  we  also  found  that  besides  this  deficiency,  it  labors 
under  a characteristic  imperfection,  tending  to  render  uncertain  even  such 
conclusions  as  it  is  in  itself  adajited  to  prove.  This  imperfection  arises 
from  Plurality  of  Causes.  Although  two  or  more  cases  in  which  the  phe- 
nomenon a has  been  met  with  may  have  no  common  antecedent  except  A, 
this  does  not  prove  that  there  is  any  connection  between  a and  A,  since  a 
may  have  many  causes,  and  may  have  been  produced,  in  these  different 
instances,  not  by  any  thing  which  the  instances  had  in  common,  but  by 
some  of  those  elements  in  them  which  were  different.  We  nevertheless 


Supra,  book  iii.,  chap,  x.,  § 2. 


CHANCE,  AND  ITS  ELIMINATION. 


373 


observed,  that  in  proportion  to  the  multiplication  of  instances  pointing  to  A 
as  the  antecedent,  the  characteristic  uncertainty  of  the  method  diminishes, 
and  the  existence  of  a law  of  connection  between  A and  a more  nearly 
approaches  to  certainty.  It  is  now  to  be  determined  after  what  amount 
of  experience  this  certainty  may  be  deemed  to  be  practically  attained,  and 
the  connection  between  A and  a may  be  received  as  an  empirical  law. 

This  question  may  be  otherwise  stated  in  more  familiar  terms  : After  how 
many  and  what  sort  of  instances  may  it  be  concluded  that  an  observed 
coincidence  between  two  phenomena  is  not  the  effect  of  chance? 

It  is  of  the  utmost  importance  for  understanding  the  logic  of  induction, 
that  we  should  form  a distinct  conception  of  what  is  meant  by  chance,  and 
how  the  phenomena  which  common  language  ascribes  to  that  abstraction 
are  really  produced. 

§ 2.  Chance  is  usually  spoken  of  in  direct  antithesis  to  law ; whatever,  it 
is  supposed,  can  not  be  ascribed  to  any  law  is  attributed  to  chance.  It  is, 
however,  certain  that  whatever  happens  is  the  result  of  some  law;  is  an 
effect  of  causes,  and  could  have  been  predicted  from  a knowledge  of  the 
existence  of  those  causes,  and  from  their  laws.  If  I turn  up  a particular 
card,  that  is  a consequence  of  its  place  in  the  pack.  Its  place  in  the  pack 
was  a consequence  of  the  manner  in  which  the  cards  were  shuffled,  or  of 
the  order  in  which  they  were  played  in  the  last  game ; which,  again,  were 
effects  of  prior  causes.  At  every  stage,  if  we  had  possessed  an  accurate 
knowledge  of  the  causes  in  existence,  it  would  have  been  abstractedly  pos- 
sible to  foretell  the  effect. 

An  event  occurring  by  chance  may  be  better  described  as  a coincidence 
from  which  we  have  no  ground  to  infer  a uniformity — the  occurrence  of 
a phenomenon  in  certain  circumstances,  without  our  having  reason  on  that 
account  to  infer  that  it  will  happen  again  in  those  circumstances.  This, 
however,  when  looked  closely  into,  implies  that  the  enumeration  of  the  cir- 
cumstances is  not  complete.  Whatever  the  fact  be,  since  it  has  occurred 
once,  we  may  be  sure  that  if  all  the  same  circumstances  were  repeated  it 
would  occur  again;  and  not  only  if  all,  but  there  is  some  particular  portion 
of  those  circumstances  on  which  the  phenomenon  is  invariably  consequent. 
With  most  of  them,  however,  it  is  not  connected  in  any  permanent  man- 
ner; its  conjunction  with  those  is  said  to  be  the  effect  of  chance,  to  be 
merely  casual.  Facts  casually  conjoined  are  separately  the  effects  of 
causes,  and  therefore  of  laws ; but  of  different  causes,  and  causes  not  con- 
nected by  any  law. 

It  is  incorrect,  then,  to  say  that  any  phenomenon  is  produced  by  chance; 
but  we  may  say  that  two  or  more  phenomena  are  conjoined  by  chance,  that 
they  co-exist  or  succeed  one  another  only  by  chance ; meaning  that  they 
are  in  no  way  related  through  causation ; that  they  are  neither  cause  and 
effect,  nor  effects  of  the  same  cause,  nor  effects  of  causes  between  which 
there  subsists  any  law  of  co-existence,  nor  even  effects  of  the  same  colloca- 
tion of  primeval  causes. 

If  the  same  casual  coincidence  never  occurred  a second  time,  we  should 
have  an  easy  test  for  distinguishing  such  from  the  coincidences  which  are 
the  results  of  a law.  As  long  as  the  phenomena  had  been  found  together 
only  once,  so  long,  unless  we  knew  some  more  general  laws  from  which  the 
coincidence  might  have  resulted,  we  could  not  distinguish  it  from  a casual 
one ; but  if  it  occurred  twice,  we  should  know  that  the  phenomena  so  con- 
joined must  be  in  some  way  connected  through  their  causes. 


374 


INDUCTION. 


There  is,  however,  no  such  test.  A coincidence  may  occur  again  and 
again,  and  yet  be  only  casual.  Nay,  it  would  be  inconsistent  with  what  we 
know  of  the  order  of  nature  to  doubt  that  every  casual  coincidence  will 
sooner  or  later  be  repeated,  as  long  as  the  phenomena  between  which  it  oc- 
curred do  not  cease  to  exist,  or  to  be  reproduced.  The  recurrence,  there- 
fore, of  the  same  coincidence  more  than  once,  or  even  its  frequent  recur- 
rence, does  not  prove  that  it  is  an  instance  of  any  law ; does  not  prove  that 
it  is  not  casual,  or,  in  common  language,  the  effect  of  chance. 

And  yet,  when  a coincidence  can  not  be  deduced  from  known  laws,  nor 
proved  by  experiment  to  be  itself  a case  of  causation,  the  frequency  of  its 
occurrence  is  the  only  evidence  from  which  we  can  infer  that  it  is  the  re- 
sult of  a law.  Not,  however,  its  absolute  frequency.  The  question  is  not 
whether  the  coincidence  occurs  often  or  seldom,  in  the  ordinary  sense  of 
those  terms ; but  whether  it  occurs  more  often  than  chance  will  account 
for;  more  often  than  might  rationally  be  expected  if  the  coincidence  were 
casual.  We  have  to  decide,  therefore,  what  degree  of  frequency  in  a coin- 
cidence chance  will  account  for;  and  to  this  there  can  be  no  general  an- 
swer. We  can  only  state  the  principle  by  which  the  answer  must  be  de- 
termined ; the  answer  itself  will  be  different  in  every  different  case. 

Suppose  that  one  of  the  phenomena,  A,  exists  always,  and  the  other  phe- 
nomenon, B,  only  occasionally ; it  follows  that  every  instance  of  B will  be 
an  instance  of  its  coincidence  with  A,  and  yet  the  coincidence  will  be  mere- 
ly casual,  not  the  result  of  any  connection  between  them.  The  fixed  stars 
have  been  constantly  in  existence  since  the  beginning  of  human  experience, 
and  all  phenomena  that  have  come  under  human  observation  have,  in  every 
single  instance,  co-existed  with  them  ; yet  this  coincidence,  though  equally 
invariable  with  that  which  exists  between  any  of  those  phenomena  and  its 
own  cause,  does  not  prove  that  the  stars  are  its  cause,  nor  that  they  are  in 
anywise  connected  with  it.  As  strong  a case  of  coincidence,  therefore,  as 
can  possibly  exist,  and  a much  stronger  one  in  point  of  mere  frequency 
than  most  of  those  which  prove  laws,  does  not  here  prove  a law;  why?  be- 
cause, since  the  stars  exist  always,  they  must  co-exist  with  every  other  phe- 
nomenon, whether  connected  with  them  by  causation  or  not.  The  uniform- 
ity, great  though  it  be,  is  no  greater  than  would  occur  on  the  supposition 
that  no  such  connection  exists. 

On  the  other  hand,  suppose  that  we  were  inquiring  whether  there  be  any 
connection  between  rain  and  any  particular  wind.  Rain,  we  know,  occa- 
sionally occurs  with  every  wind ; therefore,  the  connection,  if  it  exists,  can 
not  be  an  actual  law;  but  still  rain  may  be  connected  with  some  particular 
wind  through  causation;  that  is,  though  they  can  not  be  always  effects  of 
the  same  cause  (for  if  so  they  would  regularly  co-exist),  there  may  be  some 
causes  common  to  the  two,  so  that  in  so  far  as  either  is  produced  by  those 
common  causes,  they  will,  from  the  laws  of  the  causes,  be  found  to  co-exist. 
How,  then,  shall  we  ascertain  this?  The  obvious  answer  is,  by  observing 
whether  rain  occurs  with  one  wind  more  frequently  than  with  any  other. 
That,  however,  is  not  enough;  for  perhaps  that  one  wind  blows  more  fre- 
quently than  any  other;  so  that  its  blowing  more  frequently  in  rainy 
weather  is  no  more  than  would  happen,  although  it  had  no  connection  with 
the  causes  of  rain,  provided  it  were  not  connected  with  causes  adverse  to 
rain.  In  England,  westerly  winds  blow  during  about  twice  as  great  a por- 
tion of  the  year  as  easterly.  If,  therefore,  it  rains  only  twice  as  often  with 
a westerly  as  with  an  easterly  wind,  we  have  no  reason  to  infer  that  any 
law  of  nature  is  concerned  in  the  coincidence.  If  it  rains  more  than  twice 


CHANCE,  AND  ITS  ELIMINATION. 


375 


as  often,  we  may  be  sure  that  some  law  is  concerned ; either  there  is  some 
cause  in  nature  which,  in  this  climate,  tends  to  produce  both  rain  and  a 
westerly  wind,  or  a westerly  wind  has  itself  some  tendency  to  produce  rain. 
But  if  it  rains  less  than  twice  as  often,  we  may  draw  a directly  opposite  in- 
ference: the  one,  instead  of  being  a cause,  or  connected  with  causes  of  the 
other,  must  be  connected  with  causes  adverse  to  it,  or  with  the  absence  of 
some  cause  which  produces  it;  and  though  it  may  still  rain  much  oftener 
with  a westerly  wind  than  with  an  easterly,  so  far  would  this  be  from  prov- 
ing any  connection  between  the  phenomena,  that  the  connection  proved 
would  be  between  rain  and  an  easterly  wind,  to  which,  in  mere  frequency 
of  coincidence,  it  is  less  allied. 

Here,  then,  are  two  examples  : in  one,  the  greatest  possible  frequency  of 
coincidence,  with  no  instance  whatever  to  the  contrary,  does  not  prove  that 
there  is  any  law;  in  the  other,  a much  less  frequency  of  coincidence,  even 
when  non-coincidence  is  still  more  frequent,  does  prove  that  there  is  a law. 
In  both  cases  the  principle  is  the  same.  In  both  we  consider  the  positive 
frequency  of  the  phenomena  themselves,  and  how  great  frequency  of  coin- 
cidence that  must  of  itself  bring  about,  without  supposing  any  connection 
between  them,  provided  there  be  no  repugnance ; provided  neither  be  con- 
nected with  any  cause  tending  to  frustrate  the  other.  If  we  find  a greater 
frequency  of  coincidence  than  this,  we  conclude  that  there  is  some  connec- 
tion ; if  a less  frequency,  that  there  is  some  repugnance.  In  the  former 
case,  we  conclude  that  one  of  the  phenomena  can  under  some  circumstances 
cause  the  other,  or  that  there  exists  something  capable  of  causing  them 
both  ; in  the  latter,  that  one  of  them,  or  some  cause  which  produces  one  of 
them,  is  capable  of  counteracting  the  production  of  the  other.  We  have 
thus  to  deduct  from  the  observed  frequency  of  coincidence  as  much  as  may 
be  the  effect  of  chance,  that  is,  of  the  mere  frequency  of  the  phenomena 
themselves ; and  if  any  thing  remains,  what  does  remain  is  the  residual 
fact  which  proves  the  existence  of  a law. 

The  frequency  of  the  phenomena  can  only  be  ascertained  within  definite 
limits  of  space  and  time;  depending  as  it  does  on  the  quantity  and  distri- 
bution of  the  primeval  natural  agents,  of  which  we  can  know  nothing  be- 
yond the  boundaries  of  human  observation,  since  no  law,  no  regularity,  can 
be  traced  in  it,  enabling  us  to  infer  the  unknown  from  the  known.  But  for 
the  present  purpose  this  is  no  disadvantage,  the  question  being  confined 
within  the  same  limits  as  the  data.  The  coincidences  occurred  in  certain 
places  and  times,  and  within  those  we  can  estimate  the  frequency  with 
which  such  coincidences  would  be  produced  by  chance.  If,  then,  we  find 
from  observation  that  A exists  in  one  case  out  of  every  two,  and  B in  one 
case  out  of  every  three ; then,  if  there  be  neither  connection  nor  repugnance 
between  them,  or  between  any  of  their  causes,  the  instances  in  which  A 
and  B will  both  exist,  that  is  to  say  will  co-exist,  will  be  one  case  in  every 
six.  For  A exists  in  three  cases  out  of  six;  and  B,  existing  in  one  case 
out  of  every  three  without  regard  to  the  presence  or  absence  of  A,  will 
exist  in  one  case  out  of  those  three.  There  will  therefore  be,  of  the  whole 
number  of  cases,  two  in  which  A exists  without  B ; one  case  of  B without 
A;  two  in  which  neither  B nor  A exists,  and  one  case  out  of  six  in  which 
they  both  exist.  If,  then,  in  point  of  fact,  they  are  found  to  co-exist  oftener 
than  in  one  case  out  of  six;  and,  consequently,  A does  not  exist  without 
B so  often  as  twice  in  three  times,  nor  B without  A so  often  as  once  in  ev- 
ery twice,  there  is  some  cause  in  existence  which  tends  to  produce  a con- 
junction between  A and  B. 


37G 


INDUCTION. 


Generalizing  the  result,  we  may  say  that  if  A occurs  in  a larger  propor- 
tion of  the  cases  where  B is  than  of  the  cases  where  B is  not,  then  will 
B also  occur  in  a larger  proportion  of  the  cases  where  A is  than  of  the 
cases  where  A is  not;  and  there  is  some  connection,  through  causation,  be- 
tween A and  B.  If  we  could  ascend  to  the  causes  of  the  two  phenomena, 
wo  should  find,  at  some  stage,  either  proximate  or  remote,  some  cause  or 
causes  common  to  both  ; and  if  we  could  ascertain  what  these  are,  we  could 
frame  a generalization  which  would  bo  true  without  restriction  of  place  or 
time;  but  until  we  can  do  so,  the  fact  of  a connection  between  the  two 
phenomena  remains  an  empirical  law. 

§ 3.  Having  considered  in  what  manner  it  may  be  determined  whether 
any  given  conjunction  of  phenomena  is  casual,  or  the  result  of  some  law, 
to  complete  the  theory  of  chance  it  is  necessary  that  we  should  now  con- 
sider those  effects  which  are  partly  the  result  of  chance  and  partly  of  law, 
or,  in  other  words,  in  which  the  effects  of  casual  conjunctions  of  causes 
are  habitually  blended  in  one  result  with  the  effects  of  a constant  cause. 

This  is  a case  of  Composition  of  Causes ; and  the  peculiarity  of  it  is, 
that  instead  of  two  or  more  causes  intermixing  their  effects  in  a regular 
manner  with  those  of  one  another,  we  have  now  one  constant  cause,  pro- 
ducing an  effect  which  is  successively  modified  by  a series  of  variable 
causes.  Thus,  as  summer  advances,  the  approach  of  the  sun  to  a vertical 
position  tends  to  produce  a constant  increase  of  temperature;  but  with 
this  effect  of  a constant  cause,  there  are  blended  the  effects  of  many  vari- 
able causes,  winds,  clouds,  evaporation,  electric  agencies  and  the  like,  so 
that  the  temperature  of  any  given  day  depends  in  part  on  these  fleeting 
causes,  and  only  in  part  on  the  constant  cause.  If  the  effect  of  the  con- 
stant cause  is  always  accompanied  and  disguised  by  effects  of  variable 
causes,  it  is  impossible  to  ascertain  the  law  of  the  constant  cause  in  the  or- 
dinary manner  by  separating  it  from  all  other  causes  and  observing  it  apart. 
Hence  arises  the  necessity  of  an  additional  rule  of  experimental  inquiry. 

When  the  action  of  a cause  A is  liable  to  be  interfered  with,  not  stead- 
ily by  the  same  cause  or  causes,  but  by  different  causes  at  different  times, 
and  when  these  are  so  frequent,  or  so  indeterminate,  that  we  can  not  pos- 
sibly exclude  all  of  them  from  any  experiment,  though  we  may  vary  them ; 
our  resource  is,  to  endeavor  to  ascertain  what  is  the  effect  of  all  the  vari- 
able causes  taken  together.  In  order  to  do  this,  we  make  as  many  trials 
as  possible,  preserving  A invariable.  The  results  of  these  different  trials 
will  naturally  be  different,  since  the  indeterminate  modifying  causes  are 
different  in  each ; if,  then,  we  do  not  find  these  results  to  be  progressive, 
but,  on  the  contrary,  to  oscillate  about  a certain  point,  one  experiment  giv- 
ing a result  a little  greater,  another  a little  less,  one  a result  tending  a little 
more  in  one  direction,  another  a little  more  in  the  contrary  direction  ; while 
the  average  or  middle  point  does  not  vary,  but  different  sets  of  experi- 
ments (taken  in  as  great  a variety  of  circumstances  as  possible)  yield  the 
same  mean,  provided  only  they  be  sufficiently  numerous;  then  that  mean, 
or  average  result,  is  the  part,  in  each  experiment,  which  is  due  to  the  cause 
A,  and  is  the  effect  which  would  have  been  obtained  if  A could  have  acted 
alone ; the  variable  remainder  is  the  effect  of  chance,  that  is,  of  causes  the 
co-existence  of  which  with  the  cause  A was  merely  casual.  The  test  of 
the  sufficiency  of  the  induction  in  this  case  is,  when  any  increase  of  the 
number  of  trials  from  which  the  average  is  struck  does  not  materially 
alter  the  average. 


CHANCE,  AND  ITS  ELIMINATION. 


377 


This  kind  of  elimination,  in  which  we  do  not  eliminate  any  one  assignable 
cause,  but  the  multitude  of  floating  unassignable  ones,  may  be  termed  the 
Elimination  of  Chance.  We  afford  an  example  of  it  when  we  repeat  an  ex- 
periment, in  order,  by  taking  the  mean  of  different  results,  to  get  rid  of  the 
effects  of  the  unavoidable  errors  of  each  individual  experiment.  When  there 
is  no  permanent  cause,  such  as  would  produce  a tendency  to  error  peculiar- 
ly in  one  direction,  we  are  warranted  by  experience  in  assuming  that  the 
errors  on  one  side  will,  in  a certain  number  of  experiments,  about  balance 
the  errors  on  the  contrary  side.  We  therefore  repeat  the  experiment,  un- 
til any  change  which  is  produced  in  the  average  of  the  whole  by  further 
repetition,  falls  within  limits  of  error  consistent  with  the  degree  of  accuracy 
required  by  the  purpose  we  have  in  view.* 

§ 4.  In  the  supposition  hitherto  made,  the  effect  of  the  constant  cause  A 
has  been  assumed  to  form  so  great  and  conspicuous  a part  of  the  general 
result,  tli at  its  existence  never  could  be  a matter  of  uncertainty,  and  the  ob- 
ject of  the  eliminating  process  was  only  to  ascertain  how  much  is  attribu- 
table to  that  cause  ; what  is  its  ex^et  law.  Cases,  however,  occur  in  which 
the  effect  of  a constant  cause  is  so  small,  compared  with  that  of  some  of  the 
changeable  causes  with  which  it  is  liable  to  be  casually  conjoined,  that  of  it- 
self it  escapes  notice,  and  the  very  existence  of  any  effect  arising  from  a 
constant  cause  is  first  learned  by  the  process  which  in  general  serves  only  for 
ascertaining  the  quantity  of  that  effect.  This  case  of  induction  may  be  char- 
acterized as  follows : A given  effect  is  known  to  be  chiefly,  and  not  known 
not  to  be  wholly,  determined  by  changeable  causes.  If  it  be  wholly  so  pro- 
duced, then  if  the  aggregate  be  taken  of  a sufficient  number  of  instances,  the 
effects  of  these  different  causes  will  cancel  one  another.  If,  therefore,  we 
do  not  find  this  to  be  the  case,  but,  on  the  contrary,  after  such  a number  of 
trials  has  been  made  that  no  further  increase  alters  the  average  result, 
we  find  that  average  to  be,  not  zero,  but  some  other  quantity,  about  which, 
though  small  in  comparison  with  the  total  effect,  the  effect  nevertheless 
oscillates,  and  which  is  the  middle  point  in  its  oscillation ; we  may  conclude 
this  to  be  the  effect  of  some  constant  cause;  which  cause,  by  some  of  the 
methods  already  treated  of,  we  may  hope  to  detect.  This  may  be  called 
the  discovery  of  a residual  phenomenon  by  eliminating  the  effects  of 
chance. 

It  is  in  this  manner,  for  example,  that  loaded  dice  may  be  discovered. 
Of  course  no  dice  are  so  clumsily  loaded  that  they  must  always  throw  cer- 
tain numbers ; otherwise  the  fraud  would  be  instantly  detected.  The  load- 
ing, a constant  cause,  mingles  with  the  changeable  causes  which  determine 
what  cast  will  be  thrown  in  each  individual  instance.  If  the  dice  were  not 

* In  the  preceding  discussion,  the  mean  is  spoken  of  as  if  it  were  exactly  the  same  thing 
with  the  average.  But  the  mean,  for  purposes  of  inductive  inquiry,  is  not  the  average,  or  ar- 
ithmetical mean,  though  in  a familiar  illustration  of  the  theory  the  difference  may  be  disre- 
garded. If  the  deviations  on  one  side  of  the  average  are  much  more  numerous  than  those  on 
the  other  (these  last  being  fewer  but  greater),  the  effect  due  to  the  invariable  cause,  as  dis- 
tinct from  the  variable  ones,  will  not  coincide  with  the  average,  but  will  be  either  below  or 
above  the  average,  the  deviation  being  toward  the  side  on  which  the  greatest  number  of  the 
instances  are  found.  This  follows  from  a truth,  ascertained  both  inductively  and  deductively, 
that  small  deviations  from  the  true  central  point  are  greatly  more  frequent  than  large  ones. 
The  mathematical  law  is,  “that  the  most  probable  determination  of  one  or  more  invariable 
elements  from  observation  is  that  in  which  the  sum  of  the  squares  of  the  individual  aberra- 
tions,” or  deviations,  “ shall  he  the  least  possible."  See  this  principle  stated,  and  its  grounds 
popularly  explained,  by  Sir  John  Herschel,  in  his  review  of  Quetelet  on  Probabilities,  Essays, 
p.  395  et  seq. 


STS 


INDUCTION. 


loaded,  and  the  throw  were  left  to  depend  entirely  on  the  changeable  causes, 
these  in  a sufficient  number  of  instances  would  balance  one  another,  and 
there  would  be  no  preponderant  number  of  throws  of  any  one  kind.  If; 
therefore,  after  such  a number  of  trials  that  no  further  increase  of  their 
number  has  any  material  effect  upon  the  average,  we  find  a preponderance 
in  favor  of  a particular  throw;  we  may  conclude  with  assurance  that  there 
is  some  constant  cause  acting  in  favor  of  that  throw,  or,  in  other  words,  that 
the  dice  are  not  fair;  and  the  exact  amount  of  the  unfairness.  In  a similar 
manner,  what  is  called  the  diurnal  variation  of  the  barometer,  which  is  very 
small  compared  with  the  variations  arising  from  the  irregular  changes  in 
the  state  of  the  atmosphere,  was  discovered  by  comparing  the  average 
height  of  the  barometer  at  different  hours  of  the  day.  When  this  compari- 
son was  made,  it  was  found  that  there  was  a small  difference,  which  on  the 
average  was  constant,  however  the  absolute  quantities  might  vary,  and  which 
difference,  therefore,  must  be  the  effect  of  a constant  cause.  This  cause 
was  afterward  ascertained,  deductively,  to  be  the  rarefaction  of  the  air, 
occasioned  by  the  increase  of  temperature  as  the  day  advances. 

§ 5.  After  these  general  remarks  on  the  nature  of  chance,  we  are  pre- 
pared to  consider  in  what  manner  assurance  may  be  obtained  that  a con- 
junction between  two  phenomena,  which  has  been  observed  a certain  num- 
ber of  times,  is  not  casual,  but  a result  of  causation,  and  to  be  received, 
therefore,  as  one  of  the  uniformities  of  nature,  though  (until  accounted  for 
a priori ) only  as  an  empirical  law. 

We  will  suppose  the  strongest  case,  namely,  that  the  phenomenon  B has 
never  been  observed  except  in  conjunction  with  A.  Even  then,  the  proba- 
bility that  they  are  connected  is  not  measured  by  the  total  number  of  in- 
stances in  which  they  have  been  found  together,  but  by  the  excess  of  that 
number  above  the  number  due  to  the  absolutely  frequency  of  A.  If,  for 
example,  A exists  always,  and  therefore  co-exists  with  every  thing,  no  num- 
ber of  instances  of  its  co-existence  with  B would  prove  a connection  ; as  in 
our  example  of  the  fixed  stars.  If  A be  a fact  of  such  common  occurrence 
that  it  may  be  presumed  to  be  present  in  half  of  all  the  cases  that  occur, 
and  therefore  in  half  the  cases  in  which  B occurs,  it  is  only  the  proportional 
excess  above  half  that  is  to  be  reckoned  as  evidence  toward  proving. a con- 
nection between  A and  B. 

In  addition  to  the  question,  What  is  the  number  of  coincidences  which, 
on  an  average  of  a great  multitude  of  trials,  may  be  expected  to  arise  from 
chance  alone?  there  is  also  another  question,  namely,  Of  what  extent  of  de- 
viation from  that  average  is  the  occurrence  credible,  from  chance  alone,  in 
some  number  of  instances  smaller  than  that  required  for  striking  a fair  av- 
erage? It  is  not  only  to  be  considered  what  is  the  general  result  of  the 
chances  in  the  long  run,  but  also  what  are  the  extreme  limits  of  variation 
from  the  general  result,  which  may  occasionally  be  expected  as  the  result 
of  some  smaller  number  of  instances. 

The  consideration  of  the  latter  question,  and  any  consideration  of  the 
former  beyond  that  already  given  to  it,  belong  to  what  mathematicians 
term  the  doctrine  of  chances,  or,  in  a phrase  of  greater  pretension,  the  The- 
ory of  Probabilities. 


OF  THE  CALCULATION  OF  CHANCES. 


379 


CHAPTER  XVIII. 

OF  THE  CALCULATION  OF  CHANCES. 

§ 1.  “Probability,”  says  Laplace,*  “has  reference  partly  to  our  igno- 
rance, partly  to  our  knowledge.  We  know  that  among  three  or  more 
events,  one,  and  only  one,  must  happen  ; but  there  is  nothing  leading  us  to 
believe  that  any  one  of  them  will  happen  rather  than  the  others.  In  this 
state  of  indecision,  it  is  impossible  for  us  to  pronounce  with  certainty  on 
their  occurrence.  It  is,  however,  probable  that  any  one  of  these  events, 
selected  at  pleasure,  will  not  take  place ; because  we  perceive  several  cases, 
all  equally  possible,  which  exclude  its  occurrence,  and  only  one  which  fa- 
vors it. 

“ The  theory  of  chances  consists  in  reducing  all  events  of  the  same-  kind 
to  a certain  number  of  cases  equally  possible,  that  is,  such  that  we  are 
equally  undecided  as  to  their  existence  ; and  in  determining  the  number  of 
these  cases  which  are  favorable  to  the  event  of  which  the  probability  is 
sought.  The  ratio  of  that  number  to  the  number  of  all  the  possible  cases 
is  the  measure  of  the  probability;  which  is  thus  a fraction,  having  for  its 
numerator  the  number  of  cases  favorable  to  the  event,  and  for  its  denom- 
inator the  number  of  all  the  cases  which  are  possible.” 

To  a calculation  of  chances,  then,  according  to  Laplace,  two  things  are 
necessary ; we  must  know  that  of  several  events  some  one  will  certainly 
happen,  and  no  more  than  one;  and  we  must  not  know,  nor  have  any  rea- 
son to  expect,  that  it  will  be  one  of  these  events  rather  than  another.  It 
has  been  contended  that  these  are  not  the  only  requisites,  and  that  Laplace 
has  overlooked,  in  the  general  theoretical  statement,  a necessary  part  of  the 
foundation  of  the  doctrine  of  chances.  To  be  able  (it  has  been  said)  to 
pronounce  two  events  equally  probable,  it  is  not  enough  that  we  should 
know  that  one  or  the  other  must  happen,  and  should  have  no  grounds  for 
conjecturing  which.  Experience  must  have  shown  that  the  two  events  are 
of  equally  frequent  occurrence.  Why,  in  tossing  up  a half-penny,  do  we  reck- 
on it  equally  probable  that  we  shall  throw  cross  or  pile  ? Because  we  know 
that  in  any  great  number  of  throws,  cross  and  pile  are  thrown  about  equally 
often  ; and  that  the  more  throws  we  make,  the  more  nearly  the  equality  is 
perfect.  We  may  know  this  if  we  please  by  actual  experiment,  or  by  the 
daily  experience  which  life  affords  of  events  of  the  same  general  character, 
or,  deductively,  from  the  effect  of  mechanical  laws  on  a symmetrical  body 
acted  upon  by  forces  varying  indefinitely  in  quantity  and  direction.  We 
may  know  it,  in  short,  either  by  specific  experience,  or  on  the  evidence  of 
our  general  knowledge  of  nature.  But,  in  one  way  or  the  other,  we  must 
know  it,  to  justify  us  in  calling  the  two  events  equally  probable;  and  if  we 
knew  it  not,  we  should  proceed  as  much  at  hap-hazard  in  staking  equal  sums 
on  the  result,  as  in  laying  odds. 

This  view  of  the  subject  was  taken  in  the  first  edition  of  the  present 
work;  but  I have  since  become  convinced  that  the  theory  of  chances,  as 


Essai  Philosophique  sur  les  Probability,  fifth  Paris  edition,  p.  7. 


3S0 


INDUCTION. 


conceived  by  Laplace  and  by  mathematicians  generally,  has  not  the  funda- 
mental fallacy  which.  I had  ascribed  to  it. 

W e must  remember  that  the  probability  of  an  event  is  not  a quality  of 
the  event  itself,  but  a mere  name  for  the  degree  of  ground  which  we,  or 
some  one  else,  have  for  expecting  it.  The  probability  of  an  event  to  one 
person  is  a different  thing  from  the  probability  of  the  same  event  to  an- 
other, or  to  the  same  person  after  he  has  acquired  additional  evidence.  The 
probability  to  me,  that  an  individual  of  whom  I know  nothing  but  his  name 
will  die  within  the  year,  is  totally  altered  by  my  being  told  the  next  minute 
that  he  is  in  the  last  stage  of  a consumption.  Yet  this  makes  no  difference 
in  the  event  itself,  nor  in  any  of  the  causes  on  which  it  depends.  Every 
event  is  in  itself  certain,  not  probable;  if  we  knew  all,  we  should  either 
know  positively  that  it  will  happen,  or  positively  that  it  will  not.  But  its 
probability  to  us  means  the  degree  of  expectation  of  its  occurrence,  which 
we  are  warranted  in  entertaining  by  our  present  evidence. 

Bearing  this  in  mind,  I think  it  must  be  admitted,  that  even  when  we 
have  no  knowledge  whatever  to  guide  our  expectations,  except  the  knowl- 
edge that  what  happens  must  be  some  one  of  a certain  number  of  possibili- 
ties, we  may  still  reasonably  judge,  that  one  supposition  is  more  probable 
to  us  than  another  supposition ; and  if  we  have  any  interest  at  stake,  we 
shall  best  provide  for  it  by  acting  conformably  to  that  judgment. 

§ 2.  Suppose  that  we  are  required  to  take  a ball  from  a box,  of  which 
we  only  know  that  it  contains  balls  both  black  and  white,  and  none  of  any 
other  color.  We  know  that  the  ball  we  select  will  be  either  a black  or  a 
white  ball ; but  we  have  no  ground  for  expecting  black  rather  than  white, 
or  white  rather  than  black.  In  that  case,  if  we  are  obliged  to  make  a choice, 
and  to  stake  something  on  one  or  the  other  supposition,  it  will,  as  a question 
of  prudence,  be  jjerfectly  indifferent  which ; and  we  shall  act  precisely  as 
we  should  have  acted  if  we  had  known  beforehand  that  the  box  contained 
an  equal  number  of  black  and  white  balls.  But  though  our  conduct  would 
be  the  same,  it  would  not  be  founded  on  any  surmise  that  the  balls  were  in 
fact  thus  equally  divided ; for  we  might,  on  the  contrary,  know  by  au- 
thentic information  that  the  box  contained  ninety-nine  balls  of  one  color, 
and  only  one  of  the  other ; still,  if  we  are  not  told  which  color  has  only  one, 
and  which  has  ninety-nine,  the  drawing  of  a white  and  of  a black  ball  will 
be  equally  probable  to  us.  We  shall  have  no  reason  for  staking  any  thing 
on  the  one  event  rather  than  on  the  other ; the  option  between  the  two  will 
be  a matter  of  indifference ; in  other  words,  it  will  be  an  even  chance. 

But  let  it  now  be  supposed  that  instead  of  two  there  are  three  colors — 
white,  black,  and  red ; and  that  we  are  entirely  ignorant  of  the  proportion 
in  which  they  are  mingled.  We  should  then  have  no  reason  for  expecting 
one  more  than  another,  and  if  obliged  to  bet,  should  venture  our  stake  on 
red,  white,  or  black  with  equal  indifference.  But  should  we  be  indifferent 
whether  we  betted  for  or  against  some  one  color,  as,  for  instance,  white  ? 
Surely  not.  From  the  very  fact  that  black  and  red  are  each  of  them  sep- 
arately equally  probable  to  us  with  white,  the  two  together  must  be  twice 
as  probable.  We  should  in  this  case  expect  not  white  rather  than  white, 
and  so  much  rather  that  we  would  lay  two  to  one  upon  it.  It  is  true,  there 
might,  for  aught  we  knew,  be  more  white  balls  than  black  and  red  together ; 
and  if  so,  our  bet  would,  if  we  knew  more,  be  seen  to  be  a disadvantageous 
one.  But  so  also,  for  aught  we  knew,  might  there  be  more  red  balls  than 
black  and  white,  or  more  black  balls  than  white  and  red,  and  in  such  case 


OF  THE  CALCULATION  OF  CHANCES. 


381 


the  effect  of  additional  knowledge  would  be  to  prove  to  us  that  our  bet 
was  more  advantageous  than  we  had  supposed  it  to  be.  There  is  in  the 
existing  state  of  our  knowledge  a rational  probability  of  two  to  one  against 
white;  a probability  tit  to  be  made  a basis  of  conduct.  ISfo  reasonable 
person  would  lay  an  even  wager  in  favor  of  white  against  black  and  red ; 
though  against  black  alone  or  red  alone  he  might  do  so  without  impru- 
dence. 

The  common  theory,  therefore,  of  the  calculation  of  chances,  appears  to 
be  tenable.  Even  when  we  know  nothing  except  the  number  of  the  possi- 
ble and  mutually  excluding  contingencies,  and  are  entirely  ignorant  of  their 
comparative  frequency,  we  may  have  grounds,  and  grounds  numerically  ap- 
preciable, for  acting  on  one  supposition  rather  than  on  another;  and  this 
is  the  meaning  of  Probability. 

§ 3.  The  principle,  however,  on  which  the  reasoning  proceeds,  is  suffi- 
ciently evident.  It  is  the  obvious  one  that  when  the  cases  which  exist  are 
shared  among  several  kinds,  it  is  impossible  that  each  of  those  kinds 
should  be  a majority  of  the  whole : on  the  contrary,  there  must  be  a ma- 
jority against  each  kind,  except  one  at  most ; and  if  any  kind  has  more 
than  its  share  in  proportion  to  the  total  number,  the  others  collectively 
must  have  less.  Granting  this  axiom,  and  assuming  that  we  have  no 
ground  for  selecting  any  one  kind  as  more  likely  than  the  rest  to  surpass 
the  average  proportion,  it  follows  that  we  can  not  rationally  presume  this 
of  any,  which  we  should  do  if  we  were  to  bet  in  favor  of  it,  receiving  less 
odds  than  in  the  ratio  of  the  number  of  the  other  kinds.  Even,  therefore, 
in  this  extreme  case  of  the  calculation  of  probabilities,  which  does  not  rest 
on  special  experience  at  all,  the  logical  ground  of  the  process  is  our  knowl- 
edge— such  knowledge  as  we  then  have — of  the  laws  governing  the  fre- 
quency of  occurrence  of  the  different  cases;  but  in  this  case  the  knowledge 
is  limited  to  that  Udiich,  being  universal  and  axiomatic,  does  not  require 
reference  to  specific  experience,  or  to  any  considerations  arising  out  of  the 
special  nature  of  the  problem  under  discussion. 

Except,  however,  in  such  cases  as  games  of  chance,  where  the  very  pur- 
pose in  view  requires  ignorance  instead  of  knowledge,  I can  conceive  no 
case  in  which  we  ought  to  be  satisfied  with  such  an  estimate  of  chances  as 
this— -an  estimate  founded  on  the  absolute  minimum  of  knowledge  respect- 
ing the  subject.  It  is  plain  that,  in  the  case  of  the  colored  balls,  a very 
slight  ground  of  surmise  that  the  white  balls  were  really  more  numerous 
than  either  of  the  other  colors,  would  suffice  to  vitiate  the  whole  of  the  cal- 
culations made  in  our  previous  state  of  indifference.  It  would  place  us  in 
that  position  of  more  advanced  knowledge,  in  which  the  probabilities,  to  us, 
would  be  different  from  what  they  were  before ; and  in  estimating  these 
new  probabilities  we  should  have  to  proceed  on  a totally  different  set  of 
data,  furnished  no  longer  by  mere  counting  of  possible  suppositions,  but  by 
specific  knowledge  of  facts.  Such  data  it  should  always  be  our  endeavor 
to  obtain;  and  in  all  inquiries,  unless  on  subjects  equally  beyond  the  range 
of  our  means  of  knowledge  and  our  practical  uses,  they  may  be  obtained, 
if  not  good,  at  least  better  than  none  at  all.* 

* It  even  appears  to  me  that  the  calculation  of  chances,  where  there  are  no  data  grounded 
either  on  special  experience  or  on  special  inference,  must,  in  an  immense  majority  of  cases, 
break  down,  from  sheer  impossibility  of  assigning  any  principle  by  which  to  be  guided  in  set- 
ting out  the  list  of  possibilities.  In  the  case  of  the  colored  balls  we  have  no  difficulty  in  mak- 
ing the  enumeration,  because  we  ourselves  determine  what  the  possibilities  shall  be.  But 


382 


INDUCTION. 


It  is  obvious,  too,  that  even  when  the  probabilities  are  derived  from  ob- 
servation and  experiment,  a very  slight-  improvement  in  the  data,  by  better 
observations,  or  by  taking  into  fuller  consideration  the  special  circumstances 
of  the  case,  is  of  more  use  than  the  most  elaborate  application  of  the  cal- 
culus to  probabilities  founded  on  the  data  in  their  previous  state  of  inferi- 
ority. The  neglect  of  this  obvious  reflection  has  given  rise  to  misapplica- 
tions of  the  calculus  of  probabilities  which  have  made  it  the  real  oppro- 
brium of  mathematics.  It  is  sufficient  to  refer  to  the  applications  made  of 
it  to  the  credibility  of  witnesses,  and  to  the  correctness  of  the  verdicts  of 
juries.  In  regard  to  the  first,  common  sense  would  dictate  that  it  is  im- 
possible to  strike  a general  average  of  the  veracity  and  other  qualifications 
for  true  testimony  of  mankind,  or  of  any  class  of  them  ; and  even  if  it  were 
possible,  the  employment  of  it  for  such  a purpose  implies  a misapprehen- 
sion of  the  use  of  averages,  which  serve,  indeed,  to  protect  those  whose  in- 
terest is  at  stake,  against  mistaking  the  general  result  of  large  masses  of 
instances,  but  are  of  extremely  small  value  as  grounds  of  expectation  in  any 
one  individual  instance,  unless  the  case  be  one  of  those  in  which  the  great 
majority  of  individual  instances  do  not  differ  much  from  the  average.  In 
the  case  of  a witness,  persons  of  common  sense  would  draw  their  conclu- 
sions from  the  degree  of  consistency  of  his  statements,  his  conduct  under 
cross-examination,  and  the  relation  of  the  case  itself  to  his  interests,  his 
partialities,  and  his  mental  capacity,  instead  of  applying  so  rude  a standard 
(even  if  it  were  capable  of  being  verified)  as  the  ratio  between  the  num- 
ber of  true  and  the  number  of  erroneous  statements  which  he  may  be  sup- 
posed to  make  in  the  course  of  his  life. 

Again,  on  the  subject  of  juries  or  other  tribunals,  some  mathematicians 
have  set  out  from  the  proposition  that  the  judgment  of  any  one  judge  or 
juryman  is,  at  least  in  some  small  degree,  more  likely  to  be  right  than 
wrong,  and  have  concluded  that  the  chance  of  a number  of  persons  concur- 
ring in  a wrong  verdict  is  diminished  the  more  the  rtatuber  is  increased; 
so  that  if  the  judges  are  only  made  sufficiently  numerous,  the  correctness 
of  the  judgment  may  be  reduced  almost  to  certainty.  I say  nothing  of  the 
disregard  shown  to  the  effect  produced  on  the  moral  position  of  the  judges 
by  multiplying  their  numbers,  the  virtual  destruction  of  their  individual 
responsibility,  and  weakening  of  the  application  of  their  minds  to  the  sub- 
ject. I remark  only  the  fallacy  of  reasoning  from  a wide  average  to  cases 
necessarily  differing  greatly  from  any  average.  It  may  be  true  that,  taking- 
all  causes  one  with  another,  the  opinion  of  any  one  of  the  judges  would  be 
oftener  right  than  wrong;  but  the  argument  forgets  that  in  all  but  the 
more  simple  cases,  in  all  cases  in  which  it  is  really  of  much  consequence 
what  the  tribunal  is,  the  proposition  might  probably  be  reversed ; besides 
which,  the  cause  of  error,  whether  arising  from  the  intricacy  of  the  case  or 
from  some  common  prejudice  or  mental  infirmity,  if  it  acted  upon  one 
judge,  would  be  extremely  likely  to  affect  all  the  others  in  the  same  man- 

snppose  a case  more  analogous  to  those  which  occur  in  nature : instead  of  three  colors,  let 
there  he  in  the  box  all  possible  colors,  we  being  supposed  ignorant  of  the  comparative  fre- 
quency with  which  different  colors  occur  in  nature,  or  in  the  productions  of  art.  How  is  the 
list  of  cases  to  be  made  out?  Is  every  distinct  shade  to  count  as  a color?  If  so,  is  the  test 
to  be  a common  eye,  or  an  educated  eye — a painter’s,  for  instance?  On  the  answer  to  these 
questions  would  depend  whether  the  chances  against  some  particular  color  would  be  esti- 
mated at  ten,  twenty,  or  perhaps  five  hundred  to  one.  While  if  we  knew  from  experience 
that  the  particular  color  occurs  on  an  average  a certain  number  of  times  in  every  hundred  or 
thousand,  we  should  not  require  to  know  any  thing  either  of  the  frequency  or  of  the  number 
of  the  other  possibilities. 


OF  THE  CALCULATION  OF  CHANCES. 


383 


ner,  or  at  least  a majority,  and  thus  render  a wrong  instead  of  a right  de- 
cision more  probable  the  more  the  number  was  increased. 

These  are  but  samples. of  the  errors  frequently  committed  by  men  who, 
having  made  themselves  familiar  with  the  difficult  formulae  which  algebra 
affords  for  the  estimation  of  chances  under  suppositions  of  a complex  char- 
acter, like  better  to  employ  those  formulae  in  computing  what  are  the  prob- 
abilities to  a person  half  informed  about  a case  than  to  look  out  for  means 
of  being  better  informed.  Before  applying  the  doctrine  of  chances  to  any 
scientific  purpose,  the  foundation  must  be  laid  for  an  evaluation  of  the 
chances,  by  possessing  ourselves  of  the  utmost  attainable  amount  of  posi- 
tive knowledge.  The  knowledge  required  is  that  of  the  comparative  fre- 
quency with  which  the  different  events  in  fact  occur.  For  the  purposes, 
therefore,  of  the  present  work,  it  is  allowable  to  suppose  that  conclusions 
respecting  the  probability  of  a fact  of  a particular  kind  rest  on  our  knowl- 
edge of  the  proportion  between  the  cases  in  which  facts  of  that  kind  occur, 
and  those  in  which  they  do  not  occur;  this  knowledge  being  either  de- 
rived from  specific  experiment,  or  deduced  from  our  knowledge  of  the 
causes  in  operation  which  tend  to  produce,  compared  with  those  which 
tend  to  prevent,  the  fact  in  question. 

Such  calculation  of  chances  is  grounded  on  an  induction ; and  to  render 
the  calculation  legitimate,  the  induction  must  be  a valid  one.  It  is  not 
less  an  induction,  though  it  does  not  prove  that  the  event  occurs  in  all 
cases  of  a given  description,  but  only  that  out  of  a given  number  of  such 
cases  it  occurs  in  about  so  many.  The  fraction  which  mathematicians  use 
to  designate  the  probability  of  an  event  is  the  ratio  of  these  two  numbers ; 
the  ascertained  proportion  between  the  number  of  cases  in  which  the  event 
occurs  and  the  sum  of  all  the  cases,  those  in  which  it  occurs  and  in  which 
it  does  not  occur,  taken  together.  In  playing  at  cross  and  pile,  the  descrip- 
tion of  cases  concerned  are  throws,  and  the  probability  of  cross  is  one-half, 
because  if  we  throw  often  enough  cross  is  thrown  about  once  in  every  two 
throws.  In  the  cast  of  a die,  the  probability  of  ace  is  one-sixth ; not  sim- 
ply because  there  are  six  possible  throws,  of  which  ace  is  one,  and  because 
we  do  not  know  any  reason  why  one  should  turn  up  rather  than  another — 
though  I have  admitted  the  validity  of  this  ground  in  default  of  a better — 
but  because  we  do  actually  know,  either  by  reasoning  or  by  experience, 
that  in  a hundred  or  a million  of  throws  ace  is  thrown  in  about  one-sixth 
of  that  number,  or  once  in  six  times. 

§ 4.  I say,  “ either  by  reasoning  or  by  experience,”  meaning  specific  ex- 
perience. But  in  estimating  probabilities,  it  is  not  a matter  of  indifference 
from  which  of  these  two  sources  we  derive  our  assurance.  The  probabili- 
ty of  events,  as  calculated  from  their  mere  frequency  in  past  experience, 
affords  a less  secure  basis  for  practical  guidance  than  their  probability  as 
deduced  from  an  equally  accurate  knowledge  of  the  frequency  of  occur- 
rence of  their  causes. 

The  generalization  that  an  event  occurs  in  ten  out  of  every  hundred  cases 
of  a given  description,  is  as  real  an  induction  as  if  the  generalization  were 
that  it  occurs  in  all  cases.  But  when  we  arrive  at  the  conclusion  by  mere- 
ly counting  instances  in  actual  experience,  and  comparing  the  number  of 
cases  in  which  A has  been  present  with  the  number  in  which  it  lias  been 
absent,  the  evidence  is  only  that  of  the  Method  of  Agreement,  and  the  con- 
clusion amounts  only  to  an  empirical  law.  We  can  make  a step  beyond 
this  when  we  can  ascend  to  the  causes  on  which  the  occurrence  of  A or  its 


3S4 


INDUCTION. 


non-occurrence  will  depend,  and  form  an  estimate  of  the  comparative  fre- 
quency of  the  causes  favorable  and  of  those  unfavorable  to  the  occurrence. 
These  are  data  of  a higher  order,  by  which  the  empirical  law  derived  from 
a mere  numerical  comparison  of  affirmative  and  negative  instances  will  be 
either  corrected  or  confirmed,  and  in  either  case  we  shall  obtain  a more 
correct  measure  of  probability  than  is  given  by  that  numerical  comparison. 
It  has  been  well  remarked  that  in  the  kind  of  examples  by  which  the  doc- 
trine of  chances  is  usually  illustrated,  that  of  balls  in  a box,  the  estimate 
of  probabilities  is  supported  by  reasons  of  causation,  stronger  than  specific 
experience.  “ What  is  the  reason  that  in  a box  where  there  are  nine  black 
balls  and  one  white,  we  expect  to  draw  a black  ball  nine  times  as  much  (in 
other  words,  nine  times  as  often,  frequency  being  the  gauge  of  intensity  in 
expectation)  as  a white  ? Obviously  because  the  local  conditions  are  nine 
times  as  favorable;  because  the  hand  may  alight  in  nine  places  and  get  a 
black  ball,  while  it  can  only  alight  in  one  place  and  find  a white  ball;  just 
lor  the  same  reason  that  we  do  not  expect  to  succeed  in  finding  a friend 
in  a crowd,  the  conditions  in  order  that  we  and  he  should  come  together 
being  many  and  difficult.  This  of  course  would  not  hold  to  the  same  ex- 
tent were  the  white  balls  of  smaller  size  than  the  black,  neither  would  the 
probability  remain  the  same ; the  larger  ball  would  be  much  more  likely 
to  meet  the  hand.”* 

It  is,  in  fact,  evident  that  when  once  causation  is  admitted  as  a universal 
law,  our  expectation  of  events  can  only  be  rationally  grounded  on  that  law. 
To  a person  who  recognizes  that  every  event  depends  on  causes,  a thing’s 
having  happened  once  is  a reason  for  expecting  it  to  happen  again,  only  be- 
cause proving  that  there  exists,  or  is  liable  to  exist,  a cause  adequate  to 
produce  it.f  The  frequency  of  the  particular  event,  apart  from  all  surmise 
respecting  its  cause,  can  give  rise  to  no  other  induction  than  that  per  enu- 
merationem  simplicem ; and  the  precarious  inferences  derived  from  this  are 
superseded,  and  disappear  from  the  field  as  soon  as  the  principle  of  causa- 
tion makes  its  appearance  there. 

Notwithstanding,  however,  the  abstract  superiority  of  an  estimate  of 
probability  grounded  on  causes,  it  is  a fact  that  in  almost  all  cases  in 
which  chances  admit  of  estimation  sufficiently  precise  to  render  their 
numerical  appreciation  of  any  practical  value,  the  numerical  data  are  not 
drawn  from  knowledge  of  the  causes,  but  from  experience  of  the  events 

* Prospective  Review  for  February,  1 850. 

+ “If  this  be  npt  so,  why  do  we  feel  so  much  more  probability  added  by  the  first  instance 
than  by  any  single  subsequent  instance?  Why,  except  that  the  first  instance  gives  us  its  pos- 
sibility (a  cause  adequate  to  it),  while  every  other  only  gives  us  the  frequency  of  its  conditions? 
If  no  reference  to  a cause  be  supposed,  possibility  would  have  no  meaning;  yet  it  is  clear  that, 
antecedent  to  its  happening,  we  might  have  supposed  the  event  impossible,  i.  e.,  have  believed 
that  there  was  no  physical  energy  really  existing  in  the  world  equal  to  producing  it Af- 

ter the  first  time  of  happening,  which  is,  then,  more  important  to  the  whole  probability  than 
any  other  single  instance  (because  proving  the  possibility),  the  number  of  times  becomes  im- 
portant as  an  index  to  the  intensity  or  extent  of  the  cause,  and  its  independence  of  any  par- 
ticular time.  If  we  took  the  case  of  a tremendous  leap,  for  instance,  and  wished  to  form  an 
estimate  of  the  probability  of  its  succeeding  a certain  number  of  times;  the  first  instance,  by 
showing  its  possibility  (before  doubtful)  is  of  the  most  importance ; but  every  succeeding  leap 
shows  the  power  to  be  more  perfectly  under  control,  greater  and  more  invariable,  and  so  in- 
creases the  probability;  and  no  one  would  tbink  of  reasoning  in  this  case  straight  from  one 
instance  to  the  next,  without  referring  to  the  physical  energy  which  each  leap  indicated.  Is 
it  not,  then,  clear  that  we  do  not  ever”  (let  us  rather  say,  that  we  do  not  in  an  advanced  state 
of  our  knowledge)  “ conclude  directly  from  the  happening  of  an  event  to  the  probability  of  its 
happening  again ; but  that  we  refer  to  the  cause,  regarding  the  past  cases  as  an  index  to  the 
cause,  and  the  cause  as  our  guide  to  the  future?” — Ibid. 


OF  THE  CALCULATION  OF  CHANCES. 


385 


themselves.  The  probabilities  of  life  at  different  ages  or  in  different  cli- 
mates; the  probabilities  of  recovery  from  a particular  disease;  the  chances 
of  the  birth  of  male  or  female  offspring ; the  chances  of  the  destruction  of 
houses  or  other  property  by  tire;  the  chances  of  the  loss  of  a ship  in  a 
particular  voyage,  are  deduced  from  bills  of  mortality,  returns  from  hos- 
pitals, registers  of  births,  of  shipwrecks,  etc.,  that  is,  from  the  observed 
frequency  not  of  the  causes,  but  of  the  effects.  The  reason  is,  that  in  all 
these  classes  of  facts  the  causes  are  either  not  amenable  to  direct  observa- 
tion at  all,  or  not  with  the  requisite  precision,  and  we  have  no  means  of 
judging  of  their  frequency  except  from  the  empirical  law  afforded  by  the 
frequency  of  the  effects.  The  inference  does  not  the  less  depend  on  cau- 
sation alone.  We  reason  from  an  effect  to  a similar  effect  by  passing 
through  the  cause.  If  the  actuary  of  an  insurance  office  infers  from  his 
tables  that  among  a hundred  persons  now  living  of  a particular  age,  five 
on  the  average  will  attain  the  age  of  seventy,  his  inference  is  legitimate, 
not  for  the  simple  reason  that  this  is  the  proportion  who  have  lived  till 
seventy  in  times  past,  but  because  the  fact  of  their  having  so  lived  shows 
that  this  is  the  proportion  existing,  at  that  place  and  time,  between  the 
causes  which  prolong  life  to  the  age  of  seventy  and  those  tending  to  bring 
it  to  an  earlier  close.* 

§ 5.  From  the  preceding  principles  it  is  easy  to  deduce  the  demonstra- 
tion of  that  theorem  of  the  doctrine  of  probabilities  which  is  the  founda- 
tion of  its  application  to  inquiries  for  ascertaining  the  occurrence  of  a 
given  event,  or  the  reality  of  an  individual  fact.  The  signs  or  evidences  by 
which  a fact  is  usually  proved  are  some  of  its  consequences ; and  the  in- 
quiry hinges  upon  determining  what  cause  is  most  likely  to  have  produced 
a given  effect.  The  theorem  applicable  to  such  investigations  is  the  Sixth 
Principle  in  Laplace’s  “Pssai  Philosophique  sur  les  Probability ,”  which  is 
described  by  him  as  the  “ fundamental  principle  of  that  branch  of  the  Analy- 
sis of  Chances  which  consists  in  ascending  front  events  to  their  causes.”! 

Given  an  effect  to  be  accounted  for,  and  there  being  several  causes  which 
might  have  produced  it,  but  of  the  presence  of  which  in  the  particular  case 
nothing  is  known  ; the  probability  that  the  effect  was  produced  by  any  one 
of  these  causes  is  as  the  antecedent  probability  of  the  cause,  multiplied  by 
the  probability  that  the  cause,  if  it  existed,  icould  have  produced  the  given 
effect. 

Let  M be  the  effect,  and  A,  B,  two  causes,  by  either  of  which  it  might 

* The  writer  last  quoted  says  that  the  valuation  of  chances  by  comparing  the  number  of 
cases  in  which  the  event  occurs  with  the  number  in  which  it  does  not  occur,  “would  gen- 
erally be  wholly  erroneous,”  and  “is  not  the  true  theory  of  probability.”  It  is  at  least  that 
which  forms  the  foundation  of  insurance,  and  of  all  those  calculations  of  chances  in  the  busi- 
ness of  life  which  experience  so  abundantly  verifies.  The  reason  which  the  reviewer  gives  for 
rejecting  the  theory  is,  that  it  “would  regard  an  event  as  certain  which  had  hitherto  never 
failed;  which  is  exceedingly  far  from  the  truth,  even  for  a very  large  number  of  constant  suc- 
cesses.” This  is  not  a defect  in  a particular  theory,  but  in  any  theory  of  chances.  No  prin- 
ciple of  evaluation  can  provide  for  such  a case  as  that  which  the  reviewer  supposes.  If  an 
event  has  never  once  failed,  in  a number  of  trials  sufficient  to  eliminate  chance,  it  really  has 
all  the  certainty  which  can  be  given  by  an  empirical  law;  it  is  certain  during  the  continuance 
of  the  same  collocation  of  causes  which  existed  during  the  observations.  If  it  ever  fails,  it  is 
in  consequence  of  some  change  in  that  collocation.  Now,  no  theory  of  chances  will  enable  us 
to  infer  the  future  probability  of  an  event  from  the  past,  if  the  causes  in  operation,  capable  of 
influencing  the  event,  have  intermediately  undergone  a change. 

t Pp.  18,  19.  The  theorem  is  not  stated  by  Laplace  in  the  exact  terms  in  which  I have 
stated  it ; but  the  identity  of  import  of  the  two  modes  of  expression  is  easily  demonstrable. 

25 


386 


INDUCTION. 


have  been  produced.  To  find  the  probability  that  it  was  produced  by  the 
one  and  not  by  the  other,  ascertain  which  of  the  two  is  most  likely  to  have 
existed,  and  which  of  them,  if  it  did  exist,  was  most  likely  to  produce  the 
effect  M:  the  probability  sought  is  a compound  of  these  two  probabilities. 

Case  I.  Let  the  causes  be  both  alike  in  the  second  respect:  either  A or 
B,  when  it  exists,  being  supposed  equally  likely  (or  equally  certain)  to  pro- 
duce M;  but  let  A be  in  itself  twice  as  likely  as  B to  exist,  that  is,  twice 
as  frequent  a phenomenon.  Then  it  is  twice  as  likely  to  have  existed  in 
this  case,  and  to  have  been  the  cause  which  produced  M. 

For,  since  A exists  in  nature  twice  as  often  as  B,  in  any  300  cases  in 
which  one  or  other  existed,  A has  existed  200  times  and  B 100.  But  ei- 
ther A or  B must  have  existed  wherever  M is  produced;  therefore,  in  300 
times  that  M is  produced,  A was  the  producing  cause  200  times,  B only 
100,  that  is,  in  the  ratio  of  2 to  1.  Thus,  then,  if  the  causes  are  alike  in 
their  capacity  of  producing  the  effect,  the  probability  as  to  which  actually 
produced  it  is  in  the  ratio  of  their  antecedent  probabilities. 

Case  II.  Reversing  the  last  hypothesis,  let  us  suppose  that  the  causes 
are  equally  frequent,  equally  likely  to  have  existed,  but  not  equally  likely,  if 
they  did  exist,  to  produce  M;  that  in  three  times  in  which  A occurs,  it 
produces  that  effect  twice,  while  B,  in  three  times,  produces  it  only  once. 
Since  the  two  causes  are  equally  frequent  in  their  occurrence;  in  every  six 
times  that  either  one  or  the  other  exists,  A exists  three  times  and  B three 
times.  A,  of  its  three  times,  produces  M in  two;  B,  of  its  three  times, 
produces  M in  one.  Thus,  in  the  whole  six  times,  M is  only  produced 
thrice;  but  of  that  thrice  it  is  produced  twice  by  A,  once  only  by  B.  Con- 
sequently, when  the  antecedent  probabilities  of  the  causes  are  equal,  the 
chances  that  the  effect  was  produced  by  them  are  in  the  ratio  of  the  proba- 
bilities that  if  they  did  exist  they  would  produce  the  effect. 

Case  III.  The  third  case,  that  in  which  the  causes  are  unlike  in  both  re- 
spects, is  solved  by  what  has  preceded.  For,  when  a quantity  depends  on 
two  other  quantities,  in  such  a manner  that  while  either  of  them  remains 
constant  it  is  proportional  to  the  other,  it  must  necessarily  be  proportional 
to  the  product  of  the  two  quantities,  the  product  being  the  oidy  function 
of  the  two  which  obeys  that  law  of  variation.  Therefore,  the  probability 
that  M was  produced  by  either  cause,  is  as  the  antecedent  probability  of 
the  cause,  multiplied  by  the  probability  that  if  it  existed  it  would  produce 
M.  Which  was  to  be  demonstrated. 

Or  we  may  prove  the  third  case  as  we  proved  the  first  and  second.  Let 
A be  twice  as  frequent  as  B,  and  let  them  also  be  unequally  likely,  when 
they  exist,  to  produce  M;  let  A produce  it  twice  in  four  times,  B thrice  in 
four  times.  The  antecedent  probability  of  A is  to  that  of  B as  2 to  1 ; 
the  probabilities  of  their  producing  M are  as  2 to  3 ; the  product  of  these 
ratios  is  the  ratio  of  4 to  3 ; and  this  will  be  the  ratio  of  the  probabilities 
that  A or  B was  the  producing  cause  in  the  given  instance.  For,  since  A 
is  twice  as  frequent  as  B,  out  of  twelve  cases  in  which  one  or  other  exists, 
A exists  in  8 and  B in  4.  But  of  its  eight  cases,  A,  by  the  supposition, 
produces  M in  only  4,  while  B of  its  four  cases  produces  M in  3.  M,  there- 
fore, is  only  produced  at  all  in  seven  of  the  twelve  cases;  but  in  four  of 
these  it  is  produced  by  A,  in  three  by  B;  hence  the  probabilities  of  its  be- 
ing produced  by  A and  by  B are  as  4 to  3,  and  are  expressed  by  the  frac- 
tions $ and  f.  Which  was  to  be  demonstrated. 

§ 6.  It  remains  to  examine  the  bearing  of  the  doctrine  of  chances  on 


OF  THE  CALCULATION  OF  CHANCES. 


3S7 


the  peculiar  problem  which  occupied  us  in  the  preceding  chapter,  namely, 
how  to  distinguish  coincidences  which  are  casual  from  those  which  are  the 
result  of  law;  from  those  in  which  the  facts  which  accompany  or  follow 
one  another  are  somehow  connected  through  causation. 

The  doctrine  of  chances  affords  means  by  which,  if  we  knew  the  average 
number  of  coincidences  to  be  looked  for  between  two  phenomena  connected 
only  casually,  we  could  determine  how  often  any  given  deviation  from  that 
average  will  occur  by  chance.  If  the  probability  of  any  casual  coincidence, 

considered  in  itself,  be  — , the  probability  that  the  same  coincidence  will 

m 

be  repeated  n times  in  succession  is  — . For  example,  in  one  throw  of  a 
die  the  probability  of  ace  being  the  probability  of  throwing  ace  twice 

in  succession  will  be  1 divided  by  the  square  of  6,  or  — . For  ace  is  thrown 

at  the  first  throw  once  in  six,  or  six  in  thirty-six  times,  and  of  those  six,  the 
die  being  cast  again,  ace  will  be  thrown  but  once ; being  altogether  once  in 
thirty-six  times.  The  chance  of  the  same  cast  three  times  successively  is, 

by  a similar  reasoning,  ~ or  — j— ; that  is,  the  event  will  happen,  on  a large 

D jj  L U 

average,  only  once  in  two  hundred  and  sixteen  throws. 

We  have  thus  a rule  by  which  to  estimate  the  probability  that  any  given 
series  of  coincidences  arises  from  chance,  provided  we  can  measure  correct- 
ly the  probability  of  a single  coincidence.  If  we  can  obtain  an  equally 
precise  expression  for  the  probability  that  the  same  series  of  coincidences 
arises  from  causation,  we  should  only  have  to  compare  the  numbers.  This, 
however,  can  rarely  be  done.  Let  us  see  what  degree  of  approximation 
can  practically  be  made  to  the  necessary  precision. 

The  question  falls  within  Laplace’s  sixth  principle,  just  demonstrated. 
The  given  fact,  that  is  to  say,  the  series  of  coincidences,  may  have  origi- 
nated either  in  a casual  conjunction  of  causes  or  in  a law  of  nature.  The 
probabilities,  therefore,  that  the  fact  originated  in  these  two  modes,  are  as 
their  antecedent  probabilities,  multiplied  by  the  probabilities  that  if  they 
existed  they  would  produce  the  effect.  But  the  particular  combination  of 
chances,  if  it  occurred,  or  the  law  of  nature  if  real,  would  certainly  produce 
the  series  of  coincidences.  The  probabilities,  therefore,  that  the  coinci- 
dences are  produced  by  the  two  causes  in  question  are  as  the  antecedent 
probabilities  of  the  causes.  One  of  these,  the  antecedent  probability  of  the 
combination  of  mere  chances  which  would  produce  the  given  result,  is  an 
appreciable  quantity.  The  antecedent  probability  of  the  other  supposition 
may  be  susceptible  of  a more  or  less  exact  estimation,  according  to  the  na- 
ture of  the  case. 

In  some  cases,  the  coincidence,  supposing  it  to  be  the  result  of  causation 
at  all,  must  be  the  result  of  a known  cause ; as  the  succession  of  aces,  if  not 
accidental,  must  arise  from  the  loading  of  the  die.  In  such  cases  we  may 
be  able  to  form  a conjecture  as  to  the  antecedent  probability  of  such  a cir- 
cumstance from  the  characters  of  the  parties  concerned,  or  other  such  evi- 
dence ; but  it  would  be  impossible  to  estimate  that  probability  with  any- 
thing like  numerical  precision.  The  counter-probability,  however,  that  of 
the  accidental  origin  of  the  coincidence,  dwindling  so  rapidly  as  it  does  at 
each  new  trial,  the  stage  is  soon  reached  at  which  the  chance  of  unfairness 


3S8 


INDUCTION. 


in  the  die,  however  small  in  itself,  must  be  greater  than  that  of  a casual 
coincidence ; and  on  this  ground,  a practical  decision  can  generally  be  come 
to  without  much  hesitation,  if  there  be  the  power  of  repeating  the  experi- 
ment. 

When,  however,  the  coincidence  is  one  which  can  not  be  accounted  for 
by  any  known  cause,  and  the  connection  between  the  two  phenomena,  if 
produced  by  causation,  must  be  the  result  of  some  law  of  nature  hitherto 
unknown;  which  is  the  case  we  had  in  view  in  the  last  chapter;  then, 
though  the  probability  of  a casual  coincidence  may  be  capable  of  apprecia- 
tion, that  of  the  counter-supposition,  the  existence  of  an  undiscovered  law 
of  nature,  is  clearly  unsusceptible  of  even  an  approximate  valuation.  In 
order  to  have  the  data  which  such  a case  would  require,  it  would  be  neces- 
sary to  know  what  proportion  of  all  the  individual  sequences  or  co-exist- 
ences  occurring  in  nature  are  the  result  of  law,  and  what  proportion  are 
mere  casual  coincidences.  It  being  evident  that  we  can  not  form  any 
plausible  conjecture  as  to  this  proportion,  much  less  appreciate  it  numer- 
ically, we  can  not  attempt  any  precise  estimation  of  the  comparitive  proba- 
bilities. But  of  this  we  are  sure,  that  the  detection  of  an  unknown  law  of 
nature — of  some  previously  unrecognized  constancy  of  conjunction  among 
phenomena — is  no  uncommon  event.  If,  therefore,  the  number  of  instances 
in  which  a coincidence  is  observed,  over  and  above  that  which  would  arise 
on  the  average  from  the  mere  concurrence  of  chances,  be  such  that  so  great 
an  amount  of  coincidences  from  accident  alone  would  be  an  extremely  un- 
common event ; we  have  reason  to  conclude  that  the  coincidence  is  the  ef- 
fect of  causation,  and  may  be  received  (subject  to  correction  from  further 
experience)  as  an  empirical  law.  Further  than  this,  in  point  of  precision, 
we  can  not  go;  nor,  in  most  cases,  is  greater  precision  required,  for  the 
solution  of  any  practical  doubt.* 


CHAPTER  XIX. 

OF  THE  EXTENSION  OF  DERIVATIVE  LAWS  TO  ADJACENT  CASES. 

§ 1.  We  have  had  frequent  occasion  to  notice  the  inferior  generality  of 
derivative  laws,  compared  with  the  ultimate  laws  from  which  they  are  de- 
rived. This  inferiority,  which  affects  not  only  the  extent  of  the  proposi- 
tions themselves,  but  their  degree  of  certainty  within  that  extent,  is  most 
conspicuous  in  the  uniformities  of  co-existence  and  sequence  obtaining  be- 
tween effects  which  depend  ultimately  on  different  primeval  causes.  Such 
uniformities  will  only  obtain  where  there  exists  the  same  collocation  of 
those  primeval  causes.  If  the  collocation  varies,  though  the  laws  them- 
selves remain  the  same,  a totally  different  set  of  derivative  uniformities 
may,  and  generally  will,  be  the  result. 

Even  where  the  derivative  uniformity  is  between  different  effects  of  the 
same  cause,  it  will  by  no  means  obtain  as  universally  as  the  law  of  the 

* For  a fuller  treatment  of  the  many  interesting  questions  raised  by  the  theory  of  probabili- 
ties, I may  now  refer  to  a recent  work  by  Mr.  Venn,  Fellow  of  Caius  College,  Cambridge, 
“The  Logic  of  Chance;”  one  of  the  most  thoughtful  and  philosophical  treatises  on  any  sub- 
ject connected  with  Logic  and  Evidence  which  have  been  produced,  to  my  knowledge,  for 
many  years.  Some  criticisms  contained  in  it  have  been  very  useful  to  me  in  revising  the  cor- 
responding chapters  of  the  present  work.  In  several  of  Mr.  Venn’s  opinions,  however,  I do 
not  agree.  What  these  are  will  be  obvious  to  any  reader  of  Mr.  Venn’s  work  who  is  also  a 
reader  of  this. 


EXTENSION  OF  LAWS  TO  ADJACENT  CASES. 


389 


cause  itself.  If  a and  b accompany  or  succeed  one  another  as  effects  of  the 
cause  A,  it  by  no  means  follows  that  A is  the  only  cause  which  can  pro- 
duce them,  or  that  if  there  be  another  cause,  as  B,  capable  of  producing  a, 
it  must  produce  b likewise.  The  conjunction,  therefore,  of  a and  b perhaps 
does  not  hold  universally,  but  only  in  the  instances  in  which  a arises  from 
A.  When  it  is  produced  by  a cause  other  than  A,  a and  b may  be  dissev- 
ered. Day  (for  example)  is  always  in  our  experience  followed  by  night; 
but  day  is  not  the  cause  of  night ; both  are  successive  effects  of  a common 
cause,  the  periodical  passage  of  the  spectator  into  and  out  of  the  earth’s 
shadow,  consequent  on  the  earth’s  rotation,  and  on  the  illuminating  prop- 
erty of  the  sun.  If,  therefore,  day  is  ever  produced  by  a different  cause 
or  set  of  causes  from  this,  day  will  not,  or  at  least  may  not,  be  followed  by 
night.  On  the  sun’s  own  surface,  for  instance,  this  may  be  the  case. 

Finally,  even  when  the  derivative  uniformity  is  itself  a law  of  causation 
(resulting  from  the  combination  of  several  causes),  it  is  not  altogether  in- 
dependent of  collocations.  If  a cause  supervenes,  capable  of  wholly  or  par- 
tially counteracting  the  effect  of  any  one  of  the  conjoined  causes,  the  effect 
will  no  longer  conform  to  the  derivative  law.  While,  therefore,  each  ulti- 
mate law  is  only  liable  to  frustration  from  one  set  of  counteracting  causes, 
the  derivative  law  is  liable  to  it  from  several.  Now,  the  possibility  of  the 
occurrence  of  counteracting  causes  which  do  not  arise  from  any  of  the  con- 
ditions involved  in  the  law  itself  depends  on  the  original  collocations. 

It  is  true  that,  as  we  formerly  remarked,  laws  of  causation,  whether  ulti- 
mate or  derivative,  are,  in  most  eases,  fulfilled  even  when  counteracted ; 
the  cause  produces  its  effect,  though  that  effect  is  destroyed  by  something 
else.  That  the  effect  may  be  frustrated,  is,  therefore,  no  objection  to  the 
universality  of  laws  of  causation.  But  it  is  fatal  to  the  universality  of  the 
sequences  or  co-existences  of  effects,  which  compose  the  greater  part  of  the 
derivative  laws  flowing  from  laws  of  causation.  When,  from  the  law  of  a 
certain  combination  of  causes,  there  results  a certain  order  in  the  effects ; 
as  from  the  combination  of  a single  sun  with  the  rotation  of  an  opaque 
body  round  its  axis,  there  results,  on  the  whole  surface  of  that  opaque 
body,  an  alternation  of  day  and  night;  then,  if  we  suppose  one  of  the  com- 
bined causes  counteracted,  the  rotation  stopped,  the  sun  extinguished,  or  a 
second  sun  superadded,  the  truth  of  that  particular  law  of  causation  is  in 
no  way  affected  ; it  is  still  true  that  one  sun  shining  on  an  opaque  revolv- 
ing body  will  alternately  produce  day  and  night;  but  since  the  sun  no 
longer  does  shine  on  such  a body,  the  derivative  uniformity,  the  succession 
of  day  and  night  on  the  given  planet,  is  no  longer  true.  Those  derivative 
uniformities,  therefore,  which  are  not  laws  of  causation,  are  (except  in  the 
rare  case  of  their  depending  on  one  cause  alone,  not  on  a combination  of 
causes)  always  more  or  less  contingent  on  collocations ; and  are  hence  sub- 
ject to  the  characteristic  infirmity  of  empirical  laws — that  of  being  admis- 
sible only  where  the  collocations  are  known  by  experience  to  be  such  as 
are  requisite  for  the  truth  of  the  law ; that  is,  only  within  the  conditions 
of  time  and  place  confirmed  by  actual  observation. 

§ 2.  This  principle,  when  stated  in  general  terms,  seems  clear  and  indis- 
putable; yet  many  of  the  ordinary  judgments  of  mankind,  the  propriety 
of  which  is  not  questioned,  have  at  least  the  semblance  of  being  inconsist- 
ent with  it.  On  what  grounds,  it  may  be  asked,  do  we  expect  that  the 
sun  will  rise  to-morrow?  To-morrow  is  beyond  the  limits  of  time  compre- 
hended in  our  observations.  They  have  extended  over  some  thousands  of 


390 


INDUCTION. 


years  past,  but  they  do  not  include  the  future.  Yet  we  infer  with  confi- 
dence that  the  sun  will  rise  to-morrow;  and  nobody  doubts  that  we  are 
entitled  to  do  so.  Let  us  consider  what  is  the  warrant  for  this  confidence. 

In  the  example  in  question,  we  know  the  causes  on  which  the  derivative 
uniformity  depends.  They  arc : the  sun  giving  out  light,  the  earth  in  a 
state  of  rotation  and  intercepting  light.  The  induction  which  shows  these 
to  be  the  real  causes,  and  not  merely  prior  effects  of  a common  cause,  be- 
ing complete,  the  only  circumstances  which  could  defeat  the  derivative  law 
are  such  as  would  destroy  or  counteract  one  or  other  of  the  combined 
causes.  While  the  causes  exist  and  are  not  counteracted,  the  effect  will 
continue.  If  they  exist  and  are  not  counteracted  to-morrow,  the  sun  will 
rise  to-morrow. 

Since  the  causes,  namely,  the  sun  and  the  earth,  the  one  in  the  state  of 
giving  out  light,  the  other  in  a state  of  rotation,  will  exist  until  something 
destroys  them,  all  depends  on  the  probabilities  of  their  destruction,  or  of 
their  counteraction.  We  know  by  observation  (omitting  the  inferential 
proofs  of  an  existence  for  thousands  of  ages  anterior)  that  these  phenomena 
have  continued  for  (say)  five  thousand  years.  Within  that  time  there  has 
existed  no  cause  sufficient  to  diminish  them  appreciably,  nor  which  has 
counteracted  their  effect  in  any  appreciable  degree.  The  chance,  therefore, 
that  the  sun  may  not  rise  to-morrow  amounts  to  the  chance  that  some 
cause,  which  has  not  manifested  itself  in  the  smallest  degree  during  five 
thousand  years,  will  exist  to-morrow  in  such  intensity  as  to  destroy  the 
sun  or  the  earth,  the  sun’s  light  or  the  earth’s  rotation,  or  to  produce  an 
immense  disturbance  in  the  effect  resulting  from  those  causes. 

Nowr,  if  such  a cause  will  exist  to-morrow,  or  at  any  future  time,  some 
cause, proximate  or  remote, of  that  cause  must  exist  now,  and  must  have  ex- 
isted during  the  whole  of  the  five  thousand  years.  If,  therefore,  the  sun  do 
not  rise  to-morrow,  it  will  be  because  some  cause  has  existed,  the  effects  of 
which,  though  during  five  thousand  years  they  have  not  amounted  to  a per- 
ceptible quantity,  will  in  one  day  become  overwhelming.  Since  this  cause 
has  not  been  recognized  during  such  an  interval  of  time  by  observers  sta- 
tioned on  our  earth,  it  must,  if  it  be  a single  agent,  be  either  one  whose 
effects  develop  themselves  gradually  and  very  slowly,  or  one  which  existed 
in  regions  beyond  our  observation,  and  is  now  on  the  point  of  arriving  in 
our  part  of  the  universe.  Now  all  causes  which  we  have  experience  of  act 
according  to  laws  incompatible  with  the  supposition  that  their  effects,  af- 
ter accumulating  so  slowly  as  to  be  imperceptible  for  five  thousand  years, 
should  start  into  immensity  in  a single  day.  No  mathematical  law  of  pro- 
portion between  an  effect  and  the  quantity  or  relations  of  its  cause  could 
produce  such  contradictory  results.  The  sudden  development  of  an  effect 
of  which  there  was  no  previous  trace  always  arises  from  the  coming  to- 
gether of  several  distinct  causes,  not  previously  conjoined  ; but  if  such  sud- 
den conjunction  is  destined  to  take  place,  the  causes,  or  their  causes,  must 
have  existed  during  the  entire  five  thousand  years;  and  their  not  having 
once  come  together  during  that  period  shows  how  rare  that  particular  com- 
bination is.  We  have,  therefore,  the  warrant  of  a rigid  induction  for  con- 
sidering it  probable,  in  a degree  undistinguishable  from  certainty,  that  the 
known  conditions  requisite  for  the  sun’s  rising  will  exist  to-morrow. 

§ 3.  But  this  extension  of  derivative  laws,  not  causative,  beyond  the  lim- 
its of  observation  can  only  be  to  adjacent  cases.  If,  instead  of  to-morrow, 
we  had  said  this  day  twenty  thousand  years,  the  inductions  Avould  have 


EXTENSION  OF  LAWS  TO  ADJACENT  CASES. 


391 


been  any  thing  but  conclusive.  That  a cause  which,  in  opposition  to  very 
powerful  causes,  produced  no  perceptible  effect  during  five  thousand  years, 
should  produce  a very  considerable  one  by  the  end  of  twenty  thousand,  has 
nothing  in  it  which  is  not  in  conformity  with  our  experience  of  causes. 
We  know  many  agents,  the  effect  of  which  in  a short  period  does  not 
amount  to  a perceptible  quantity,  but  b.y  accumulating  for  a much  longer 
period  becomes  considerable.  Besides,  looking  at  the  immense  multitude 
of  the  heavenly  bodies,  their  vast  distances,  and  the  rapidity  of  the  motion 
of  such  of  them  as  are  known  to  move,  it  is  a supposition  not  at  all  contra- 
dictory to  experience  that  some  body  may  be  in  motion  toward  us,  or  we 
toward  it,  within  the  limits  of  whose  influence  we  have  not  come  during 
five  thousand  years,  but  which  in  twenty  thousand  more  may  be  producing 
effects  upon  us  of  the  most  extraordinary  kind.  Or  the  fact  which  is  ca- 
pable of  preventing  sunrise  may  be,  not  the  cumulative  effect  of  one  cause, 
but  some  new  combination  of  causes ; and  the  chances  favorable  to  that 
combination,  though  they  have  not  produced  it  once  in  five  thousand  years, 
may  produce  it  once  in  twenty  thousand.  So  that  the  inductions  which 
authorize  us  to  expect  future  events,  grow  weaker  and  weaker  the  further 
we  look  into  the  future,  and  at  length  become  inappreciable. 

We  have  considered  the  probabilities  of  the  sun’s  rising  to-morrow,  as 
derived  from  the  real  laws ; that  is,  from  the  laws  of  the  causes  on  which 
that  uniformity  is  dependent.  Let  us  now  consider  how  the  matter  would 
have  stood  if  the  uniformity  had  been  known  only  as  an  empirical  law ; if 
we  had  not  been  aware  that  the  sun’s  light  and  the  earth’s  rotation  (or  the 
sun’s  motion)  were  the  causes  on  which  the  periodical  occurrence  of  day- 
light depends.  We  could  have  extended  this  empirical  law  to  cases  adja- 
cent in  time,  though  not  to  so  great  a distance  of  time  as  we  can  now. 
Having  evidence  that  the  effects  had  remained  unaltered  and  been  punctu- 
ally conjoined  for  five  thousand  years,  we  could  infer  that  the  unknown 
causes  on  which  the  conjunction  is  dependent  had  existed  undiminished  and 
uncounteracted  during  the  same  period.  The  same  conclusions,  therefore, 
would  follow  as  in  the  preceding  case,  except  that  we  should  only  know 
that  during  five  thousand  years  nothing  had  occurred  to  defeat  perceptibly 
this  particular  effect;  while,  when  we  know  the  causes,  we  have  the  addi- 
tional assurance  that  during  that  interval  no  such  change  has  been  notice- 
able in  the  causes  themselves  as  by  any  degree  of  multiplication  or  length 
of  continuance  could  defeat  the  effect. 

To  this  must  be  added,  that  when  we  know  the  causes,  we  may  be  able 
to  judge  whether  there  exists  any  known  cause  capable  of  counteracting 
them,  while  as  long  as  they  are  unknown,  we  can  not  be  sure  but  that  if  we 
did  know  them,  we  could  predict  their  destruction  from  causes  actually  in 
existence.  A bed-ridden  savage,  who  had  never  seen  the  cataract  of  Niag-i 
ara,  but  who  lived  within  hearing  of  it,  might  imagine  that  the  sound  he 
heard  would  endure  forever ; but  if  he  knew  it  to  be  the  effect  of  a rush  of 
waters  over  a barrier  of  rock  which  is  progressively  wearing  away,  he  would 
know  that  within  a number  of  ages  which  may  be  calculated  it  will  be  heard 
no  more.  In  proportion,  therefore,  to  our  ignorance  of  the  causes  on  which 
the  empirical  law  depends,  we  can  be  less  assured  that  it  will  continue  to 
hold  good;  and  the  further  we  look  into  futurity,  the  less  improbable  is  it 
that  some  one  of  the  causes,  whose  co-existence  gives  rise  to  the  derivative 
uniformity,  may  be  destroyed  or  counteracted.  With  every  prolongation 
of  time  the  chances  multiply  of  such  an  event ; that  is  to  say,  its  non-occur- 
rence hitherto  becomes  a less  guarantee  of  its  not  occurring  within  the 


392 


INDUCTION. 


given  time.  If,  then,  it  is  only  to  cases  which  in  point  of  time  are  adjacent 
(or  nearly  adjacent)  to  those  which  we  have  actually  observed,  that  any 
derivative  law,  not  of  causation,  can  be  extended  with  an  assurance  equiv- 
alent to  certainty,  much  more  is  this  true  of  a merely  empirical  law.  Hap- 
pily, for  the  purposes  of  life  it  is  to  such  cases  alone  that  we  can  almost 
ever  have  occasion  to  extend  them. 

In  respect  of  place,  it  might  seem  that  a merely  empirical  law  could  not 
be  extended  even  to  adjacent  cases  ; that  we  could  have  no  assurance  of  its 
being  true  in  any  place  where  it  has  not  been  specially  observed.  The  past 
duration  of  a cause  is  a guarantee  for  its  future  existence,  unless  something 
occurs  to  destroy  it;  but  the  existence  of  a cause  in  one  or  any  number  of 
places  is  no  guarantee  for  its  existence  in  any  other  place,  since  there  is  no 
uniformity  in  the  collocations  of  primeval  causes.  When,  therefore,  an  em- 
pirical law  is  extended  beyond  the  local  limits  within  which  it  has  been 
found  true  by  observation,  the  cases  to  which  it  is  thus  extended  must  be 
such  as  are  presumably  within  the  influence  of  the  same  individual  agents. 
If  we  discover  a new  planet  within  the  known  bounds  of  the  solar  system 
(or  even  beyond  those  bounds,  but  indicating  its  connection  with  the  system 
by  revolving  round  the  sun),  we  may  conclude,  with  great  probability,  that 
it  revolves  on  its  axis.  For  all  the  known  planets  do  so  ; and  t his  uniform- 
ity points  to  some  common  cause,  antecedent  to  the  first  records  of  astro- 
nomical observation;  and  though  the  nature  of  this  cause  can  only  be  mat- 
ter of  conjecture,  yet  if  it  be,  as  is  not  unlikely,  and  as  Laplace’s  theory 
supposes,  not  merely  the  same  kind  of  cause,  but  the  same  individual  cause 
(such  as  an  impulse  given  to  all  the  bodies  at  once),  that  cause,  acting  at 
the  extreme  points  of  the  space  occupied  by  the  sun  and  planets,  is  likely, 
unless  defeated  by  some  counteracting  cause,  to  have  acted  at  every  inter- 
mediate point,  and  probably  somewhat  beyond;  and  therefore  acted,  in  all 
probability,  upon  the  supposed  newly-discovered  planet. 

When,  therefore,  effects  which  are  always  found  conjoined  can  be  traced 
with  any  probability  to  an  identical  (and  not  merely  a similar)  origin,  we 
may  with  the  same  probability  extend  the  empirical  law  of  their  conjunc- 
tion to  all  places  within  the  extreme  local  boundaries  within  which  the  fact 
has  been  observed,  subject  to  the  possibility  of  counteracting  causes  in  some 
portion  of  the  field.  Still  more  confidently  may  we  do  so  when  the  law  is 
not  merely  empirical;  when  the  phenomena  which  we  find  conjoined  are 
effects  of  ascertained  causes,  from  the  laws  of  which  the  conjunction  of  their 
effects  is  deducible.  In  that  case,  we  may  both  extend  the  derivative  uni- 
formity over  a larger  space,  and  with  less  abatement  for  the  chance  of 
counteracting  causes.  The  first,  because  instead  of  the  local  boundaries  of 
our  observation  of  the  fact  itself,  we  may  include  the  extreme  boundaries 
of  the  ascertained  influence  of  its  causes.  Thus  the  succession  of  day  and 
night,  we  know,  holds  true  of  all  the  bodies  of  the  solar  system  except  the 
sun  itself ; but  we  know  this  only  because  we  are  acquainted  with  the 
causes.  If  we  were  not,  we  could  not  extend  the  proposition  beyond  the 
orbits  of  the  earth  and  moon,  at  both  extremities  of  which  we  have  the 
evidence  of  observation  for  its  truth.  With  respect  to  the  probability  of 
counteracting  causes,  it  has  been  seen  that  this  calls  for  a greater  abatement 
of  confidence,  in  proportion  to  our  ignorance  of  the  causes  on  which  the 
phenomena  depend.  On  both  accounts,  therefore,  a derivative  law  which 
we  know  how  to  resolve,  is  susceptible  of  a greater  extension  to  cases  ad- 
jacent in  place,  than  a merely  empirical  law. 


ANALOGY. 


393 


CHAPTER  XX. 

OF  ANALOGY. 

§ 1.  The  word  Analogy,  as  the  name  of  a mode  of  reasoning,  is  generally 
taken  for  some  kind  of  argument  supposed  to  be  of  an  inductive  nature, 
but  not  amounting  to  a complete  induction.  There  is  no  word,  however, 
which  is  used  more  loosely,  or  in  a greater  variety  of  senses,  than  Analogy, 
It  sometimes  stands  for  arguments  which  may  be  examples  of  the  most 
rigorous  induction.  Archbishop  Whately,  for  instance,  following  Fergu- 
son and  other  writers,  defines  Analogy  conformably  to  its  primitive  accep- 
tation, that  which  was  given  to  it  by  mathematicians : Resemblance  of  Re- 
lations. In  this  sense,  when  a country  which  has  sent  out  colonies  is  term- 
ed the  mother  country,  the  expression  is  analogical,  signifying  that  the  col- 
onies of  a country  stand  in  the  same  relation  to  her  in  which  children 
stand  to  their  parents.  And  if  any  inference  be  drawn  from  this  resem- 
blance of  relations,  as,  for  instance,  that  obedience  or  affection  is  due  from 
colonies  to  the  mother  country,  this  is  called  reasoning  by  analogy.  Or,  if 
it  be  argued  that  a nation  is  most  beneficially  governed  by  an  assembly 
elected  by  the  people,  from  the  admitted  fact  that  other  associations  for  a 
common  purpose,  such  as  joint-stock  companies,  are  best  managed  by  a 
committee  chosen  by  the  parties  interested;  this,  too,  is  an  argument  from 
analogy  in  the  preceding  sense,  because  its  foundation  is,  uot  that  a nation 
is  like  a joint-stock  company,  or  Parliament  like  a board  of  directors,  but 
that  Parliament  stands  in  the  same  relation  to  the  nation  in  which  a board 
of  directors  stands  to  a joint-stock  company.  Now,  in  an  argument  of  this 
nature,  there  is  no  inherent  inferiority  of  conclusiveness.  Like  other  argu- 
ments from  resemblance,  it  may  amount  to  nothing,  or  it  may  be  a perfect 
and  conclusive  induction.  The  circumstance  in  which  the  two  cases  re- 
semble, may  be  capable  of  being  shown  to  be  the  material  circumstance ; 
to  be  that  on  which  all  the  consequences,  necessary  to  be  taken  into  ac- 
count in  the  particular  discussion,  depend.  In  the  example  last  given,  the 
resemblance  is  one  of  relation ; the  fundamentum  relationis  being  the 
management,  by  a few  persons,  of  affairs  in  which  a much  greater  number 
are  interested  along  with  them.  Now,  some  may  contend  that  this  cir- 
cumstance which  is  common  to  the  two  cases,  and  the  various  consequences 
which  follow  from  it,  have  the  chief  share  in  determining  all  the  effects 
which  make  up  Avhat  we  term  good  or  bad  administration.  If  they  can  es- 
tablish this,  their  argument  has  the  force  of  a rigorous  induction ; if  they 
can  not,  they  are  said  to  have  failed  in  proving  the  analogy  between  the 
two  cases ; a mode  of  speech  which  implies  that  when  the  analogy  can  be 
proved,  the  argument  founded  on  it  can  not  be  resisted. 

§ 2.  It  is  on  the  whole  more  usual,  however,  to  extend  the  name  of  ana- 
logical evidence  to  arguments  from  any  sort  of  resemblance,  provided  they 
do  not  amount  to  a complete  induction;  without  peculiarly  distinguishing 
resemblance  of  relations.  Analogical  reasoning,  in  this  sense,  may  be  re- 
duced to  the  following  formula : Two  things  resemble  each  other  in  one  or 


394 


INDUCTION. 


more  respects ; a certain  proposition  is  true  of  the  one ; therefore  it  is  true 
of  the  other.  But  we  have  nothing  here  by  which  to  discriminate  analogy 
from  induction,  since  this  type  will  serve  for  all  reasoning  from  experience. 
In  the  strictest  induction,  equally  with  the  faintest  analogy,  we  conclude 
because  A resembles  B in  one  or  more  properties,  that  it  does  so  in  a cer- 
tain other  property.  The  difference  is,  that  in  the  case  of  a complete  in- 
duction it  has  been  previously  shown,  by  due  comparison  of  instances,  that 
there  is  an  invariable  conjunction  between  the  former  property  or  proper- 
ties and  the  latter  property;  but  in  what  is  called  analogical  reasoning,  no 
such  conjunction  has  been  made  out.  There  have  been  no  opportunities  of 
putting  in  practice  the  Method  of  Difference,  or  even  the  Method  of  Agree- 
ment; but  we  conclude  (and  that  is  all  which  the  argument  of  analogy 
amounts  to)  that  a fact  m,  known  to  be  true  of  A,  is  more  likely  to  be  true 
of  B if  B agrees  with  A in  some  of  its  properties  (even  though  no  connec- 
tion is  known  to  exist  between  m and  those  properties),  than  if  no  resem- 
blance at  all  could  be  traced  between  B and  any  other  thing  known  to  pos- 
sess the  attribute  rn. 

To  this  argument  it  is  of  course  requisite  that  the  properties  common  to 
A with  B shall  be  merely  not  known  to  be  connected  with  m ; they  must 
not  be  properties  known  to  be  unconnected  with  it.  If,  either  by  processes 
of  elimination,  or  by  deduction  from  previous  knowledge  of  the  laws  of  the 
properties  in  question,  it  can  be  concluded  that  they  have  nothing  to  do 
with  m,  the  argument  of  analogy  is  put  out  of  court.  The  supposition 
must  be  that  m is  an  effect  really  dependent  on  some  property  of  A,  but 
we  know  not  on  which.  We  can  not  point  out  any  of  the  properties  of  A, 
which  is  the  cause  of  m,  or  united  with  it  by  any  law.  After  rejecting  all 
which  we  know  to  have  nothing  to  do  with  it,  there  remain  several  between 
which  we  are  unable  to  decide;  of  which  remaining  properties,  B possesses 
one  or  more.  This,  accordingly,  we  consider  as  affording  grounds,  of  more 
or  less  strength,  for  concluding  by  analogy  that  B possesses  the  attribute  rn. 

There  can  be  no  doubt  that  every  such  resemblance  which  can  be  point- 
ed out  between  B and  A,  affords  some  degree  of  probability,  beyond  what 
would  otherwise  exist,  in  favor  of  the  conclusion  drawn  from  it.  If  B re- 
sembled A in  all  its  ultimate  properties,  its  possessing  the  attribute  rn 
would  be  a certainty,  not  a probability;  and  every  resemblance  which  can  be 
shown  to  exist  between  them,  places  it  by  so  much  the  nearer  to  that  point. 
If  the  resemblance  be  in  an  ultimate  property,  there  will  be  resemblance  in 
all  the  derivative  properties  dependent  on  that  ultimate  property,  and  of 
these  m may  be  one.  If  the  resemblance  be  in  a derivative  property,  there 
is  reason  to  expect  resemblance  in  the  ultimate  property  on  which  it  de- 
pends, and  in  the  other  derivative  properties  dependent  on  the  same  ultimate 
property.  Every  resemblance  which  can  be  shown  to  exist,  affords  ground 
for  expecting  an  indefinite  number  of  other  resemblances;  the  particular 
resemblance  sought  wall,  therefore,  be  oftener  found  among  things  thus 
known  to  resemble,  than  among  things  between  which  we  know  of  no  re- 
semblance. 

For  example,  I might  infer  that  there  are  probably  inhabitants  in  the 
moon,  because  there  are  inhabitants  on  the  earth,  in  the  sea,  and  in  the  air: 
and  this  is  the  evidence  of  analogy.  The  circumstance  of  having  inhabit- 
ants is  here  assumed  not  to  be  an  ultimate  property,  but  (as  is  reasonable 
to  suppose)  a consequence  of  other  properties;  and  depending,  therefore, 
in  the  case  of  the  earth,  on  some  of  its  properties  as  a portion  of  the  uni- 
verse, but  on  which  of  those  properties  we  know  not.  How  the  moon  re- 


ANALOGY. 


395 


sembles  the  earth  in  being  a solid,  opaque,  nearly  spherical  substance,  ap- 
pearing to  contain,  or  to  have  contained,  active  volcanoes;  receiving  heat 
and  light  from  the  sun,  in  about  the  same  quantity  as  our  earth ; revolving 
on  its  axis ; composed  of  materials  which  gravitate,  and  obeying  all  the  va- 
rious laws  resulting  from  that  property.  And  I think  no  one  will  deny 
that  if  this  were  all  that  was  known  of  the  moon,  the  existence  of  inhabit- 
ants in  that  luminary  would  derive  from  these  various  resemblances  to 
the  earth,  a greater  degree  of  probability  than  it  would  otherwise  have ; 
though  the  amount  of  the  augmentation  it  would  be  useless  to  attempt  to 
estimate. 

If,  however,  every  resemblance  proved  between  B and  A,  in  any  point 
not  known  to  be  immaterial  with  respect  to  m,  forms  some  additional  rea- 
son for  presuming  that  B has  the  attribute  m • it  is  clear,  t!  contra , that  ev- 
ery dissimilarity  which  can  be  proved  between  them  furnishes  a counter- 
probability of  the  same  nature  on  the  other  side.  It  is  not,  indeed,  unusual 
that  different  ultimate  properties  should,  in  some  particular  instances,  pro- 
duce the  same  derivative  property;  but  on  the  whole  it  is  certain  that 
things  which  differ  in  their  ultimate  properties,  will  differ  at  least  as  much 
in  the  aggregate  of  their  derivative  properties,  and  that  the  differences 
which  are  unknown  will,  on  the  average  of  cases,  bear  some  proportion  to 
those  which  are  known.  There  will,  therefore,  be  a competition  between 
the  known  points  of  agreement  and  the  known  points  of  difference  in  A 
and  B;  and  according  as  the  one  or  the  other  may  be  deemed  to  prepon- 
derate, the  probability  derived  from  analogy  will  be  for  or  against  B’s  hav- 
ing the  property  in.  The  moon,  for  instance,  agrees  with  the  earth  in  the 
circumstances  already  mentioned ; but  differs  in  being  smaller,  in  having 
its  surface  more  unequal,  and  apparently  volcanic  throughout,  in  having,  at 
least  on  the  side  next  the  earth,  no  atmosphere  sufficient  to  refract  light,  no 
clouds,  and  (it  is  therefore  concluded)  no  water.  These  differences,  consid- 
ered merely  as  such,  might  perhaps  balance  the  resemblances,  so  that  anal- 
ogy would  afford  no  presumption  either  way.  But  considering  that  some 
of  the  circumstances  which  are  wanting  on  the  moon  are  among  those 
which,  on  the  earth,  are  found  to  be  indispensable  conditions  of  animal  life, 
we  may  conclude  that  if  that  phenomenon  does  exist  in  the  moon  (or  at  all 
events  on  the  nearer  side),  it  must  be  as  an  effect  of  causes  totally  different 
from  those  on  which  it  depends  here;  as  a consequence,  therefore,  of  the 
moon’s  differences  from  the  earth,  not  of  the  points  of  agreement.  Viewed 
in  this  light,  all  the  resemblances  which  exist  become  presumptions  against, 
not  in  favor  of,  the  moon’s  being  inhabited.  Since  life  can  not  exist  there 
in  the  manner  in  which  it  exists  here,  the  greater  the  resemblance  of  the 
lunar  world  to  the  terrestrial  in  other  respects,  the  less  reason  we  have  to 
believe  that  it  can  contain  life. 

There  are,  however,  other  bodies  in  our  system,  between  which  and  the 
earth  there  is  a much  closer  resemblance;  which  possess  an  atmosphere, 
clouds,  consequently  water  (or  some  fluid  analogous  to  it),  and  even  give 
strong  indications  of  snow  in  their  polar  regions  ; while  the  cold,  or  heat, 
though  differing  greatly  on  the  average  from  ours,  is,  in  some  parts  at  least 
of  those  planets,  possibly  not  more  extreme  than  in  some  regions  of  our 
own  which  are  habitable.  To  balance  these  agreements,  the  ascertained 
differences  are  chiefly  in  the  average  light  and  heat,  velocity  of  rotation, 
density  of  material,  intensity  of  gravity,  and  similar  circumstances  of  a sec- 
ondary kind.  With  regard  to  these  planets,  therefore,  the  argument  of 
analogy  gives  a decided  preponderance  in  favor  of  their  resembling  the 


396 


INDUCTION. 


earth  in  any  of  its  derivative  properties,  such  as  that  of  having  inhabitants; 
though  when  we  consider  how  immeasurably  multitudinous  are  those  of 
their  properties  which  we  are  entirely  ignorant  of,  compared  with  the  few 
which  we  know,  we  can  attach  but  trifling  weight  to  any  considerations  of 
resemblance  in  which  the  known  elements  bear  so  inconsiderable  a propor- 
tion to  the  unknown. 

Besides  the  competition  between  analogy  and  diversity,  there  may  be  a 
competition  of  conflicting  analogies.  The  new  case  maybe  similar  in  some 
of  its  circumstances  to  cases  in  which  the  fact  m exists,  but  in  others  to 
cases  in  which  it  is  known  not  to  exist.  Amber  has  some  properties  in 
common  with  vegetable,  others  with  mineral  products.  A painting  of  un- 
known origin  may  resemble,  in  certain  of  its  characters,  known  works  of  a 
particular  master,  but  in  others  it  may  as  strikingly  resemble  those  of  some 
other  painter.  A vase  may  bear  some  analogy  to  works  of  Grecian,  and 
some  to  those  of  Etruscan,  or  Egyptian  art.  We  are  of  course  supposing 
that  it  does  not  possess  any  quality  which  has  been  ascertained,  by  a suffi- 
cient induction,  to  be  a conclusive  mark  either  of  the  one  or  of  the  other. 

§ 3.  Since  the  value  of  an  analogical  argument  inferring  one  resemblance 
from  other  resemblances  without  any  antecedent  evidence  of  a connection 
between  them,  depends  on  the  extent  of  ascertained  resemblance,  compared 
first  with  the  amount  of  ascertained  difference,  and  next  with  the  extent  of 
the  unexplored  region  of  unascertained  properties ; it  follows  that  where 
the  resemblance  is  very  great,  the  ascertained  difference  very  small,  and  our 
knowledge  of  the  subject-matter  tolerably  extensive,  the  argument  from 
analogy  may  approach  in  strength  very  near  to  a valid  induction.  If,  afte” 
much  observation  of  B,  we  find  that  it  agrees  with  A in  nine  out  of  ten  of 
its  known  properties,  we  may  conclude  with  a probability  of  nine  to  one, 
that  it  will  possess  any  given  derivative  property  of  A.  If  we  discover, 
for  example,  an  unknown  animal  or  plant,  resembling  closely  some  known 
one  in  the  greater  number  of  the  properties  we  observe  in  it,  but  differing 
in  some  few,  we  may  reasonably  expect  to  find  in  the  unobserved  remain- 
der of  its  properties,  a general  agreement  with  those  of  the  former ; but 
also  a difference  corresponding  proportionately  to  the  amount  of  observed 
diversity. 

It  thus  appears  that  the  conclusions  derived  from  analogy  are  only  of 
any  considerable  value,  when  the  case  to  which  we  reason  is  an  adjacent 
case;  adjacent,  not  as  before,  in  place  or  time,  but  in  circumstances.  In 
the  case  of  effects  of  which  the  causes  are  imperfectly  or  not  at  all  known, 
when  consequently  the  observed  order  of  their  occurrence  amounts  only  to 
an  empirical  law,  it  often  happens  that  the  conditions  which  have  co-exist- 
ed  whenever  the  effect  was  observed,  have  been  very  numerous.  Now  if 
a new  case  presents  itself,  in  which  all  these  conditions  do  not  exist,  but 
the  far  greater  part  of  them  do,  some  one  or  a few  only  being  wanting,  the 
inference  that  the  effect  will  occur,  notwithstanding  this  deficiency  of  com- 
plete resemblance  to  the  cases  in  which  it  has  been  observed,  may,  though 
of  the  nature  of  analogy,  possess  a high  degree  of  probability.  It  is  hard- 
ly necessary  to  add  that,  however  considerable  this  probability  may  be,  no 
competent  inquirer  into  nature  will  rest  satisfied  with  it  when  a complete 
induction  is  attainable;  but  will  consider  the  analogy  as  a mere  guide- 
post,  pointing  out  the  direction  in  whicli  more  rigorous  investigations 
should  be  prosecuted. 

It  is  in  this  last  respect  that  considerations  of  analogy  have  the-  highest 


EVIDENCE  OF  UNIVERSAL  CAUSATION. 


397 


scientific  value.  The  cases  in  which  analogical  evidence  affords  in  itself 
any  very  high  degree  of  probability,  are,  as  we  have  observed,  only  those 
in  which  the  resemblance  is  very  close  and  extensive ; but  there  is  no  anal- 
ogy, however  faint,  which  may  not  be  of  the  utmost  value  in  suggesting 
experiments  or  observations  that  may  lead  to  more  positive  conclusions. 
When  the  agents  and  their  effects  are  out  of  the  reach  of  further  observa- 
tion and  experiment,  as  in  the  speculations  already  alluded  to  respecting 
the  moon  and  planets,  such  slight  probabilities  are  no  more  than  an  inter- 
esting theme  for  the  pleasant  exercise  of  imagination  ; but  any  suspicion, 
however  slight,  that  sets  an  ingenious  person  at  work  to  contrive  an  ex- 
periment, or  affords  a reason  for  trying  one  experiment  rather  thau  anoth- 
er, may  be  of  the  greatest  benefit  to  science. 

On  this  ground,  though  I can  not  accept  as  positive  truths  any  of  those 
scientific  hypotheses  which  are  unsusceptible  of  being  ultimately  brought 
to  the  test  of  actual  induction,  such,  for  instance,  as  the  two  theories  of 
light,  the  emission  theory  of  the  last  century,  and  the  undulatory  theory 
which  predominates  in  the  present,  I am  yet  unable  to  agree  with  those 
who  consider  such  hypotheses  to  be  worthy  of  entire  disregard.  As  is  well 
said  by  Hartley  (and  concurred  in  by  a thinker  in  general  so  diametrically 
opposed  to  Hartley’s  opinions  as  Dugald  Stewart),  “any  hypothesis  which 
has  so  much  plausibility  as  to  explain  a considerable  number  of  facts,  helps 
us  to  digest  these  facts  in  proper  order,  to  bring  new  ones  to  light,  and 
make  experimental,  crude  for  the  sake  of  future  inquirers.”*  If  an  hypoth- 
esis both  explains  known  facts,  and  has  led  to  the  prediction  of  others 
previously  unknown,  and  since  verified  by  experience,  the  laws  of  the  phe- 
nomenon which  is  the  subject  of  inquiry  must  bear  at  least  a great  similar- 
ity to  those  of  the  class  of  phenomena  to  which  the  hypothesis  assimi- 
lates it ; and  since  the  analogy  which  extends  so  far  may  probably  extend 
further,  nothing  is  more  likely  to  suggest  experiments  tending  to  throw 
light  upon  the  real  properties  of  the  phenomenon,  than  the  following  out 
such  an  hypothesis.  But  to  this  end  it  is  by  no  means  necessary  that  the 
hypothesis  be  mistaken  for  a scientific  truth.  On  the  contrary,  that  illu- 
sion is  in  this  respect,  as  in  every  other,  an  impediment  to  the  progress  of 
real  knowledge,  by  leading  inquirers  to  restrict  themselves  arbitrarily  to 
the  particular  hypothesis  which  is  most  accredited  at  the  time,  instead  of 
looking  out  for  every  class  of  phenomena  between  the  laws  of  which  and 
those  of  the  given  phenomenon  any  analogy  exists,  and  trying  all  such  ex- 
periments as  may  tend  to  the  discovery  of  ulterior  analogies  pointing  in 
the  same  direction. 


CHAPTER  XXI. 

OF  THE  EVIDENCE  OF  THE  LAW  OF  UNIVERSAL  CAUSATION. 

§ 1.  We  have  now  completed  our  review  of  the  logical  processes  by 
which  the  laws,  or  uniformities,  of  the  sequence  of  phenomena,  and  those 
uniformities  in  their  co-existence  which  depend  on  the  laws  of  their  se- 
quence, are  ascertained  or  tested.  As  we  recognized  in  the  commence- 
ment, and  have  been  enabled  to  see  more  clearly  in  the  progress  of  the  in- 
vestigation, the  basis  of  all  these  logical  operations  is  the  law  of  causation. 

* Hartley’s  Observations  on  Man , vol.  i.,  p.  16.  The  passage  is  not  in  Priestley’s  curtailed 
edition. 


898 


INDUCTION. 


The  validity  of  all  the  Inductive  Methods  depends  on  the  assumption  that 
every  event,  or  the  beginning  of  every  phenomenon,  must  have  some  cause ; 
some  antecedent,  on  the  existence  of  which  it  is  invariably  and  uncondi- 
tionally consequent.  In  the  Method  of  Agreement  this  is  obvious;  that 
method  avowedly  proceeding  on  the  supposition  that  we  have  found  the 
true  cause  as  soon  as  we  have  negatived  every  other.  The  assertion  is 
equally  true  of  the  Method  of  Difference.  That  method  authorizes  us  to 
infer  a general  law  from  two  instances;  one,  in  which  A exists  together 
with  a multitude  of  other  circumstances,  and  B follows;  another,  in  which, 
A being  removed,  and  all  other  circumstances  remaining  the  same,  B is 
prevented.  What,  however,  does  this  prove?  It  proves  that  B,  in  the 
particular  instance,  can  not  have  had  any  other  cause  than  A;  but  to  con- 
clude from  this  that  A was  the  cause,  or  that  A will  on  other  occasions  be 
followed  by  B,  is  only  allowable  on  the  assumption  that  B must  have  some 
cause;  that  among  its  antecedents  in  any  single  instance  in  which  it  oc- 
curs, there  must  be  one  which  has  the  capacity  of  producing  it  at  other 
times.  This  being  admitted,  it  is  seen  that  in  the  case  in  question  that 
antecedent  can  be  no  other  than  A ; but  that  if  it  be  no  other  than  A it 
must  be  A,  is  not  proved,  by  these  instances  at  least,  but  taken  for  granted. 
There  is  no  need  to  spend  time  in  proving  that  the  same  thing  is  true  of 
the  other  Inductive  Methods.  The  universality  of  the  law  of  causation  is 
assumed  in  them  all. 

But  is  this  assumption  warranted?  Doubtless  (it  may  be  said)  most 
phenomena  are  connected  as  effects  with  some  antecedent  or  cause,  that  is, 
are  never  produced  unless  some  assignable  fact  has  preceded  them  ; but  the 
very  circumstance  that  complicated  processes  of  induction  are  sometimes 
necessary,  shows  that  cases  exist  in  which  this  regular  order  of  succession 
is  not  apparent  to  our  unaided  apprehension.  If,  then,  the  processes  which 
bring  these  cases  within  the  same  category  with  the  rest,  require  that  we 
should  assume  the  universality  of  the  very  law  which  they  do  not  at  first 
sight  appear  to  exemplify,  is  not  this  a petitio  principii ? Can  we  prove  a 
proposition,  by  an  argument  which  takes  it  for  granted?  And  if  not  so 
proved,  on  what  evidence  does  it  rest? 

For  this  difficulty,  which  I have  purposely  stated  in  the  strongest  terms 
it  will  admit  of,  the  school  of  metaphysicians  who  have  long  predominated 
in  this  country  find  a ready  salvo.  They  affirm,  that  the  universality  of 
causation  is  a truth  which  we  can  not  help  believing;  that  the  belief  in  it 
is  an  instinct,  one  of  the  laws  of  our  believing  faculty.  As  the  proof  of 
this,  they  say,  and  they  have  nothing  else  to  say,  that  every  body  does  be- 
lieve it;  and  they  number  it  among  the  propositions,  rather  numerous  in 
their  catalogue,  which  may  be  logically  argued  against,  and  perhaps  can 
not  be  logically  proved,  but  which  are  of  higher  authority  than  logic,  and 
so  essentially  inherent  in  the  human  mind,  that  even  he  who  denies  them 
in  speculation,  shows  by  his  habitual  practice  that  his  arguments  make  no 
impression  upon  himself. 

Into  the  merits  of  this  question,  considered  as  one  of  psychology,  it 
would  be  foreign  to  my  purpose  to  enter  here;  but  I must  protest  against 
adducing,  as  evidence  of  the  truth  of  a fact  in  external  nature,  the  disposi- 
tion, however  strong  or  however  general,  of  the  human  mind  to  believe  it. 
Belief  is  not  proof,  and  does  not  dispense  with  the  necessity  of  proof.  I 
am  aware,  that  to  ask  for  evidence  of  a proposition  which  we  are  supposed 
to  believe  instinctively,  is  to  expose  one’s  self  to  the  charge  of  rejecting  the 
authority  of  the  human  faculties ; which  of  course  no  one  can  consistently 


EVIDENCE  OF  UNIVERSAL  CAUSATION. 


399 


do,  since  the  human  faculties  are  all  which  any  one  has  to  judge  by;  and 
inasmuch  as  the  meaning  of  the  word  evidence  is  supposed  to  be,  something 
which  when  laid  before  the  mind,  induces  it  to  believe  ; to  demand  evidence 
when  the  belief  is  insured  by  the  mind’s  own  laws,  is  supposed  to  be  ap- 
pealing to  the  intellect  against  the  intellect.  But  this,  I apprehend,  is  a 
misunderstanding  of  the  nature  of  evidence.  By  evidence  is  not  meant 
any  thing  and  every  thing  which  produces  belief.  There  are  many  things 
which  generate  belief  besides  evidence.  A mere  strong  association  of  ideas 
often  causes  a belief  so  intense  as  to  be  unshakable  by  experience  or  argu- 
ment. Evidence  is  not  that  which  the  mind  does  or  must  yield  to,  but 
that  which  it  ought  to  yield  to,  namely,  that,  by  yielding  to  which  its  belief 
is  kept  conformable  to  fact.  There  is  no  appeal  from  the  human  faculties 
generally,  but  there  is  an  appeal  from  one  human  faculty  to  another;  from 
the  judging  faculty,  to  those  which  take  cognizance  of  fact,  the  faculties  of 
sense  and  consciousness.  The  legitimacy  of  this  appeal  is  admitted  when- 
ever it  is  allowed  that  our  judgments  ought  to  be  conformable  to  fact. 
To  say  that  belief  suffices  for  its  own  justification  is  making  opinion  the 
test  of  opinion  ; it  is  denying  the  existence  of  any  outward  standard,  the 
conformity  of  an  opinion  to  which  constitutes  its  truth.  We  call  one  mode 
of  forming  opinions  right  and  another  wrong,  because  the  one  does,  and  the 
other  does  not,  tend  to  make  the  opinion  agree  with  the  fact  — to  make 
people  believe  what  really  is,  and  expect  what  really  will  be.  Now  a mere 
disposition  to  believe,  even  if  supposed  instinctive,  is  no  guarantee  for  the 
truth  of  the  thing  believed.  If,  indeed,  the  belief  ever  amounted  to  an  ir- 
resistible necessity,  there  would  then  be  no  use  in  appealing  from  it,  be- 
cause there  would  be  no  possibility  of  altering  it.  But  even  then  the  truth 
of  the  belief  would  not  follow;  it  would  only  follow  that  mankind  were 
under  a permanent  necessity  of  believing  what  might  possibly  not  be  true; 
in  other  words,  that  a case  might  occur  in  which  our  senses  or  conscious- 
ness, if  they  could  be  appealed  to,  might  testify  one  thing,  and  our  reason 
believe  another.  But  in  fact  there  is  no  such  permanent  necessity.  There 
is  no  proposition  of  which  it  can  be  asserted  that  every  human  mind  must 
eternally  and  irrevocably  believe  it.  Many  of  the  propositions  of  which 
this  is  most  confidently  stated,  great  numbers  of  human  beings  have  disbe- 
lieved. The  things  which  it  has  been  supposed  that  nobody  could  possibly 
help  believing, are  innumerable;  but  no  two  generations  would  make  out 
the  same  catalogue  of  them.  One  age  or  nation  believes  implicitly  what 
to  another  seems  incredible  and  inconceivable;  one  individual  has  not  a 
vestige  of  a belief  which  another  deems  to  be  absolutely  inherent  in  hu- 
manity. There  is  not  one  of  these  supposed  instinctive  beliefs  which  is 
really  inevitable.  It  is  in  the  power  of  every  one  to  cultivate  habits  of 
thought  which  make  him  independent  of  them.  The  habit  of  philosoph- 
ical analysis  (of  which  it  is  the  surest  effect  to  enable  the  mind  to  command, 
instead  of  being  commanded  by,  the  laws  of  the  merely  passive  part  of  its 
own  nature),  by  showing  to  us  that  things  are  not  necessarily  connected  in 
fact  because  their  ideas  are  connected  in  our  minds,  is  able  to  loosen  innu- 
merable associations  which  reign  despotically  over  the  undisciplined  or 
early -prejudiced  mind.  And  this  habit  is  not  without  power  even  over 
those  associations  which  the  school  of  which  I have  been  speaking  regard 
as  connate  and  instinctive.  I am  convinced  that  any  one  accustomed  to 
abstraction  and  analysis,  who  will  fairly  exert  his  faculties  for  the  purpose, 
will,  when  his  imagination  has  once  learned  to  entertain  the  notion,  find 
no  difficulty  in  conceiving  that  in  some  one,  for  instance,  of  the  many  fir- 


400 


INDUCTION. 


maments  into  which  sidereal  astronomy  now  divides  the  universe,  events 
may  succeed  one  another  at  random,  without  any  fixed  law ; nor  can  any 
thing  in  our  experience,  or  in  our  mental  nature,  constitute  a sufficient,  or 
indeed  any,  reason  for  believing  that  this  is  nowhere  the  case. 

Were  we  to  suppose  (what  it  is  perfectly  possible  to  imagine)  that  the 
present  order  of  the  universe  were  brought  to  an  end,  and  that  a chaos  suc- 
ceeded in  which  there  was  no  fixed  succession  of  events,  and  the  past  gave 
no  assurance  of  the  future;  if  a human  being  were  miraculously  kept  alive 
to  witness  this  change,  he  surely  would  soon  cease  to  believe  in  any  uni- 
formity, the  uniformity  itself  no  longer  existing.  If  this  be  admitted,  the 
belief  in  uniformity  either  is  not  an  instinct,  or  it  is  an  instinct  conquera- 
ble, like  all  other  instincts,  by  acquired  knowledge. 

But  there  is  no  need  to  speculate  on  what  might  be,  when  we  have  posi- 
tive and  certain  knowledge  of  what  has  been.  It  is  not  true,  as  a matter 
of  fact,  that  mankind  have  always  believed  that  all  the  successions  of  events 
were  uniform  and  according  to  fixed  laws.  The  Greek  philosophers,  not 
even  excepting  Aristotle,  recognized  Chance  and  Spontaneity  (jv^n  and  to 
uvroj-iaTor)  as  among  the  agents  in  nature ; in  other  words,  they  believed 
that  to  that  extent  there  was  no  guarantee  that  the  past  had  been  similar 
to  itself,  or  that  the  future  would  resemble  the  past.  Even  now  a full  half 
of  the  philosophical  world,  including  the  very  same  metaphysicians  who 
contend  most  for  the  instinctive  character  of  the  belief  in  uniformity,  con- 
sider one  important  class  of  phenomena,  volitions,  to  be  an  exception  to 
the  uniformity,  and  not  governed  by  a fixed  law.* 

§ 2.  As  was  observed  in  a former  place, f the  belief  we  entertain  in  the 
universality,  throughout  nature,  of  the  law  of  cause  and  effect,  is  itself  an 
instance  of  induction ; and  by  no  means  one  of  the  earliest  which  any  of 

* I am  happy  to  be  able  to  quote  the  following  excellent  passage  from  Mr.  Baden  Powell’s 
Essay  on  the  Inductive  Philosophy , in  confirmation,  both  in  regard  to  history  and  to  doctrine, 
of  the  statement  made  in  the  text.  Speaking  of  the  “ conviction  of  the  universal  and  perma- 
nent uniformity  of  nature,”  Mr.  Powell  says  (pp.  98-100)  : 

“We  may  remark  that  this  idea,  in  its  proper  extent,  is  by  no  means  one  of  popular  ac- 
ceptance or  natural  growth.  Just  so  far  as  the  daily  experience  of  every  one  goes,  so  far  in- 
deed he  comes  to  embrace  a certain  persuasion  of  this  kind,  but  merely  to  this  limited  extent, 
that  what  is  going  on  around  him  at  present,  in  his  own  narrow  sphere  of  observation,  will 
go  on  in  like  manner  in  future.  The  peasant  believes  that  the  sun  which  rose  to-day  will  rise 
again  to-morrow ; that  the  seed  put  into  the  ground  will  be  followed  in  due  time  by  the  har- 
vest this  year  as  it  was  last  year,  and  the  like ; but  has  no  notion  of  such  inferences  in  sub- 
jects beyond  his  immediate  observation.  And  it  should  be  observed  that  each  class  of  per- 
sons, in  admitting  this  belief  within  the  limited  range  of  his  own  experience,  though  he 
doubt  or  deny  it  in  every  thing  beyond,  is,  in  fact,  bearing  unconscious  testimony  to  its  uni- 
versal truth.  Nor,  again,  is  it  only  among  the  most  ignorant  that  this  limitation  is  put  upon 
the  truth.  There  is  a very  general  propensity  to  believe  that  every  tiling  beyond  common  ex- 
perience, or  especially  ascertained  laws  of  nature,  is  left  to  the  dominion  of  chance  or  fate  or 
arbitrary  intervention ; and  even  to  object  to  any  attempted  explanation  by  physical  causes, 
if  conjecturally  thrown  out  for  an  apparently  unaccountable  phenomenon. 

“The  precise  doctrine  of  the  generalization  of  this  idea  of  the  uniformity  of  nature,  so  far 
from  being  obvious,  natural,  or  intuitive,  is  utterly  beyond  the  attainment  of  the  many.  In 
all  the  extent  of  its  universality  it  is  characteristic  of  the  philosopher.  It  is  clearly  the  re- 
sult of  philosophic  cultivation  and  training,  and  by  no  means  the  spontaneous  offspring  of  any 
primary  principle  naturally  inherent  in  the  mind,  as  some  seem  to  believe.  It  is  no  mere 
vague  persuasion  taken  up  without  examination,  as  a common  prepossession  to  which  we  are 
always  accustomed  ; on  the  contrary,  all  common  prejudices  and  associations  are  against  it.  It 
is  pre-eminently  an  acquired  idea.  It  is  not  attained  without  deep  study  and  reflection.  The 
best  informed  philosopher  is  the  man  who  most  firmly  believes  it,  even  in  opposition  to  received 
notions ; its  acceptance  depends  on  the  extent  and  profoundness  of  his  inductive  studies.” 

t Supra,  book  iii.,  chap,  iii.,  § 1. 


EVIDENCE  OF  UNIVERSAL  CAUSATION. 


401 


us,  O'.'  which  mankind  in  general,  can  have  made.  We  arrive  at  this  uni- 
versal law,  by  generalization  from  many  laws  of  inferior  generality.  We 
should  never  have  had  the  notion  of  causation  {in  the  philosophical  meaning 
of  the  term)  as  a condition  of  all  phenomena,  unless  many  cases  of  causation, 
or  in  other  words,  many  partial  uniformities  of  sequence,  had  previously  be- 
come familiar.  The  more  obvious  of  the  particular  uniformities  suggest, 
and  give  evidence  of,  the  general  uniformity,  and  the  general  uniformity,  once 
established,  enables  us  to  prove  the  remainder  of  thQ  oarticular  uniformities 
of  which  it  is  made  up.  As,  however,  all  rigorous  processes  of  induction 
presuppose  the  general  uniformity,  our  knowledge  of  the  particular  uniform- 
ities from  which  it  was  first  inferred  was  not,  of  course,  derived  from  rigor- 
ous induction,  but  from  the  loose  and  uncertain  mode  of  induction  per  enu- 
mercitionem  simplicem • and  the  law  of  universal  causation,  being  collected 
from  results  so  obtained,  can  not  itself  rest  on  any  better  foundation. 

It  would  seem,  therefore,  that  induction  per  enumcrationem  simplicem 
not  only  is  not  necessarily  an  illicit  logical  process,  but  is  in  reality  the  only 
kind  of  induction  possible ; since  the  more  elaborate  process  depends  for 
its  validity  on  a law,  itself  obtained  in  that  inartificial  mode.  Is  there  not 
then  an  inconsistency  in  contrasting  the  looseness  of  one  method  with  the 
rigidity  of  another,  when  that  other  is  indebted  to  the  looser  method  for 
its  own  foundation  ? 

The  inconsistency,  however,  is  only  apparent.  Assuredly,  if  induction 
by  simple  enumeration  were  an  invalid  process,  no  process  grounded  on 
it  could  be  valid;  just  as  no  reliance  could  be  placed  on  telescopes,  if  we 
could  not  trust  our  eyes.  But  though  a valid  process,  it  is  a fallible  one, 
and  fallible  in  very  different  degrees:  if,  therefore,  we  can  substitute  for 
the  more  fallible  forms  of  the  process,  an  operation  grounded  on  the  same 
process  in  a less  fallible  form,  we  shall  have  effected  a very  material  im- 
provement. And  this  is  what  scientific  induction  does. 

A mode  of  concluding  from  experience  must  be  pronounced  untrust- 
worthy  when  subsequent  experience  refuses  to  confirm  it.  According  to 
this  criterion,  induction  by  simple  enumeration — in  other  words,  generaliza- 
tion of  an  observed  fact  from  the  mere  absence  of  any  known  instance  to 
the  contrary — affords  in  general  a precarious  and  unsafe  ground  of  assur- 
ance ; for  such  generalizations  are  incessantly  discovered,  on  further  expe- 
rience, to  be  false.  Still,  however,  it  affords  some  assurance,  sufficient,  in 
many  cases,  for  the  ordinary  guidance  of  conduct.  It  would  be  absurd  to 
say,  that  the  generalizations  arrived  at  by  mankind  in  the  outset  of  their 
experience,  such  as  these — food  nourishes,  fire  burns,  water  drowns— were 
unworthy  of  reliance.*  There  is  a scale  of  trustworthiness  in  the  results 

* It  deserves  remark,  that  these  early  generalizations  did  not,  like  scientific  inductions,  pre- 
suppose causation.  What  they  did  presuppose,  was  uniformity  in  physical  facts.  But  the  ob- 
servers were  as  ready  to  presume  uniformity  in  the  co-existence  of  tacts  as  in  the  sequences. 
On  the  other  hand,  they  never  thought  of  assuming  that  this  uniformity  was  a principle  per- 
vading all  nature : their  generalizations  did  not  imply  that  there  was  uniformity  in  every  thing, 
but  only  that  as  much  uniformity  as  existed  within  their  observation,  existed  also  beyond  it. 
The  induction,  fire  burns,  does  not  require  for  its  validity  that  all  nature  should  observe  uni- 
form laws,  but  only  that  there  should  be  uniformity  in  one  particular  class  of  natural  phe- 
nomena ; the  effects  of  fire  on  the  senses  and  on  combustible  substances.  And  uniformity  to 
this  extent  was  not  assumed,  anterior  to  the  experience,  but  proved  by  the  experience.  The 
same  observed  instances  which  proved  the  narrower  truth,  proved  as  much  of  the  wider  one  as 
corresponded  to  it.  It  is  from  losing  sight  of  this  fact,  and  considering  the  law  of  causation 
in  its  full  extent  as  necessarily  presupposed  in  the  very  earliest  generalizations,  that  persons 
have  been  led  into  the  belief  that  the  law  of  causation  is  known  a priori , and  is  not  itself  a 
conclusion  from  experience. 


26 


402 


INDUCTION. 


of  the  original  unscientific  induction ; and  on  this  diversity  (as  observed  in 
the  fourth  chapter  of  the  present  book)  depend  the  rules  for  the  improve- 
ment of  the  process.  The  improvement  consists  in  correcting  one  of  these 
inartificial  generalizations  by  means  of  another.  As  has  been  already  point- 
ed out,  this  is  all  that  art  can  do.  To  test  a generalization,  by  showing 
that  it  either  follows  from,  or  conflicts  with,  some  stronger  induction,  some 
generalization  resting  on  a broader  foundation  of  experience,  is  the  begin- 
ning and  end  of  the  logic  of  induction. 

§ 3.  Now  the  precariousness  of  the  method  of  simple  enumeration  is  in 
an  inverse  ratio  to  the  largeness  of  the  generalization.  The  process  is 
delusive  and  insufficient,  exactly  in  proportion  as  the  subject-matter  of  the 
observation  is  special  and  limited  in  extent.  As  the  sphere  widens,  this 
uuscientific  method  becomes  less  and  less  liable  to  mislead ; and  the  most 
universal  class  of  truths,  the  law  of  causation,  for  instance,  and  the  princi- 
ples of  number  and  of  geometry,  are  duly  and  satisfactorily  proved  by  that 
method  alone,  nor  are  they  susceptible  of  any  other  proof. 

With  respect  to  the  whole  class  of  generalizations  of  which  we  have  re- 
cently treated,  the  uniformities  which  depend  on  causation,  the  truth  of 
the  remark  just  made  follows  by  obvious  inference  from  the  principles  laid 
down  in  the  preceding  chapters.  When  a fact  has  been  observed  a cer- 
tain number  of  times  to  be  true,  and  is  not  in  any  instance  known  to  be 
false,  if  we  at  once  affirm  that  fact  as  a universal  truth  or  law  of  nature, 
without  either  testing  it'  by  any  of  the  four  methods  of  induction,  or  de- 
ducing it  from  other  known  laws,  we  shall  in  general  err  grossly;  but  we 
are  perfectly  justified  in  affirming  it  as  an  empirical  law,  true  within  cer- 
tain limits  of  time,  place,  and  circumstance,  provided  the  number  of  coin 
cidences  be  greater  than  can  with  any  probability  be  ascribed  to  chance. 
The  reason  for  not  extending  it  beyond  those  limits  is,  that  the  fact  of  its 
holding  true  within  them  may  be  a consequence  of  collocations,  which  can 
not  be  concluded  to  exist  in  one  place  because  they  exist  in  another;  or 
may  be  dependent  on  the  accidental  absence  of  counteracting  agencies, 
which  any  variation  of  time,  or  the  smallest  change  of  circumstances,  may 
possibly  bring  into  play.  If  we  suppose,  then,  the  subject-matter  of  any 
generalization  to  be  so  widely  diffused  that  there  is  no  time,  no  place,  and 
no  combination  of  circumstances,  but  must  afford  an  example  either  of  its 
truth  or  of  its  falsity,  and  if  it  be  never  found  otherwise  than  true,  its 
truth  can  not  be  contingent  on  any  collocations,  unless  such  as  exist  at  all 
times  and  places ; nor  can  it  be  frustrated  by  any  counteracting  agencies, 
unless  by  such  as  never  actually  occur.  It  is,  therefore,  an  empirical  law 
co-extensive  with  all  human  experience;  at  which  point  the  distinction  be- 
tween empirical  laws  and  laws  of  nature  vanishes,  and  the  proposition 
takes  its  place  among  the  most  firmly  established  as  well  as  largest  truths 
accessible  to  science. 

Now,  the  most  extensive  in  its  subject-matter  of  all  generalizations 
which  experience  warrants,  respecting  the  sequences  and  co-existences  of 
phenomena,  is  the  law  of  causation.  It  stands  at  the  head  of  all  observed 
uniformities,  in  point  of  universality,  and  therefore  (if  the  preceding  ob- 
servations are  correct)  in  point  of  certainty.  And  if  we  consider,  not  what 
mankind  would  have  been  justified  in  believing  in  the  infancy  of  their 
knowledge,  but  what  may  rationally  be  believed  in  its  present  more  ad- 
vanced state,  we  shall  find  ourselves  warranted  in  considering  this  funda- 
mental la w,  though  itself  obtained  by  induction  from  particular  laws  of  causa- 


EVIDENCE  OF  UNIVERSAL  CAUSATION. 


403 


tion,  as  not  less  certain,  but  on  the  contrary,  more  so,  than  any  of  those  from 
which  it  was  drawn.  It  adds  to  them  as  much  proof  as  it  receives  from 
them.  For  there  is  probably  no  one  even  of  the  best  established  laws  of 
causation  which  is  not  sometimes  counteracted,  and  to  which,  therefore, 
apparent  exceptions  do  not  present  themselves,  which  would  have  neces- 
sarily and  justly  shaken  the  confidence  of  mankind  in  the  universality  of 
those  laws,  if  inductive  processes  founded  on  the  universal  law  had  not 
enabled  us  to  refer  those  exceptions  to  the  agency  of  counteracting  causes, 
and  thereby  reconcile  them  with  the  law  with  which  they  apparently  con- 
flict. Errors,  moreover,  may  have  slipped  into  the  statement  of  any  one 
of  the  special  laws,  through  inattention  to  some  material  circumstance  : and 
instead  of  the  true  proposition,  another  may  have  been  enunciated,  false  as 
a universal  law,  though  leading,  in  all  cases  hitherto  observed,  to  the  same 
result.  To  the  law  of  causation,  on  the  contrary,  we  not  only  do  not  know 
of  any  exception,  but  the  exceptions  which  limit  or  apparently  invalidate 
the  special  laws,  are  so  far  from  contradicting  the  universal  one,  that  they 
confirm  it ; since  in  all  cases  which  are  sufficiently  open  to  our  observation, 
we  are  able  to  trace  the  difference  of  result,  either  to  the  absence  of  a cause 
which  had  been  present  in  ordinary  cases,  or  to  the  presence  of  one  which 
had  been  absent. 

The  law  of  cause  and  effect,  being  thus  certain,  is  capable  of  imparting 
its  certainty  to  all  other  inductive  propositions  which  can  be  deduced  from 
it;  and  the  narrower  inductions  may  be  regarded  as  receiving  their  ulti- 
mate sanction  from  that  law,  since  there  is  no  one  of  them  which  is  not 
rendered  more  certain  than  it  was  before,  when  we  are  able  to  connect  it 
with  that  larger  induction,  and  to  show  that  it  can  not  be  denied,  consist- 
ently with  the  law  that  every  thing  which  begins  to  exist  has  a cause. 
And  hence  we  are  justified  in  the  seeming  inconsistency,  of  holding  induc- 
tion by  simple  enumeration  to  be  good  for  proving  this  general  truth,  the 
foundation  of  scientific  induction,  and  yet  refusing  to  rely  on  it  for  any  of 
the  narrower  inductions.  I fully  admit  that  if  the  law  of  causation  were 
unknown,  generalization  in  the  more  obvious  cases  of  uniformity  in  phe- 
nomena would  nevertheless  be  possible,  and  though  in  all  cases  more  or 
less  precarious,  and  in  some  extremely  so,  would  suffice  to  constitute  a cer- 
tain measure  of  probability ; but  what  the  amount  of  this  probability  might 
be,  we  are  dispensed  from  estimating,  since  it  never  could  amount  to  the 
degree  of  assurance  which  the  proposition  acquires,  when,  by  the  applica- 
tion to  it  of  the  Four  Methods,  the  supposition  of  its  falsity  is  shown  to 
be  inconsistent  with  the  Law  of  Causation.  We  are  therefore  logically 
entitled,  and,  by  the  necessities  of  scientific  induction,  required,  to  disre- 
gard the  probabilities  derived  from  the  early  rude  method  of  generalizing, 
and  to  consider  no  minor  generalization  as  proved  except  so  far  as  the  law 
of  causation  confirms  it,  nor  probable  except  so  far  as  it  may  reasonably 
be  expected  to  be  so  confirmed. 

§ 4.  The  assertion,  that  our  inductive  processes  assume  the  law  of  causa- 
tion, while  the  law  of  causation  is  itself  a case  of  induction,  is  a paradox, 
only  on  the  old  theory  of  reasoning,  which  supposes  the  universal  truth,  or 
major  premise,  in  a ratiocination,  to  be  the  real  proof  of  the  particular 
truths  which  are  ostensibly  inferred  from  it.  According  to  the  doctrine 
maintained  in  the  present  treatise,*  the  major  premise  is  not  the  proof  oi 


Book  ii. , chap.  iii.. 


404 


INDUCTION. 


the  conclusion,  but  is  itself  proved,  along  with  the  conclusion  from  the 
same  evidence.  “All  men  are  mortal”  is  not  the  proof  that  Lord  Palmer- 
ston is  mortal;  but  our  past  experience  of  mortality  authorizes  us  to  infer 
both  the  general  truth  and  the  particular  fact,  and  the  one  with  exactly  the 
same  degree  of  assurance  as  the  other.  The  mortality  of  Lord  Palmerston 
is  not  an  inference  from  the  mortality  of  all  men,  but  from  the  experience 
which  proves  the  mortality  of  all  men;  and  is  a correct  inference  from  ex- 
perience, if  that  general  truth  is  so  too.  This  relation  between  our  general 
beliefs  and  their  particular  applications  holds  equally  true  in  the  more  com- 
prehensive case  which  we  are  now  discussing.  Any  new  fact  of  causation 
inferred  by  induction,  is  rightly  inferred,  if  no  other  objection  can  be  made 
to  the  inference  than  can  be  made  to  the  general  truth  that  every  event  has 
a cause.  The  utmost  certainty  which  can  be  given  to  a conclusion  arrived 
at  in  the  way  of  inference,  stops  at  this  point.  When  we  have  ascertained 
that  the  particular  conclusion  must  stand  or  fall  with  the  general  uniform- 
ity of  the  laws  of  nature — that  it  is  liable  to  no  doubt  except  the  doubt 
whether  every  event  has  a cause — we  have  done  all  that  can  be  done  for  it. 
The  strongest  assurance  we  can  obtain  of  any  theory  respecting  the  cause 
of  a given  phenomenon,  is  that  the  phenomenon  has  either  that  cause  or 
none. 

The  latter  supposition  might  have  been  an  admissible  one  in  a very  early 
period  of  our  study  of  nature.  But  we  have  been  able  to  perceive  that  in 
the  stage  which  mankind  have  now  reached,  the  generalization  which  gives 
the  Law  of  Universal  Causation  has  grown  into  a stronger  and  better  in- 
duction, one  deserving  of  greater  reliance,  than  any  of  the  subordinate  gen- 
eralizations. We  may  even,  I think,  go  a step  further  than  this,  and  regard 
the  certainty  of  that  great  induction  as  not  merely  comparative,  but,  for  all 
practical  purposes,  complete. 

The  considerations,  which,  as  I apprehend,  give,  at  the  present  day,  to  the 
proof  of  the  law  of  uniformity  of  succession  as  true  of  all  phenomena  with- 
out exception,  this  character  of  completeness  and  conclusiveness,  are  the 
following : First,  that  we  now  know  it  directly  to  be  true  of  far  the  great- 
est number  of  phenomena;  that  there  are  none  of  which  we  know  it  not  to 
be  true,  the  utmost  that  can  be  said  being,  that  of  some  we  can  not  positive- 
ly from  direct  evidence  affirm  its  truth ; while  phenomenon  after  phenome- 
non, as  they  become  better  known  to  us,  are  constantly  passing  from  the 
latter  class  into  the  former;  and  in  all  cases  in  which  that  transition  has 
not  yet  taken  place,  the  absence  of  direct  proof  is  accounted  for  by  the  rar- 
ity or  the  obscurity  of  the  phenomena,  our  deficient  means  of  observing 
them,  or  the  logical  difficulties  arising  from  the  complication  of  the  circum- 
stances in  which  they  occur;  insomuch  that,  notwithstanding  as  rigid  a 
dependence  on  given  conditions  as  exists  in  the  case  of  any  other  phenome- 
non, it  was  not  likely  that  we  should  be  better  acquainted  with  those  con- 
ditions than  we  are.  Besides  this  first  class  of  considerations,  there  is  a 
second,  which  still  further  corroborates  the  conclusion.  Although  there  are 
phenomena  the  production  and  changes  of  which  elude  all  our  attempts  to 
reduce  them  universally  to  any  ascertained  law  ; yet  in  every  such  case,  the 
phenomenon,  or  the  objects  concerned  in  it,  are  found  in  some  instances  to 
obey  the  known  laws  of  nature.  The  wind,  for  example,  is  the  type  of  un- 
certainty and  caprice,  yet  we  find  it  in  some  cases  obeying  with  as  much 
constancy  as  any  phenomenon  in  nature  the  law  of  the  tendency  of  fluids 
to  distribute  themselves  so  as  to  equalize  the  pressure  on  every  side  of  each 
of  their  particles ; as  in  the  case  of  the  trade-winds  and  the  monsoons. 


EVIDENCE  OF  UNIVERSAL  CAUSATION. 


405 


Lightning  might  once  have  been  supposed  to  obey  no  laws ; but  since  it 
has  been  ascertained  to  be  identical  with  electricity,  we  know  that  the  very 
same  phenomenon  in  some  of  its  manifestations  is  implicitly  obedient  to  the 
action  of  fixed  causes.  I do  not  believe  that  there  is  now  one  object  or 
event  in  all  our  experience  of  nature,  within  the  bounds  of  the  solar  system 
at  least,  which  has  not  either  been  ascertained  by  direct  observation  to  fol- 
low laws  of  its  own,  or  been  proved  to  be  closely  similar  to  objects  and 
events  which,  in  more  familiar  manifestations,  or  on  a more  limited  scale, 
follow  strict  laws ; our  inability  to  trace  the  same  laws  on  a larger  scale  and 
in  the  more  recondite  instances,  being  accounted  for  by  the  number  and 
complication  of  the  modifying  causes,  or  by  their  inaccessibility  to  observa- 
tion. 

The  progress  of  experience,  therefore,  has  dissipated  the  doubt  which 
must  have  rested  on  the  universality  of  the  law  of  causation  while  there 
were  phenomena  which  seemed  to  be  sui  generis , not  subject  to  the  same 
laws  with  any  other  class  of  phenomena,  and  not  as  yet  ascertained  to  have 
peculiar  laws  of  their  own.  This  great  generalization,  however,  might  rea- 
sonably have  been,  as  it  in  fact  was,  acted  on  as  a probability  of  the  high- 
est order,  before  there  were  sufficient  grounds  for  receiving  it  as  a certainty. 
In  matters  of  evidence,  as  in  all  other  human  things,  we  neither  require,  nor 
can  attain,  the  absolute.  We  must  hold  even  our  strongest  convictions 
with  an  opening  left  in  our  minds  for  the  reception  of  facts  which  contra- 
dict them;  and  only  when  we  have  taken  this  precaution,  have  we  earned 
the  right  to  act  upon  our  convictions  with  complete  confidence  when  no 
such  contradiction  appears.  Whatever  has  been  found  true  in  innumerable 
instances,  and  never  found  to  be  false  after  due  examination  in  any,  we  are 
safe  in  acting  on  as  universal  provisionally,  until  an  undoubted  exception 
appears ; provided  the  nature  of  the  case  be  such  that  a real  exception 
could  scarcely  have  escaped  notice.  When  every  phenomenon  that  we  ever 
knew  sufficiently  well  to  be  able  to  answer  the  question,  had  a cause  on 
which  it  was  invariably  consequent,  it  was  more  rational  to  suppose  that 
our  inability  to  assign  the  causes  of  other  phenomena  arose  from  our  igno- 
rance, than  that  there  were  phenomena  which  were  uncaused,  and  which 
happened  to  be  exactly  those  which  we  had  hitherto  had  no  sufficient  op- 
portunity of  studying. 

It  must,  at  the  same  time,  be  remarked,  that  the  reasons  for  this  reliance 
do  not  hold  in  circumstances  unknown  to  us,  and  beyond  the  possible  range 
of  our  experience.  In  distant  parts  of  the  stellar  regions,  where  the  phe- 
nomena may  be  entirely  unlike  those  with  which  we  are  acquainted,  it 
would  be  folly  to  affirm  confidently  that  this  general  law  prevails,  any  more 
than  those  special  ones  which  we  have  found  to  hold  universally  on  our 
own  planet.  The  uniformity  in  the  succession  of  events,  otherwise  called 
the  law  of  causation,  must  be  received  not  as  a law  of  the  universe,  but  of 
that  portion  of  it  only  which  is  within  the  range  of  our  means  of  sure  ob- 
servation, with  a reasonable  degree  of  extension  to  adjacent  cases.  To  ex- 
tend it  further  is  to  make  a supposition  without  evidence,  and  to  which,  in 
the  absence  of  any  ground  from  experience  for  estimating  its  degree  of 
probability,  it  would  be  idle  to  attempt  to  assign  any.* 

* One  of  the  most  rising  thinkers  of  the  new  generation  in  France,  M.  Taine  (who  ha3 
given,  in  the  Revue  des  Deux  Mondes,  the  most  masterly  analysis,  at  least  in  one  point  of 
view,  ever  made  of  the  present  work),  though  he  rejects,  on  this  and  similar  points  of  psy- 
chology, the  intuition  theory  in  its  ordinary  form,  nevertheless  assigns  to  the  law  of  causation, 
and  to  some  other  of  the  most  universal  laws,  that  certainty  beyond  the  bounds  of  human  ex- 


406 


INDUCTION. 


CHAPTER  XXII. 

OF  UNIFORMITIES  OF  CO-EXISTENCE  NOT  DEPENDENT  ON  CAUSATION. 

§ 1.  The  order  of  the  occurrence  of  phenomena  in  time,  is  either  succes- 
sive or  simultaneous;  the  uniformities,  therefore,  which  obtain  in  their  oc- 

perience,  which  I have  not  been  able  to  accord  to  them.  He  does  this  on  the  faith  of  our 
faculty  of  abstraction,  in  which  he  seems  to  recognize  an  independent  source  of  evidence,  not 
indeed  disclosing  truths  not  contained  in  our  experience,  but  affording  an  assurance  which 
experience  can  not  give,  of  the  universality  of  those  which  it  does  contain.  By  abstraction 
M.  Taine  seems  to  think  that  we  are  able,  not  merely  to  analyze  that  part  of  nature  which  we 
see,  and  exhibit  apart  the  elements  which  pervade  it,  but  to  distinguish  such  of  them  as  are 
elements  of  the  system  of  nature  considered  as  a whole,  not  incidents  belonging  to  our  limited 
terrestrial  experience.  I am  not  sure  that  I fully  enter  into  M.  Taine’s  meaning ; but  I con- 
fess I do  not  see  how  any  mere  abstract  conception,  elicited  by  our  minds  from  our  experi- 
ence, can  be  evidence  of  an  objective  fact  in  universal  Nature,  beyond  what  the  experience  it- 
self bears  witness  of ; or  how,  in  the  process  of  interpreting  in  general  language  the  testimony 
of  experience,  the  limitations  of  the  testimony  itself  can  be  cast  off. 

Dr.  Ward,  in  an  able  article  in  the  Dublin  Review  for  October,  1871,  contends  that  the  uni- 
formity of  nature  can  not  be  proved  from  experience,  but  from  “transcendental  considera- 
tions” only,  and  that,  consequently,  all  physical  science  would  be  deprived  of  its  basis,  if  such 
transcendental  proof  were  impossible. 

When  physical  science  is  said  to  depend  on  the  assumption  that  the  course  of  nature  is  in- 
variable, all  that  is  meant  is  that  the  conclusions  of  physical  science  are  not  known  as  absolute 
truths : the  truth  of  them  is  conditional  on  the  uniformity  of  the  course  of  nature ; and  all 
that  the  most  conclusive  observations  and  experiments  can  prove,  is  that  the  result  arrived  at 
will  be  true  if,  and  as  long  as,  the  present  laws  of  nature  are  valid.  But  this  is  all  the  as- 
surance we  require  for  the  guidance  of  our  conduct.  Dr.  Ward  himself  does  not  think  that 
his  transcendental  proofs  make  it  practically  greater;  for  he  believes,  as  a Catholic,  that  the 
course  of  nature  not  only  has  been,  but  frequently  and  even  daily  is,  suspended  by  supernatu- 
ral intervention. 

But  though  this  conditional  conclusiveness  of  the  evidence  of  experience,  which  is  sufficient 
for  the  purposes  of  life,  is  all  that  I was  necessarily  concerned  to  prove,  I have  given  reasons 
for  thinking  that  the  uniformity,  as  itself  a part  of  experience,  is  sufficiently  proved  to  justify 
undoubting  reliance  on  it.  This  Dr.  Ward  contests,  for  the  following  reasons  : 

First  (p.  315),  supposing  it  true  that  there  has  hitherto  been  no  well  authenticated  case  of 
a breach  in  the  uniformity  of  nature;-  “the  number  of  natural  agents  constantly  at  work  is 
incalculably  large;  and  the  observed  cases  of  uniformity  in  their  action  must  be  immeasur- 
ably fewer  than  one  thousandth  of  the  whole.  Scientific  men,  we  assume  for  the  moment, 
have  discovered  that  in  a certain  proportion  of  instances — immeasurably  fewer  than  one 
thousandth  of  the  whole — a certain  fact  has  prevailed;  the  fact  of  uniformity ; and  they  have 
not  found  a single  instance  in  which  that  fact  does  not  prevail.  Are  they  justified,  we  ask, 
in  inferring  from  these  premises  that  the  fact  is  universal?  Surely  the  question  answers  it- 
self. Let  us  make  a very  grotesque  supposition,  in  which,  however,  the  conclusion  would 
really  be  tried  according  to  the  arguments  adduced.  In  some  desert  of  Africa  there  is  an 
enormous  connected  edifice,  surrounding  some  vast  space,  in  which  dwell  certain  reasonable 
beings,  who  are  unable  to'  leave  the  inclosure.  In  this  edifice  are  more  than  a thousand 
chambers,  which  some  years  ago  were  entirely  locked  up,  and  the  keys  no  one  knew  where. 
By  constant  diligence  twenty-five  keys  have  been  found,  out  of  the  whole  number;  and  the 
corresponding  chambers,  situated  promiscuously  throughout  the  edifice,  have  been  opened. 
Each  chamber,  when  examined,  is  found  to  be  in  the  precise  shape  of  a dodecahedron.  Are 
the  inhabitants  justified  on  that  account  in  holding  with  certitude  that  the  remaining  975 
chambers  are  built  on  the  same  plan  ?” 

Not  with  perfect  certitude,  but  (if  the  chambers  to  which  the  keys  have  been  found  are 
really  “situated  promiscuously”)  with  so  high  a degree  of  probability  that  they  would  be  justi- 
fied in  acting  upon  the  presumption  until  an  exception  appeared. 

Dr.  Ward’s  argument,  however,  does  not  touch  mine  as  it  stands  in  the  text.  My  argu- 
ment is  grounded  on  the  fact  that  the  uniformity  of  the  course  of  nature  as  a whole,  is  con- 


CO-EXISTENCES  INDEPENDENT  OF  CAUSATION. 


407 


cuvrence,  are  either  uniformities  of  succession  or  of  co-existence.  Uniform- 
ities of  succession  are  all  comprehended  under  the  law  of  causation  and 
its  consequences.  Every  phenomenon  has  a cause,  which  it  invariably  fol- 
lows ; and  from  this  are  derived  other  invariable  sequences  among  the  suc- 
cessive stages  of  the  same  effect,  as  well  as  between  the  effects  resulting 
from  causes  which  invariably  succeed  one  another. 

In  the  same  manner  with  these  derivative  uniformities  of  succession,  a 
great  variety  of  uniformities  of  co-existence  also  take  their  rise.  Co-ordi- 
nate effects  of  the  same  cause  naturally  co-exist  with  one  another.  High 
water  at  any  point  on  the  earth’s  surface,  and  high  water  at  the  point  dia- 
metrically opposite  to  it,  are  effects  uniformly  simultaneous,  resulting  from 
the  direction  in  which  the  combined  attractions  of  the  sun  and  moon  act 
upon  the  waters  of  the  ocean.  An  eclipse  of  the  sun  to  us,  and  an  eclipse 
of  the  earth  to  a spectator  situated  in  the  moon,  are  in  like  manner  phe- 

stituted  by  the  uniform  sequences  of  special  effects  from  special  natural  agencies ; that  the 
number  of  these  natural  agencies  in  the  part  of  the  universe  known  to  us  is  not  incalculable, 
nor  even  extremely  great ; that  we  have  now  reason  to  think  that  at  least  the  far  greater 
number  of  them,  if  not  separately,  at  least  in  some  of  the  combinations  into  which  they  en- 
ter, have  been  made  sufficiently  amenable  to  observation,  to  have  enabled  us  actually  to  as- 
certain some  of  their  fixed  laws;  and  that  this  amount  of  experience  justifies  the  same  de- 
gree of  assurance  that  the  course  of  nature  is  uniform  throughout,  which  we  previously  had 
of  the  uniformity  of  sequence  among  the  phenomena  best  known  to  us.  This  view  of  the 
subject,  if  correct,  destroys  the  force  of  Dr.  Ward’s  first  argument. 

His  second  argument  is,  that  many  or  most  persons,  both  scientific  and  unscientific,  believe 
that  there  are  well  authenticated  cases  of  breach  in  the  uniformity  of  nature,  namely,  mira- 
cles. Neither  does  this  consideration  touch  what  I have  said  in  the  text.  I admit  no  other 
uniformity  in  the  events  of  nature  than  the  law  of  Causation  ; and  (as  I have  explained  in 
the  chapter  of  this  volume  which  treats  of  the  Grounds  of  Disbelief)  a miracle  is  no  excep- 
tion to  that  law.  In  every  case  of  alleged  miracle,  a new  antecedent  is  affirmed  to  exist;  a 
counteracting  cause , namely,  the  volition  of  a supernatural  being.  To  all,  therefore,  to  whom 
beings  with  superhuman  power  over  nature  are  a vera  causa , a miracle  is  a case  of  the  Law 
of  Universal  Causation,  not  a deviation  from  it. 

Dr.  Ward’s  last,  and  as  he  says,  strongest  argument,  is  the  familiar  one  of  Eeid,  Stewart,  and 
their  followers — that  whatever  knowledge  experience  gives  us  of  the  past  and  present,  it  gives 
us  none  of  the  future.  I confess  that  I see  no  force  whatever  in  this  argument.  Wherein 
does  a future  fact  differ  from  a present  or  a past  fact,  except  in  their  merely  momentary  re- 
lation to  the  human  beings  at  present  in  existence  ? The  answer  made  by  Priestley,  in  his 
Examination  of  Reid,  seems  to  me  sufficient,  viz.,  that  though  we  have  had  no  experience  of 
what  is  future,  we  have  had  abundant  experience  of  what  was  future.  The  ‘‘leap  in  the 
dark”  (as  Professor  Bain  calls  it)  from  the  past  to  the  future,  is  exactly  as  much  in  the 
dark  and  no  more,  as  the  leap  from  a past  which  we  have  personally  observed,  to  a past 
which  we  have  not.  I agree  with  Mr.  Bain  in  the  opinion  that  the  resemblance  of  what  we 
have  not  experienced  to  what  we  have,  is,  by  a law  of  our  nature,  presumed  through  the 
mere  energy  of  the  idea,  before  experience  has  proved  it.  This  psychological  truth,  however, 
is  not,  as  Dr.  Ward  when  criticising  Mr.  Bain  appears  to  think,  inconsistent  with  the  logical 
truth  that  experience  does  prove  it.  The  proof  comes  after  the  presumption,  and  consists  in 
its  invariable  verification  by  experience  when  the  experience  arrives.  The  fact  which  while 
it  was  future  could  not  be  observed,  having  as  yet  no  existence,  is  always,  when  it  becomes 
present  and  can  be  observed,  found  conformable  to  the  past. 

Dr.  M'Cosh  maintains  ( Examination  of  Mr.  J.  S.  Mill's  Philosophy,  p.  257)  that  the  uni- 
formity of  the  course  of  nature  is  a different  thing  from  the  law  of  causation  ; and  while  he 
allows  that  the  former  is  only  proved  by  a long  continuance  of  experience,  and  that  it  is  not 
inconceivable  nor  necessarily  incredible  that  there  may  be  worlds  in  which  it  does  not  pre- 
vail, he  considers  the  law  of  causation  to  be  known  intuitively.  There  is,  however,  no  other 
uniformity  in  the  events  of  nature  than  that  which  arises  from  the  law  of  causation  : so  long 
therefore  as  there  remained  any  doubt  that  the  course  of  nature  was  uniform  throughout,  at 
least  when  not  modified  by  the  intervention  of  a new  (supernatural)  cause,  a doubt  was  nec- 
essarily implied,  not  indeed  of  the  reality  of  causation,  but  of  its  universality.  If  the  uni- 
formity of  the  course  of  nature  has  any  exceptions — if  any  events  succeed  one  another  without 
fixed  laws — to  that  extent  the  law  of  causation  fails ; there  are  events  which  do  not  depend 
on  causes. 


408 


INDUCTION. 


noraena  invariably  co-existent;  and  their  co-existence  can  equally  be  de- 
duced from  the  laws  of  their  production. 

It  is  an  obvious  question,  therefore,  whether  all  the  uniformities  of  co-ex- 
istence among  phenomena  may  not  be  accounted  for  in  this  manner.  And 
it  can  not  be  doubted  that  between  phenomena  which  are  themselves  ef- 
fects, the  co-existences  must  necessarily  depend  on  the  causes  of  those  phe- 
nomena. If  they  are  effects  immediately  or  remotely  of  the  same  cause, 
they  can  not  co-exist  except  by  virtue  of  some  laws  or  properties  of  that 
cause;  if  they  are  effects  of  different  causes,  they  can  not  co-exist  unless  it 
be  because  their  causes  co-exist;  and  the  uniformity  of  co-existence,  if  such 
there  be,  between  the  effects,  proves  that  those  particular  causes,  within  the 
limits  of  our  observation,  have  uniformly  been  co-existent. 

§ 2.  But  these  same  considerations  compel  us  to  recognize  that  there 
must  be  one  class  of  co-existences  which  can  not  depend  on  causation:  the 
co-existences  between  the  ultimate  properties  of  things- — those  properties 
which  are  the  causes  of  all  phenomena,  but  are  not  themselves  caused  by 
any  phenomenon,  and  a cause  for  which  could  only  be  sought  by  ascending 
to  the  origin  of  all  things.  Yet  among  these  ultimate  properties  there  are 
not  only  co-existences,  but  uniformities  of  co-existence.  General  proposi- 
tions may  be,  and  are,  formed,  which  assert  that  whenever  certain  proper- 
ties are  found,  certain  others  are  found  along  with  them.  We  perceive  an 
object ; say,  for  instance,  water.  We  recognize  it  to  be  water,  of  course  by 
certain  of  its  properties.  Having  recognized  it,  we  are  able  to  affirm  of  it 
innumerable  other  properties ; which  we  could  not  do  unless  it  were  a gen- 
eral truth,  a law  or  uniformity  in  nature,  that  the  set  of  properties  by 
which  we  identify  the  substance  as  water  always  have  those  other  proper- 
ties conjoined  with  them. 

In  a former  place*  it  has  been  explained,  in  some  detail,  what  is  meant 
by  the  Kinds  of  objects;  those  classes  which  differ  from  one  another  not 
by  a limited  and  definite,  but  by  an  indefinite  and  unknown,  number  of  dis- 
tinctions. To  this  we  have  now  to  add,  that  every  proposition  by  which 
any  thing  is  asserted  of  a Kind,  affirms  a uniformity  of  co-existence. 
Since  we  know  nothing  of  Kinds  but  their  properties,  the  Kind,  to  us,  is 
the  set  of  properties  by  which  it  is  identified,  and  which  must  of  course  be 
sufficient  to  distinguish  it  from  every  other  kind. f In  affirming  any  thing, 
therefore,  of  a Kind,  we  are  affirming  something  to  be  uniformly  co-exist- 
ent  with  the  properties  by  which  the  kind  is  recognized ; and  that  is  the 
sole  meaning  of  the  assertion. 

Among  the,  uniformities  of  co-existence  which  exist  in  nature,  may  hence 
be  numbered  all  the  properties  of  Kinds.  The  whole  of  these,  however, 
are  not  independent  of  causation,  but  only  a portion  of  them.  Some  are 
ultimate  properties,  others  derivative:  of  some,  no  cause  can  be  assigned, 
but  others  are  manifestly  dependent  on  causes.  Thus,  pure  oxygen  gas  is 
a Kind,  and  one  of  its  most  unequivocal  properties  is  its  gaseous  form ; 

* Book  i.,  chap.  vii. 

t In  some  cases,  a Kind  is  sufficiently  identified  by  some  one  remarkable  property  : but 
most  commonly  several  are  required  ; each  property  considered  singly,  being  a joint  property 
of  that  and  of  other  Kinds.  The  color  and  brightness  of  the  diamond  are  common  to  it  with 
the  paste  from  which  false  diamonds  are  made  ; its  octohedral  form  is  common  to  it  with 
alum,  and  magnetic  iron  ore ; but  the  color  and  brightness  and  the  form  together,  identify  its 
Kind ; that  is,  are  a mark  to  us  that  it  is  combustible ; that  when  burned  it  produces  carbon- 
ic acid  ; that  it  can  not  be  cut  with  any  known  substance  ; together  with  many  other  ascer- 
tained properties,  and  the  fact  that  there  exist  an  indefinite  number  still  unascertained. 


CO-EXISTENCES  INDEPENDENT  OF  CAUSATION. 


409 


this  property,  however,  has  for  its  cause  the  presence  of  a certain  quantity 
of  latent  heat ; and  if  that  heat  could  be  taken  away  (as  has  been  done  from 
so  many  gases  in  Faraday’s  experiments),  the  gaseous  form  would  doubt- 
less disappear,  together  with  numerous  other  properties  which  depend  on, 
or  are  caused  by,  that  property. 

In  regard  to  all  substances  which  are  chemical  compounds,  and  which 
therefore  may  be  regarded  as  products  of  the  juxtaposition  of  substances 
different  in  Kind  from  themselves,  there  is  considerable  reason  to  presume 
that  the  specific  properties  of  the  compound  are  consequent,  as  effects,  on 
some  of  the  properties  of  the  elements,  though  little  progress  has  yet  been 
made  in  tracing  any  invariable  relation  between  the  latter  and  the  former. 
Still  more  strongly  will  a similar  presumption  exist,  when  the  object  itself, 
as  in  the  case  of  organized  beings,  is  no  primeval  agent,  but  an  effect,  which 
depends  on  a cause  or  causes  for  its  very  existence.  The  Kinds,  therefore, 
which  are  called  in  chemistry  simple  substances,  or  elementary  natural 
agents,  are  the  only  ones,  any  of  tvhose  properties  can  with  certainty  be 
considered  ultimate ; and  of  these  the  ultimate  properties  are  probably 
much  more  numerous  than  we  at  present  recognize,  since  every  successful 
instance  of  the  resolution  of  the  properties  of  their  compounds  into  simpler 
laws,  generally  leads  to  the  recognition  of  properties  in  the  elements  dis- 
tinct from  any  previously  known.  The  resolution  of  the  laws  of  the  heav- 
enly motions  established  the  previously  unknown  ultimate  property  of  a 
mutual  attraction  between  all  bodies ; the  resolution,  so  far  as  it  has  yet 
proceeded,  of  the  laws  of  crystallization,  of  chemical  composition,  electricity, 
magnetism,  etc.,  points  to  various  polarities,  ultimately  inherent  in  the  par- 
ticles of  which  bodies  are  composed ; the  comparative  atomic  weights  of 
different  kinds  of  bodies  were  ascertained  by  resolving  into  more  general 
laws  the  uniformities  observed  in  the  proportions  in  which  substances  com- 
bine with  one  another,  and  so  forth.  Thus,  although  every  resolution  of  a 
complex  uniformity  into  simpler  and  more  elementary  laws  has  an  appar- 
ent tendency  to  diminish  the  number  of  the  ultimate  properties,  and  really 
does  remove  many  properties  from  the  list;  yet  (since  the  result  of  this 
simplifying  process  is  to  trace  up  an  ever  greater  variety  of  different  ef- 
fects to  the  same  agents)  the  further  we  advance  in  this  direction,  the 
greater  number  of  distinct  properties  we  are  forced  to  recognize  in  one 
and  the  same  object;  the  co-existences  of  which  properties  must  accord- 
ingly be  ranked  among  the  ultimate  generalities  of  nature. 

§ 3.  There  are,  therefore,  only  two  kinds  of  propositions  which  assert 
uniformity  of  co-existence  between  properties.  Either  the  properties  de- 
pend on  causes  or  they  do  not.  If  they  do,  the  proposition  which  affirms 
them  to  be  co-existent  is  a derivative  law  of  co-existence  between  effects, 
and,  until  resolved  into  the  laws  of  causation  on  which  it  depends,  is  an 
empirical  law,  and  to  be  tried  by  the  principles  of  induction  to  which  such 
laws  are  amenable.  If,  on  the  other  hand,  the  properties  do  not  depend 
on  causes,  but  are  ultimate  properties,  then,  if  it  be  true  that  they  invaria- 
bly co-exist,  they  must  all  be  ultimate  properties  of  one  and  the  same 
Kind;  and  it  is  of  these  only  that  the  co-existences  can  be  classed  as  a 
peculiar  sort  of  laws  of  nature. 

When  we  affirm  that  all  crows  are  black,  or  that  all  negroes  have  woolly 
hair,  we  assert  a uniformity  of  co-existence.  We  assert  that  the  property 
of  blackness  or  of  having  woolly  hair  invariably  co-exists  with  the  proper- 
ties which,  in  common  language,  or  in  the  scientific  classification  that  we 


410 


INDUCTION. 


adopt,  are  taken  to  constitute  the  class  crow,  or  the  class  negro.  Now, 
supposing  blackness  to  be  an  ultimate  property  of  black  objects,  or  woolly 
hair  an  ultimate  property  of  the  animals  which  possess  it;  supposing  that 
these  properties  are  not  results  of  causation,  are  not  connected  with  ante- 
cedent phenomena  by  any  law  ; then  if  all  crows  are  black,  and  all  negroes 
have  woolly  hair,  these  must  be  ultimate  properties  of  the  kind  crow,  or 
negro,  or  of  some  kind  which  includes  them.  If,  on  the  contrary,  black- 
ness or  woolly  hair  be  an  effect  depending  on  causes,  these  general  propo- 
sitions are  manifestly  empirical  laws  ; and  all  that  has  already  been  said 
respecting  that  class  of  generalizations  may  be  applied  without  modifica- 
tion to  these. 

Now,  we  have  seen  that  in  the  case  of  all  compounds — of  all  things,  in 
short,  except  the  elementary  substances  and  primary  powers  of  nature — 
the  presumption  is,  that  the  properties  do  really  depend  upon  causes;  and 
it  is  impossible  in  any  case  whatever  to  be  certain  that  they  do  not.  We 
therefore  should  not  be  safe  in  claiming  for  any  generalization  respecting 
the  co-existence  of  properties,  a degree  of  certainty  to  which,  if  the  prop- 
erties should  happen  to  be  the  result  of  causes,  it  would  have  no  claim. 
A generalization  respecting  co-existence,  or,  in  other  words,  respecting  the 
properties  of  kinds,  may  be  an  ultimate  truth,  but  it  may  also  be  merely  a 
derivative  one ; and  since,  if  so,  it  is  one  of  those  derivative  laws  which 
are  neither  laws  of  causation  nor  have  been  resolved  into  the  laws  of  cau- 
sation on  which  they  depend,  it  can  possess  no  higher  degree  of  evidence 
than  belongs  to  an  empirical  law. 

§ 4.  This  conclusion  will  be  confirmed  by  the  consideration  of  one  great 
deficiency,  which  precludes  the  application  to  the  ultimate  uniformities  of 
co-existence,  of  a system  of  rigorous  scientific  induction,  such  as  the  uni- 
formities in  the  succession  of  phenomena  have  been  found  to  admit  of. 
The  basis  of  such  a system  is  wanting;  there  is  no  general  axiom  standing 
in  the  same  relation  to  the  uniformities  of  co-existence  as  the  law  of  causa- 
tion does  to  those  of  succession.  The  Methods  of  Induction  applicable  to 
the  ascertainment  of  causes  and  effects  are  grounded  on  the  principle  that 
every  thing  which  has  a beginning  must  have  some  cause  or  other;  that 
among  the  circumstances  which  actually  existed  at  the  time  of  its  com- 
mencement, there  is  certainly  some  one  combination,  on  which  the  effect 
in  question  is  unconditionally  consequent,  and  on  the  repetition  of  which 
it  would  certainly  again  recur.  But  in  an  inquiry  whether  some  kind  (as 
crow)  universally  possesses  a certain  property  (as  blackness),  there  is  no 
room  for  any  assumption  analogous  to  this.  We  have  no  previous  certain- 
ty that  the  property  must  have  something  which  constantly  co-exists  with 
it;  must  have  an  invariable  co-existent,  in  the  same  manner  as  an  event 
must  have  an  invariable  antecedent.  When  we  feel  pain,  we  must  be  in 
some  circumstances  under  which,  if  exactly  repeated,  we  should  always  feel 
pain.  But  when  we  are  conscious  of  blackness,  it  does  not  follow  that 
there  is  something  else  present  of  which  blackness  is  a constant  accompani- 
ment. There  is,  therefore,  no  room  for  elimination;  no  method  of  Agree- 
ment or  Difference,  or  of  Concomitant  Variations  (which  is  but  a modifi- 
cation either  of  the  Method  of  Agreement  or  of  the  Method  of  Difference). 
We  can  not  conclude  that  the  blackness  we  see  in  crows  must  be  an  in- 
variable property  of  crows  merely  because  there  is  nothing  else  present  of 
which  it  can  be  an  invariable  property.  We  therefore  inquire  into  the 
truth  of  a proposition  like  “All  crows  are  black,”  under  the  same  disad- 


CO-EXISTENCES  INDEPENDENT  OF  CAUSATION. 


411 


vantage  as  if,  in  our  inquiries  into  causation,  we  were  compelled  to  let  in,  as 
one  of  the  possibilities,  that  the  effect  may  in  that  particular  instance  have 
arisen  without  any  cause  at  all. 

To  overlook  this  grand  distinction  was,  as  it  seems  to  me,  the  capital 
error  in  Bacon’s  view  of  inductive  philosophy.  The  principle  of  elimina- 
tion, that  great  logical  instrument  which  he  had  the  immense  merit  of  first 
bringing  into  general  use,  he  deemed  applicable  in  the  same  sense,  and  in 
as  unqualified  a manner,  to  the  investigation  of  the  co-existences,  as  to  that 
of  the  successions  of  phenomena.  He  seems  to  have  thought  that  as  every 
event  has  a cause,  or  invariable  antecedent,  so  every  property  of  an  object 
has  an  invariable  co-existent,  which  he  called  its  form  ; and  the  examples 
he  chiefly  selected  for  the  application  and  illustration  of  his  method,  were 
inquiries  into  such  forms  ; attempts  to  determine  in  what  else  all  those 
objects  resembled,  which  agreed  in  some  one  general  property,  as  hardness 
or  softness,  dryness  or  moistuess,  heat  or  coldness.  Such  inquiries  could 
lead  to  no  result.  The  objects  seldom  have  any  such  circumstances  in 
common.  They  usually  agree  in  the  one  point  inquired  into,  and  in  noth- 
ing else.  A great  proportion  of  the  properties  which,  so  far  as  we  can 
conjecture,  are  the  likeliest  to  be  really  ultimate,  would  seem  to  be  inher- 
ently properties  of  many  different  kinds  of  things  not  allied  in  any  other 
respect.  And  as  for  the  properties  which,  being  effects  of  causes,  we  are 
able  to  give  some  account  of,  they  have  generally  nothing  to  do  with  the 
ultimate  resemblances  or  diversities  in  the  objects  themselves,  but  depend 
on  some  outward  circumstances,  under  the  influence  of  which  any  objects 
whatever  are  capable  of  manifesting  those  properties ; as  is  emphatically 
the  case  with  those  favorite  subjects  of  Bacon’s  scientific  inquiries,  hotness 
and  coldness,  as  well  as  with  hardness  and  softness,  solidity  and  fluidity, 
and  many  other  conspicuous  qualities. 

In  the  absence,  then,  of  any  universal  law  of  co-existence  similar  to  the 
universal  law  of  causation  which  regulates  sequence,  we  are  thrown  back 
upon  the  unscientific  induction  of  the  ancients,  joe?’  enumerationem  simpli- 
cem,  ubi  non  reperitur  instantia  contradictoria.  The  reason  we  have  for 
believing  that  all  crows  are  black,  is  simply  that  we  have  seen  and  heard  of 
many  black  crows,  and  never  one  of  any  other  color.  It  remains  to  be 
considered  how  far  this  evidence  can  reach,  and  how  we  are  to  measure  its 
strength  in  any  given  case. 

§ 5.  It  sometimes  happens  that  a mere  change  in  the  mode  of  verbally 
enunciating  a question,  though  nothing  is  really  added  to  the  meaning  ex- 
pressed, is  of  itself  a considerable  step  toward  its  solution.  This,  I think, 
happens  in  the  present  instance.  The  degree  of  certainty  of  any  generaliza- 
tion which  rests  on  no  other  evidence  than  the  agreement,  so  far  as  it  goes, 
of  all  past  observation,  is  but  another  phrase  for  the  degree  of  improbability 
that  an  exception,  if  any  existed,  could  have  hitherto  remained  unobserved. 
The  reason  for  believing  that  all  crows  are  black,  is  measured  by  the  im- 
probability that  crows  of  any  other  color  should  have  existed  to  the  pres- 
ent time  without  our  being  aware  of  it.  Let  us  state  the  question  in  this 
last  mode,  and  consider  what  is  implied  in  the  supposition  that  there  may 
be  crows  which  are  not  black,  and  under  what  conditions  we  can  bo  justi- 
fied in  regarding  this  as  incredible. 

If  there  really  exist  crows  which  are  not  black,  one  of  two  things  must 
be  the  fact.  Either  the  circumstance  of  blackness,  in  all  crows  hitherto 
observed,  must  be,  as  it  were,  an  accident,  not  connected  with  any  distinc- 


412 


INDUCTION. 


lion  of  Kind ; or  if  it  be  a property  of  Kind,  the  crows  which  are  not 
black  must  be  a new  Kind,  a Kind  hitherto  overlooked,  though  coming 
under  the  same  general  description  by  which  crows  have  hitherto  been 
characterized.  The  first  supposition  would  be  proved  true  if  we  were  to 
discover  casually  a white  crow  among  black  ones,  or  if  it  were  found  that 
black  crows  sometimes  turn  white.  The  second  would  be  shown  to  be  the 
fact  if  in  Australia  or  Central  Africa  a species  or  a race  of  white  or  gray 
crows  were  found  to  exist. 

§ 6.  The  former  of  these  suppositions  necessarily  implies  that  the  color 
is  an  effect  of  causation.  If  blackness,  in  the  crows  in  which  it  has  been 
observed,  be  not  a property  of  Kind,  but  can  be  present  or  absent  without 
any  difference  generally  in  the  properties  of  the  object,  then  it  is  not  an 
ultimate  fact  in  the  individuals  themselves,  but  is  certainly  dependent  on  a 
cause.  There  are,  no  doubt,  many  properties  which  vary  from  individual 
to  individual  of  the  same  Kind,  even  the  same  infima  species , or  lowest 
Kind.  Some  dowers  may  be  either  white  or  red,  without  differing  in  any 
other  respect.  But  these  properties  are  not  ultimate;  they  depend  on 
causes.  So  far  as  the  properties  of  a thing  belong  to  its  own  nature,  and 
do  not  arise  from  some  cause  extrinsic  to  it,  they  are  always  the  same  in 
the  same  Kind.  Take,  for  instance,  all  simple  substances  and  elementary 
powers ; the  only  things  of  which  we  are  certain  that  some  at  least  of  then- 
properties  are  really  ultimate.  Color  is  generally  esteemed  the  most  varia- 
ble of  all  properties:  yet  we  do  not  find  that  sulphur  is  sometimes  yellow 
and  sometimes  white,  or  that  it  varies  in  color  at  all,  except  so  far  as  color 
is  the  effect  of  some  extrinsic  cause,  as  of  the  sort  of  light  thrown  upon  it, 
the  mechanical  arrangement  of  the  particles  (as  after  fusion),  etc.  We  do 
not  find  that  iron  is  sometimes  fluid  and  sometimes  solid  at  the  same  tem- 
perature; gold  sometimes  malleable  and  sometimes  brittle;  that  hydrogen 
will  sometimes  combine  with  oxygen  and  sometimes  not;  or  the  like.  If 
from  simple  substances  we  pass  to  any  of  their  definite  compounds,  as 
water,  lime,  or  sulphuric  acid,  there  is  the  same  constancy  in  their  proper- 
ties. When  properties  vary  from  individual  to  individual,  it  is  either  in 
the  case  of  miscellaneous  aggregations,  such  as  atmospheric  air  or  rock, 
composed  of  heterogeneous  substances,  and  not  constituting  or  belonging 
to  any  real  Kind,*  or  it  is  in  the  case  of  organic  beings.  In  them,  indeed, 
there  is  variability  in  a high  degree.  Animals  of  the  same  species  and 
race,  human  beings  of  the  same  age,  sex,  and  country,  will  be  most  differ- 
ent, for  example,  in  face  and  figure.  But  organized  beings  (from  the  ex- 
treme complication  of  the  laws  by  which  they  are  regulated)  being  more 
eminently  modifiable,  that  is,  liable  to  be  influenced  by  a greater  number 
and  variety  of  causes,  than  any  other  phenomena  whatever;  having  also 
themselves  had  a beginning,  and  therefore  a cause;  there  is  reason  to  be- 
lieve that  none  of  their  properties  are  ultimate,  but  all  of  them  deriva- 
tive, and  produced  by  causation.  And  the  presumption  is  confirmed,  by 
the  fact  that  the  properties  which  vary  from  one  individual  to  another,  also 
generally  vary  more  or  less  at  different  times  in  the  same  individual;  which 
variation,  like  any  other  event,  supposes  a cause,  and  implies,  consequently, 
that  the  properties  are  not  independent  of  causation. 

If,  therefore,  blackness  be  merely  accidental  in  crows,  and  capable  of 

* This  doctrine  of  course  assumes  that  the  allotropic  forms  of  what  is  chemically  the  same 
substance  are  so  many  different  Kinds;  and  such,  in  the  sense  in  which  the  word  Kind  is 
used  in  this  treatise,  they  really  are. 


CO-EXISTENCES  INDEPENDENT  OF  CAUSATION. 


413 


varying  while  the  Kind  remains  the  same,  its  presence  or  absence  is  doubt- 
less no  ultimate  fact,  but  the  effect  of  some  unknown  cause:  and  in  that 
case  the  universality  of  the  experience  that  all  crows  are  black  is  sufficient 
proof  of  a common  cause,  and  establishes  the  generalization  as  an  empirical 
law.  Since  there  are  innumerable  instances  in  the  affirmative,  and  hitherto 
none  at  all  in  the  negative,  the  causes  on  which  the  property  depends  must 
exist  everywhere  in  the  limits  of  the  observations  which  have  been  made; 
and  the  proposition  may  be  received  as  universal  within  those  limits,  and 
with  the  allowable  degree  of  extension  to  adjacent  cases. 

§ 7.  If,  in  the  second  place,  the  property,  in  the  instances  in  which  it  has 
been  observed,  is  not  an  effect  of  causation,  it  is  a property  of  Kind  ; and 
in  that  case  the  generalization  can  only  be  set  aside  by  the  discovery  of  a 
new  Kind  of  crow.  That,  however,  a peculiar  Kind  not  hitherto  discover- 
ed should  exist  in  nature,  is  a supposition  so  often  realized  that  it  can  not 
be  considered  at  all  improbable.  We  have  nothing  to  authorize  us  in  at- 
tempting to  limit  the  Kinds  of  things  which  exist  in  nature.  The  only 
unlikelihood  would  be  that  a new  Kind  should  be  discovered  in  localities 
which  there  wTas  previously  reason  to  believe  had  been  thoroughly  ex- 
plored ; and  even  this  improbability  depends  on  the  degree  of  conspicuous- 
ness of  the  difference  between  the  newly-discovered  Kind  and  all  others, 
since  new  kinds  of  minerals,  plants,  and  even  animals,  previously  overlooked 
or  confounded  with  known  species,  are  still  continually  detected  in  the 
most  frequented  situations.  On  this  second  ground,  therefore,  as  well  as 
on  the  first,  the  observed  uniformity  of  co-existence  can  only  hold  good  as 
an  empirical  law,  within  the  limits  not  only  of  actual  observation,  but  of  an 
observation  as  accurate  as  the  nature  of  the  case  required.  And  hence  it 
is  that  (as  remarked  in  an  early  chapter  of  the  present  book)  we  so  often 
give  up  generalizations  of  this  class  at  the  first  summons,  if  any  credible 
witness  stated  that  he  had  seen  a white  crow,  under  circumstances  which 
made  it  not  incredible  that  it  should  have  escaped  notice  previously,  we 
should  give  full  credence  to  the  statement. 

It  appears,  then,  that  the  uniformities  which  obtain  in  the  co-existence  of 
phenomena — those  which  we  have  reason  to  consider  as  ultimate,  no  less 
than  those  which  arise  from  the  laws  of  causes  yet  undetected — are  entitled 
to  reception  only  as  empirical  laws  ; are  not  to  be  presumed  true  except 
within  the  limits  of  time,  place,  and  circumstance,  in  which  the  observa- 
tions were  made,  or  except  in  cases  strictly  adjacent. 

§ 8.  We  have  seen  in  the  last  chapter  that  there  is  a point  of  generality 
at  which  empirical  laws  become  as  certain  as  laws  of  nature,  or,  rather,  at 
which  there  is  no  longer  any  distinction  between  empirical  laws  and  laws 
of  nature.  As  empirical  laws  approach  this  point,  in  other  w'ords,  as  they 
rise  in  their  degree  of  generality,  they  become  more  certain ; their  univer- 
sality may  be  more  strongly  relied  on.  For,  in  the  first  place,  if  they  are 
results  of  causation  (which,  even  in  the  class  of  uniformities  treated  of  in 
the  present  chapter,  we  never  can  be  certain  that  they  are  not)  the  more 
general  they  are,  the  greater  is  proved  to  be  the  space  over  which  the 
necessary  collocations  prevail,  and  within  which  no  causes  exist  capable  of 
counteracting  the  unknown  causes  on  which  the  empirical  law  depends. 
To  say  that  any  thing  is  an  invariable  property  of  some  very  limited  class 
of  objects,  is  to  say  that  it  invariably  accompanies  some  very  numerous 
and  complex  group  of  distinguishing  properties ; which,  if  causation  be  at 


INDUCTION. 


114 

all  concerned  in  the  matter,  argues  a combination  of  many  causes,  and 
therefore  a great  liability  to  counteraction ; while  the  comparatively  nar- 
row range  of  the  observations  renders  it  impossible  to  predict  to  what  ex- 
tent unknown  counteracting  causes  may  be  distributed  throughout  nature. 
But  when  a generalization  has  been  found  to  hold  good  of  a very  large 
proportion  of  all  things  whatever,  it  is  already  proved  that  nearly  all  the 
causes  which  exist  in  nature  have  no  power  over  it;  that  very  few  changes 
in  the  combination  of  causes  can  affect  it ; since  the  greater  number  of 
possible  combinations  must  have  already  existed  in  some  one  or  other  of 
the  instances  in  which  it  has  been  found  true.  If,  therefore,  any  empirical 
law  is  a result  of  causation,  the  more  general  it  is,  the  more  it  may  be  de- 
pended on.  And  even  if  it  be  no  result  of  causation,  but  an  ultimate  co- 
existence, the  more  general  it  is,  the  greater  amount  of  experience  it  is  de- 
rived from,  and  the  greater  therefore  is  the  probability  that  if  exceptions 
had  existed,  some  would  already  have  presented  themselves. 

For  these  reasons,  it  requires  much  more  evidence  to  establish  an  excep- 
tion to  one  of  the  more  general  empirical  laws  than  to  the  more  special 
ones.  We  should  not  have  any  difficulty  in  believing  that  there  might  be 
a new  Kind  of  crow ; or  a new  kind  of  bird  resembling  a crow  in  the 
properties  hitherto  considered  distinctive  of  that  Kind.  But  it  would  re- 
quire stronger  proof  to  convince  us  of  the  existence  of  a Kind  of  crow  hav- 
ing properties  at  variance  with  any  generally  recognized  universal  property 
of  birds  ; and  a still  higher  degree  if  the  properties  conflict  with  any  rec- 
ognized universal  property  of  animals.  And  this  is  conformable  to  the 
mode  of  judgment  recommended  by  the  common  sense  and  general  prac- 
tice of  mankind,  who  are  more  incredulous  as  to  any  novelties  in  nature, 
according  to  the  degree  of  generality  of  the  experience  which  these  novel- 
ties seem  to  contradict. 

§ 9.  It  is  conceivable  that  the  alleged  properties  might  conflict  with 
some  recognized  universal  property  of  all  matter.  In  that  case  their  im- 
probability would  be  at  the  highest,  but  would  not  even  then  amount  to 
incredibility.  There  are  only  two  known  properties  common  to  all  mat- 
ter ; in  other  words,  there  is  but  one  known  uniformity  of  co-existence  of 
properties  co-extensive  with  all  physical  nature,  namely,  that  whatever  op- 
poses resistance  to  movement  gravitates,  or,  as  Professor  Bain  expresses  it, 
Inertia  and  Gravity  are  co-existent  through  all  matter,  and  proportionate 
in  their  amount.  These  properties,  as  he  truly  says,  are  not  mutually  im- 
plicated ; from  neither  of  them  could  we,  on  grounds  of  causation,  presume 
the  other.  But,  for  this  very  reason,  we  are  never  certain  that  a Kind  may 
not  be  discovered  possessing  one  of  the  properties  without  the  other.  The 
hypothetical  ether,  if  it  exists,  may  be  such  a Kind.  Our  senses  can  not 
recognize  in  it  either  resistance  or  gravity;  but  if  the  reality  of  a resisting 
medium  should  eventually  be  proved  (by  alteration,  for  example,  in  the 
times  of  revolution  of  periodic  comets,  combined  with  the  evidences  afford- 
ed by  the  phenomena  of  light  and  heat),  it  would  be  rash  to  conclude  from 
this  alone,  without  other  proofs,  that  it  must  gravitate. 

For  even  the  greater  generalizations,  which  embrace  comprehensive  Kinds 
containing  under  them  a great  number  and  variety  of  infimce  species,  are 
only  empirical  laws,  resting  on  induction  by  simple  enumeration  merely,  and 
not  on  any  process  of  elimination  — a process  wholly  inapplicable  to  this 
sort  of  case.  Such  generalizations,  therefore,  ought  to  be  grounded  on  an 
examination  of  all  the  mfimce  species  comprehended  in  them,  and  not  of  a 


CO-EXISTENCES  INDEPENDENT  OF  CAUSATION. 


415 


portion  only.  We  can  not  conclude  (where  causation  is  not  concerned), 
because  a proposition  is  true  of  a number  of  things  resembling  one  another 
only  in  being  animals,  that  it  is  therefore  true  of  all  animals.  If,  indeed, 
any  thing  be  true  of  species  which  differ  more  from  one  another  than  either 
differs  from  a third,  especially  if  that  third  species  occupies  in  most  of  its 
known  properties  a position  between  the  two  former,  there  is  some  proba- 
bility that  the  same  thing  will  also  be  true  of  that  intermediate  species;  for 
it  is  often,  though  by  no  means  universally,  found,  that  there  is  a sort  of 
parallelism  in  the  properties  of  different  Kinds,  and  that  their  degree  of 
unlikeness  in  one  respect  bears  some  proportion  to  their  unlikeness  in  oth- 
ers. We  see  this  parallelism  in  the  properties  of  the  different  metals;  in 
those  of  sulphur,  phosphorus,  and  carbon  ; of  chlorine,  iodine,  and  bromine; 
in  the  natural  orders  of  plants  and  animals,  etc.  But  there  are  innumera- 
ble anomalies  and  exceptions  to  this  sort  of  conformity;  if  indeed  the  con- 
formity itself  be  any  thing  but  an  anomaly  and  an  exception  in  nature. 

Universal  propositions,  therefore,  respecting  the  properties  of  superior 
Kinds,  unless  grounded  on  proved  or  presumed  connection  by  causation, 
ought  not  to  be  hazarded  except  after  separately  examining  every  known 
sub-kind  included  in  the  larger  Kind.  And  even  then  such  generalizations 
must  be  held  in  readiness  to  be  given  up  on  the  occurrence  of  some  new 
anomaly,  which,  when  the  uniformity  is  not  derived  from  causation,  can 
never,  even  in  the  case  of  the  most  general  of  these  empirical  laws,  be  con- 
sidered very  improbable.  Thus,  all  the  universal  propositions  which  it  has 
been  attempted  to  lay  down  respecting  simple  substances,  or  concerning 
any  of  the  classes  which  have  been  formed  among  simple  substances  (and 
the  attempt  has  been  often  made),  have,  with  the  progress  of  experience, 
either  faded  into  inanity,  or  been  proved  to  be  erroneous  ; and  each  Kind 
of  simple  substance  remains,  with  its  own  collection  of  properties  apart 
from  the  rest,  saving  a certain  parallelism  with  a few  other  Kinds,  the  most 
similar  to  itself.  In  organized  beings,  indeed,  there  are  abundance  of 
propositions  ascertained  to  be  universally  true  of  superior  genera,  to  many 
of  which  the  discovery  hereafter  of  any  exceptions  must  be  regarded  as 
extremely  improbable.  But  these,  as  already  observed,  are,  we  have  every 
reason  to  believe,  properties  dependent  on  causation.* 

* Professor  Bain  (Logie,  ii. , 13)  mentions  two  empirical  laws,  which  he  considers  to  be,  with 
the  exception  of  the  law  connecting  Gravity  with  Resistance  to  motion,  “ the  two  most  wide- 
ly operating  laws  as  yet  discovered  whereby  two  distinct  properties  are  conjoined  throughout 
substances  generally.”  The  first  is,  “ a law  connecting  Atomic  Weight  and  Specific  Heat  by 
an  inverse  proportion.  For  equal  weights  of  the  simple  bodies,  the  atomic  weight  multiplied 
bv  a number  expressing  the  specific  heat,  gives  a nearly  uniform  product.  The  products,  for 
all  the  elements,  are  near  the  constant  number  6.”  The  other  is  a law  which  obtains  “be- 
tween the  specific  gravity  of  substances  in  the  gaseous  state,  and  the  atomic  weights.  The 
relationship  of  the  two  numbers  is  in  some  instances  equality  ; in  other  instances  the  one  is  a 
multiple  of  the  other.  ” 

Neither  of  these  generalizations  has  the  smallest  appearance  of  being  an  ultimate  law. 
They  point  unmistakably  to  higher  laws.  Since  the  heat  necessary  to  raise  to  a given  tem- 
perature the  same  weight  of  different  substances  (called  their  specific  heat)  is  inversely  as 
their  atomic  weight,  that  is,  directly  as  the  number  of  atoms  in  a given  weight  of  the  sub- 
stance, it  follows  that  a single  atom  of  every  substance  requires  the  same  amount  of  heat  to 
raise  it  to  a given  temperature;  a most  interesting  and  important  law,  but  a law  of  causation. 
The  other  law  mentioned  by  Mr.  Bain  points  to  the  conclusion,  that  in  the  gaseous  state  all 
substances  contain,  in  the  same  space,  the  same  number  of  atoms;  which,  as  the  gaseoffs 
state  suspends  all  cohesive  force,  might  naturally  be  expected,  though  it  could  not  have  been 
positively  assumed.  This  law  may  also  be  a result  of  the  mode  of  action  of  causes,  namely, 
of  molecular  motions.  The  cases  in  which  one  of  the  numbers  is  not  identical  with  the  oth- 
er, but  a multiple  of  it,  may  be  explained  on  the  nowise  unlikely  supposition,  that  in  our  pres- 
ent estimate  of  the  atomic  weights  of  some  substances,  we  mistake  two,  or  three,  atoms  t'oi 
one,  or  one  for  several. 


416 


INDUCTION. 


Uniformities  of  co-existence,  then,  not  only  when  they  are  consequences 
of  laws  of  succession,  but  also  when  they  are  ultimate  truths,  must  be 
ranked,  for  the  purpose  of  logic,  among  empirical  laws ; and  are  amenable 
in  every  respect  to  the  same  rules  with  those  unresolved  uniformities  which 
are  known  to  be  dependent  on  causation.* 


CHAPTER  XXIII. 

OF  APPROXIMATE  GENERALIZATIONS,  AND  PROBABLE  EVIDENCE. 

§ 1.  In  our  inquiries  into  the  nature  of  the  inductive  process,  we  must 
not  confine  our  notice  to  such  generalizations  from  experience  as  profess  to 
be  universally  true.  There  is  a class  of  inductive  truths  avowedly  not  uni- 
versal ; in  which  it  is  not  pretended  that  the  predicate  is  always  true  of 
the  subject;  but  the  value  of  which,  as  generalizations,  is  nevertheless  ex- 
tremely great.  An  important  portion  of  the  field  of  inductive  knowledge 
does  not  consist  of  universal  truths,  but  of  approximations  to  such  truths; 
and  when  a conclusion  is  said  to  rest  on  probable  evidence,  the  premises  it 
is  drawn  from  are  usually  generalizations  of  this  sort. 

As  every  certain  inference  respecting  a particular  case  implies  that  there 
is  ground  for  a general  proposition  of  the  form,  every  A is  B ; so  does  ev- 
ery probable  inference  suppose  that  there  is  ground  for  a proposition  of  the 
form,  Most  A are  B ; and  the  degree  of  probability  of  the  inference  in  an  av- 
erage case  will  depend  on  the  proportion  between  the  number  of  instances 
existing  in  nature  which  accord  with  the  generalization,  and  the  number  of 
those  which  conflict  with  it. 

§ 2.  Propositions  in  the  form,  Most  A are  B,  are  of  a very  different  de- 
gree of  importance  in  science,  and  in  the  practice  of  life.  To  the  scientific 
inquirer  they  are  valuable  chiefly  as  materials  for,  and  steps  toward  uni- 
versal truths.  The  discovery  of  these  is  the  proper  end  of  science ; its  work 
is  not  done  if  it  stops  at  the  proposition  that  a majority  of  A are  B,  with- 
out circumscribing  that  majority  by  some  common  character,  fitted  to  dis- 
tinguish them  from  the  minority.  Independently  of  the  inferior  precision 
of  such  imperfect  generalizations,  and  the  inferior  assurance  with  which 
they  can  be  applied  to  individual  cases,  it  is  plain  that,  compared  with  ex- 
act generalizations,  they  are  almost  useless  as  means  of  discovering  ulterior 

* Dr.  M‘Cosh  (p.  324  of  his  book)  considers  the  laws  of  the  chemical  composition  of  bodies 
as  not  coining  under  the  principle  of  Causation  ; and  thinks  it  an  omission  in  this  work  not 
to  have  provided  special  canons  for  their  investigation  and  proof.  But  every  case  of  chem- 
ical composition  is,  as  I have  explained,  a case  of  causation.  When  it  is  said  that  water  is 
composed  of  hydrogen  and  oxygen,  the  affirmation  is  that  hydrogen  and  oxygen,  by  the  ac- 
tion on  one  another  which  they  exert  under  certain  conditions,  generate  the  properties  of  wa- 
ter. The  Canons  of  Induction,  therefore,  as  laid  down  in  this  treatise,  are  applicable  to  the 
case.  Such  special  adaptations  as  the  Inductive  methods  may  require  in  their  application  to 
chemistry,  or  any  other  science,  are  a proper  subject  for  any  one  who  treats  of  the  logic  of 
the  special  sciences,  as  Professor  Bain  has  done  in  the  latter  part  of  his  work;  but  they  do 
not  appertain  to  General  Logic. 

Dr.  M'Cosh  also  complains  (p.  325)  that  I have  given  no  canons  for  those  sciences  in  which 
“the  end  sought  is  not  the  discovery  of  Causes  or  of  Composition,  but  of  Classes;  that  is, 
Natural  Classes.”  Such  canons  could  be  no  other  than  the  principles  and  rules  of  Natural 
Classification,  which  I certainly  thought  that  I had  expounded  at  considerable  length.  But 
this  is  far  from  the  only  instance  in  which  Dr.  M‘Cosh  does  not  appear  to  be  aware  of  the 
contents  of  the  books  he  is  criticising. 


APPROXIMATE  GENERALIZATIONS. 


411 


truths  by  way  of  deduction.  We  may,  it  is  true,  by  combining  the  prop- 
osition Most  A are  B,  with  a universal  proposition,  Every  B is  C,  arrive 
at  the  conclusion  that  Most  A are  C.  But  when  a second  proposition  of 
the  approximate  kind  is  introduced — or  even  when  there  is  but  one,  if  that 
one  be  the  major  premise — nothing  can,  in  general,  be  positively  concluded. 
When  the  major  is  Most  B are  D,  then,  even  if  the  minor  be  Every  A is  B, 
we  can  not  infer  that  most  A are  D,or  with  any  certainty  that  even  some 
A are  D.  Though  the  majority  of  the  class  B have  the  attribute  signified 
by  D,  the  whole  of  the  sub-class  A may  belong  to  the  minority.* 

Though  so  little  use  can  be  made,  in  science,  of  approximate  generaliza- 
tions, except  as  a stage  on  the  road  to  something  better,  for  practical  guid- 
ance they  are  often  all  we  have  to  rely  on.  Even  when  science  has  really 
determined  the  universal  laws  of  any  phenomenon,  not  only  are  those  laws 
generally  too  much  encumbered  with  conditions  to  be  adapted  for  every- 
day use,  but  the  cases  which  present  themselves  in  life  are  too  complicated, 
and  our  decisions  require  to  be  taken  too  rapidly,  to  admit  of  waiting  till 
the  existence  of  a phenomenon  can  be  proved  by  what  have  been  scientific- 
ally ascertained  to  be  universal  marks  of  it.  To  be  indecisive  and  reluc- 
tant to  act,  because  we  have  not  evidence  of  a perfectly  conclusive  character 
to  act  on,  is  a defect  sometimes  incident  to  scientific  minds,  but  which, 
wherever  it  exists,  renders  them  unfit  for  practical  emergencies.  If  we 
would  succeed  in  action,  we  must  judge  by  indications  which,  though  they 
do  not  generally  mislead  us,  sometimes  do,  and  must  make  up,  as  far  as 
possible,  for  the  incomplete  conclusiveness  of  any  one  indication,  by  ob- 
taining others  to  corroborate  it.  The  principles  of  induction  applicable  to 
approximate  generalization  are  therefore  a not  less  important  subject  of  in- 
quiry than  the  rules  for  the  investigation  of  universal  truths ; and  might 
reasonably  be  expected  to  detain  us  almost  as  long,  were  it  not  that  these 
principles  are  mere  corollaries  from  those  which  have  been  already  treat- 
ed of. 

§ 3.  There  are  two  sorts  of  cases  in  which  we  are  forced  to  guide  our- 
selves by  generalizations  of  the  imperfect  form,  Most  A are  B.  The  first 
is,  when  we  have  no  others;  when  we  have  not  been  able  to  carry  our  in- 
vestigation of  the  laws  of  the  phenomena  any  further;  as  in  the  following 
propositions — Most  dark-eyed  persons  have  dark  hair;  Most  springs  con- 
tain mineral  substances;  Most  stratified  formations  contain  fossils.  The 
importance  of  this  class  of  generalizations  is  not  very  great;  for, though  it 
frequently  happens  that  we  see  no  reason  why  that  which  is  true  of  most 
individuals  of  a class  is  not  true  of  the  remainder,  nor  are  able  to  bring  the 
former  under  any  general  description  which  can  distinguish  them  from  the 
latter,  yet  if  we  are  willing  to  be  satisfied  with  propositions  of  a less  de- 
gree of  generality,  and  to  break  down  the  class  A into  sub-classes,  we  may 
generally  obtain  a collection  of  propositions  exactly  true.  We  do  not  know 
why  most  wood  is  lighter  than  water,  nor  can  we  point  out  any  general 
property  which  discriminates  wood  that  is  lighter  than  water  from  that 
which  is  heavier.  But  we  know  exactly  what  species  are  the  one  and 
what  the  other.  And  it  we  meet  with  a specimen  not  conformable  to  any 

* Mr.  De  Morgan,  in  his  Formal  Logic , makes  the  just  remark,  that  from  two  such  prem- 
ises as  Most  A are  B,  and  Most  A are  C,  we  may  infer  with  certainty  that  some  B are  C. 
But  this  is  the  utmost  limit  of  the  conclusions  which  can  be  drawn  from  two  approximate 
generalizations,  when  the  precise  degree  of  their  approximation  to  universality  is  unknown  cr 
undefined. 


27 


41S 


INDUCTION. 


known  species  (the  only  case  in  which  our  previous  knowledge  affords  no 
other  guidance  than  the  approximate  generalization),  we  can  generally 
make  a specific  experiment,  which  is  a surer  resource:- 

It  often  happens,  however,  that  the  proposition,  Most  A are  B,  is  not 
the  ultimatum  of  our  scientific  attainments,  though  the  knowledge  we  pos- 
sess beyond  it  can  not  conveniently  be  brought  to  bear  upon  the  particular 
instance.  W e may  know  well  enough  what  circumstances  distinguish  the 
portion  of  A which  has  the  attribute  B from  the  portion  which  has  it  not, 
but  may  have  no  means,  or  may  not  have  time,  to  examine  whether  those 
characteristic  circumstances  exist  or  not  in  the  individual  case.  This  is 
the  situation  we  are  generally  in  when  the  inquiry  is  of  the  kind  called 
moral,  that  is,  of  the  kind  which  has  in  view  to  predict  human  actions. 
To  enable  us  to  affirm  any  thing  universally  concerning  the  actions  of 
classes  of  human  beings,  the  classification  must  be  grounded  on  the  circum- 
stances of  their  mental  culture  and  habits,  which  in  an  individual  case  are 
seldom  exactly  known ; and  classes  grounded  on  these  distinctions  would 
never  precisely  accord  with  those  into  which  mankind  are  divided  for  so- 
cial purposes.  All  propositions  which  can  be  framed  respecting  the  actions 
of  human  beings  as  ordinarily  classified,  or  as  classified  according  to  any 
kind  of  outward  indications,  are  merely  approximate.  We  can  only  say, 
Most  persons  of  a particular  age,  profession,  country,  or  rank  in  society, 
have  such  and  such  qualities ; or,  Most  persons,  when  placed  in  certain 
circumstances,  act  in  such  and  such  a way.  Not  that  we  do  not  often 
know  well  enough  on  what  causes  the  qualities  depend,  or  what  sort  of 
persons  they  are  who  act  in  that  particular  way;  but  we  have  seldom  the 
means  of  knowing  whether  any  individual  person  has  been  under  the  influ- 
ence of  those  causes,  or  is  a person  of  that  particular  sort.  We  could  re- 
place the  approximate  generalizations  by  propositions  universally  true; 
but  these  would  hardly  ever  be  capable  of  being  applied  to  practice.  We 
should  be  sure  of  our  majors,  but  we  should  not  be  able  to  get  minors  to 
fit;  we  are  forced,  therefore,  to  draw  our  conclusions  from  coarser  and 
more  fallible  indications. 

§ 4.  Proceeding  now  to  consider  what  is  to  be  regarded  as  sufficient  evi- 
dence of  an  approximate  generalization,  we  can  have  no  difficulty  in  at 
once  recognizing  that,  when  admissible  at  all,  it  is  admissible  only  as  an 
empirical  law.  Propositions  of  the  form,  Every  A is  B,  are  not  necessarily 
laws  of  causation,  or  ultimate  uniformities  of  co-existence;  propositions 
like  Most  A are  B,  can  not  be  so.  Propositions  hitherto  found  true  in  ev- 
ery observed  instance  may  yet  be  no  necessary  consequence  of  laws  of  cau- 
sation, or  of  ultimate  uniformities,  and  unless  they  are  so,  may,  for  aught 
we  know,  be  false  beyond  the  limits  of  actual  observation ; still  more  evi- 
dently must  this  be  the  case  with  propositions  which  are  only  true  in  a 
mere  majority  of  the  observed  instances. 

There  is  some  difference,  however,  in  the  degree  of  certainty  of  the 
proposition,  Most  A are  B,  according  as  that  approximate  generalization 
composes  the  whole  of  our  knowledge  of  the  subject,  or  not.  Suppose, 
first,  that  the  former  is  the  case.  We  know  only  that  most  A are  B,  not 
why  they  are  so,  nor  in  what  respect  those  which  are  differ  from  those 
which  are  not.  How,  then,  did  we  learn  that  most  A are  B?  Precisely 
in  the  manner  in  which  we  should  have  learned,  had  such  happened  to  be 
the  fact  that  all  A are  B.  We  collected  a number  of  instances  sufficient 
to  eliminate  chance,  and,  having  done  so,  compared  the  number  of  instances 


APPROXIMATE  GENERALIZATIONS. 


419 


in  the  affirmative  with  the  number  in  the  negative.  The  result,  like  other 
unresolved  derivative  laws,  can  be  relied  on  solely  within  the  limits  not 
only  of  place  and  time,  but  also  of  circumstance,  under  which  its  truth  has 
been  actually  observed ; for,  as  we  are  supposed  to  be  ignorant  of  the 
causes  which  make  the  proposition  true,  we  can  not  tell  in  what  manner 
any  new  circumstance  might  perhaps  affect  it.  The  proposition,  Most 
judges  are  inaccessible  to  bribes,  would  probably  be  found  true  of  English- 
men, Frenchmen,  Germans,  North  Americans,  and  so  forth;  but  if  on  this 
evidence  alone  we  extended  the  assertion  to  Orientals,  we  should  step  be- 
yond the  limits,  not  only  of  place  but  of  circumstance,  within  which  the 
fact  had  been  observed,  and  should  let  in  possibilities  of  the  absence  of  the 
determining  causes,  or  the  presence  of  counteracting  ones,  which  might  be 
fatal  to  the  approximate  generalization. 

In  the  case  where  the  approximate  proposition  is  not  the  ultimatum  of 
our  scientific  knowledge,  but  only  the  most  available  form  of  it  for  practi- 
cal guidance ; where  we  know,  not  only  that  most  A have  the  attribute  B, 
but  also  the  causes  of  B,  or  some  properties  by  which  the  portion  of  A 
which  has  that  attribute  is  distinguished  from  the  portion  which  has  it 
not,  we  are  rather  more  favorably  situated  than  in  the  preceding  case. 
For  we  have  now  a double  mode  of  ascertaining  whether  it  be  true  that 
most  A are  B;  the  direct  mode,  as  before,  and  an  indirect  one,  that  of  ex- 
amining whether  the  proposition  admits  of  being  deduced  from  the  known 
cause,  or  from  any  known  criterion,  of  B.  Let  the  question,  for  example, 
be  whether  most  Scotchmen  can  read?  We  may  not  have  observed,  or 
received  the  testimony  of  others  respecting,  a sufficient  number  and  variety 
of  Scotchmen  to  ascertain  this  fact;  but  when  we  consider  that  the  cause 
of  being  able  to  read  is  the  having  been  taught  it,  another  mode  of  deter- 
mining the  question  presents  itself,  namely,  by  inquiring  whether  most 
Scotchmen  have  been  sent  to  schools  where  reading  is  effectually  taught. 
Of  these  two  modes,  sometimes  one  and  sometimes  the  other  is  the  more 
available.  In  some  cases,  the  frequency  of  the  effect  is  the  more  accessi- 
ble to  that  extensive  and  varied  observation  which  is  indispensable  to  the 
establishment  of  an  empirical  law ; at  other  times,  the  frequency  of  the 
causes,  or  of  some  collateral  indications.  It  commonly  happens  that  nei- 
ther is  susceptible  of  so  satisfactory  an  induction  as  could  be  desired,  and 
that  the  grounds  on  which  the  conclusion  is  received  are  compounded  of 
both.  Thus  a person  may  believe  that  most  Scotchmen  can  read,  because, 
so  far  as  his  information  extends,  most  Scotchmen  have  been  sent  to  school, 
and  most  Scotch  schools  teach  reading  effectually;  and  also  because  most 
of  the  Scotchmen  whom  he  has  known  or  heard  of  could  read ; though  nei- 
ther of  these  two  sets  of  observations  may  by  itself  fulfill  the  necessary 
conditions  of  extent  and  variety. 

Although  the  approximate  generalization  may  in  most  cases  be  indis- 
pensable for  our  guidance,  even  when  we  know  the  cause,  or  some  certain 
mark,  of  the  attribute  predicated,  it  needs  hardly  be  observed  that  we  may 
always  replace  the  uncertain  indication  by  a certain  one,  in  any  case  in 
which  we  can  actually  recognize  the  existence  of  the  cause  or  mark.  For 
example,  an  assertion  is  made  by  a witness,  and  the  question  is  whether  to 
believe  it.  If  we  do  not  look  to  any  of  the  individual  circumstances  of  the 
case,  we  have  nothing  to  direct  us  but  the  approximate  generalization, 
that  truth  is  more  common  than  falsehood,  or,  in  other  words,  that  most 
persons,  on  most  occasions,  speak  truth.  But  if  we  consider  in  what  cir- 
cumstances the  cases  where  truth  is  spoken  differ  from  those  in  which  it  is 


420 


INDUCTION. 


not,  we  find,  for  instance,  the  following : the  witness’s  being  an  honest  per- 
son  or  not;  his  being  an  accurate  observer  or  not;  his  having  an  interest 
to  serve  in  the  matter  or  not.  Now,  not  only  may  we  be  able  to  obtain 
other  approximate  generalizations  respecting  the  degree  of  frequency  of 
these  various  possibilities,  but  we  may  know  which  of  them  is  positively 
realized  in  the  individual  case.  That  the  witness  has  or  has  not  an  inter- 
est to  serve,  we  perhaps  know  directly ; and  the  other  two  points  indirect- 
ly, by  means  of  marks;  as,  for  example,  from  his  conduct  on  some  former 
occasion;  or  from  his  reputation,  which, though  a very  uncertain  mark, af- 
fords an  approximate  generalization  (as,  for  instance,  Most  persons  who 
are  believed  to  be  honest  by  those  with  whom  they  have  had  frequent  deal- 
ings, are  really  so),  which  approaches  nearer  to  a universal  truth  than  the 
approximate  general  proposition  with  which  we  set  out,  viz.,  Most  persons 
on  most  occasions  speak  truth. 

As  it  seems  unnecessary  to  dwell  further  on  the  question  of  the  evidence 
of  approximate  generalizations,  we  shall  proceed  to  a not  less  important 
topic,  that  of  the  cautions  to  be  observed  in  arguing  from  these  incomplete- 
ly universal  propositions  to  particular  cases. 

§ 5.  So  far  as  regards  the  direct  application  of  an  approximate  generali 
zation  to  an  individual  instance,  this  question  presents  no  difficulty.  If  the 
proposition,  Most  A are  B,  has  been  established,  by  a sufficient  induction, 
as  an  empirical  law,  we  may  conclude  that  any  particular  A is  B with  a 
probability  proportioned  to  the  preponderance  of  the  number  of  affirmative 
instances  over  the  number  of  exceptions.  If  it  has  been  found  practicable 
to  attain  numerical  precision  in  the  data,  a corresponding  degree  of  precis- 
ion may  be  given  to  the  evaluation  of  the  chances  of  error  in  the  conclu- 
sion. If  it  can  be  established  as  an  empirical  law  that  nine  out  of  every  ten 
A are  B,  there  will  be  one  chance  in  ten  of  error  in  assuming  that  any  A, 
not  individually  known  to  us,  is  a B:  but  this  of  course  holds  only  within 
the  limits  of  time,  place,  and  circumstance,  embraced  in  the  observations, 
and  therefore  can  not  be  counted  on  for  any  sub-class  or  variety  of  A (or 
for  A in  any  set  of  external  circumstances)  which  were  not  included  in  the 
average.  It  must  be  added,  that  we  can  guide  ourselves  by  the  proposition, 
Nine  out  of  every  ten  A are  B,  only  in  cases  of  which  we  know  nothing  ex- 
cept that  they  fall  within  the  class  A.  For  if  we  know,  of  any  particular 
instances  i,  not  only  that  it  falls  under  A,  but  to  what  species  or  variety  of 
A it  belongs,  we  shall  generally  err  in  applying  to  i the  average  struck  for 
the  whole  genus,  from  which  the  average  corresponding  to  that  species 
alone  would,  in  all  probability,  materially  differ.  And  so  if  i,  instead  of  be- 
ing a particular  sort  of  instance,  is  an  instance  known  to  be  under  the  in- 
fluence of  a particular  set  of  circumstances,  the  presumption  drawn  from 
the  numerical  proportions  in  the  rvhole  genus  would  probably,  in  such  a 
case,  only  mislead.  A general  average  should  only  be  applied  to  cases  which 
are  neither  known,  nor  can  be  presumed,  to  be  other  than  average  cases. 
Such  averages,  therefore,  are  commonly  of  little  use  for  the  practical  guid- 
ance of  any  affairs  but  those  which  concern  large  numbers.  Tables  of  the 
chances  of  life  are  useful  to  insurance  offices,  but  they  go  a very  little  way 
toward  informing  any  one  of  the  chances  of  his  own  life,  or  any  other  life 
in  which  he  is  interested,  since  almost  every  life  is  either  better  or  worse 
than  the  average.  Such  averages  can  only  be  considered  as  supplying  the 
first  term  in  a series  of  approximations ; the  subsequent  terms  proceeding 
on  an  appreciation  of  the  circumstances  belonging  to  the  particular  case. 


APPROXIMATE  GENERALIZATIONS. 


421 


§ 8.  From  the  application  of  a single  approximate  generalization  to  in- 
dividual cases,  we  proceed  to  the  application  of  two  or  more  of  them  to- 
gether to  the  same  case. 

When  a judgment  applied  to  an  individual  instance  is  grounded  on  two 
approximate  generalizations  taken  in  conjunction,  the  propositions  may  co- 
operate toward  the  result  in  two  different  ways.  In  the  one,  each  proposi- 
tion is  separately  applicable  to  the  case  in  hand,  and  our  object  in  combin- 
ing them  is  to  give  to  the  conclusion  in  that  particular  case  the  double 
probability  arising  from  the  two  propositions  separately.  This  may  be 
called  joining  two  probabilities  by  way  of  Addition;  and  the  result  is  a 
probability  greater  than  either.  The  other  mode  is,  when  only  one  of  the 
propositions  is  directly  applicable  to  the  case,  the  second  being  only  appli- 
cable to  it  by  virtue  of  the  application  of  the  first.  This  is  joining  two 
probabilities  by  way  of  Ratiocination  or  Deduction;  the  result  of  which  is 
a less  probability  than  either.  The  type  of  the  first  argument  is,  Most  A 
are  B ; most  C are  B ; this  thing  is  both  an  A and  a C ; therefore  it  is 
probably  a B.  The  type  of  the  second  is,  Most  A are  B ; most  C are  A ; 
this  is  a C ; therefore  it  is  probably  an  A,  therefore  it  is  probably  a B. 
The  first  is  exemplified  when  we  prove  a fact  by  the  testimony  of  two  un- 
connected witnesses ; the  second,  when  we  adduce  only  the  testimony  of  one 
witness  that  he  has  heard  the  thing  asserted  by  another.  Or  again,  in  the 
first  mode  it  may  be  argued  that  the  accused  committed  the  crime,  because 
he  concealed  himself,  and  because  his  clothes  were  stained  with  blood ; in 
the  second,  that  he  committed  it  because  he  washed  or  destroyed  his  clothes, 
which  is  supposed  to  render  it  probable  that  they  were  stained  with  blood. 
Instead  of  only  two  links,  as  in  these  instances,  we  may  supjDOse  chains  of 
any  length.  A chain  of  the  former  kind  was  termed  by  Bentham*  a self- 
corroborative  chain  of  evidence;  the  second,  a self-infirmative  chain. 

When  approximate  generalizations  are  joined  by  way  of  addition,  we  may 
deduce  from  the  theory  of  probabilities  laid  down  in  a former  chapter,  in 
what  manner  each  of  them  adds  to  the  probability  of  a conclusion  which 
has  the  warrant  of  them  all.  r 

If,  on  an  average,  two  of  every  three  As  are  Bs,  and  three  of  every  four 
Cs  are  Bs,  the  probability  that  something  which  is  both  an  A and  a C is  a 
B,  will  be  more  than  two  in  three,  or  than  three  in  four.  Of  every  twelve 
things  which  are  As,  all  except  four  are  Bs  by  the  supposition ; and  if  the 
whole  twelve,  and  consequently  those  four,  have  the  characters  of  C like- 
wise, three  of  these  will  be  Bs  on  that  ground.  Therefore,  out  of  twelve 
which  are  both  As  and  Cs,  eleven  are  Bs.  To  state  the  argument  in  anoth- 
er way ; a thing  which  is  both  an  A and  a C,  but  which  is  not  a B,  is  found 
in  only  one  of  three  sections  of  the  class  A,  and  in  only  one  of  four  sections 
of  the  class  C;  but  this  fourth  of  C being  spread  over  the  whole  of  A in- 
discriminately, only  one-third  part  of  it  (or  one-twelfth  of  the  whole  num- 
ber) belongs  to  the  third  section  of  A;  therefore  a thing  which  is  not  a B 
occurs  only  once,  among  twelve  things  which  are  both  As  and  Cs.  The 
argument  would,  in  the  language  of  the  doctrine  of  chances,  be  thus  ex- 
pressed : the  chance  that  an  A is  not  a B is  the  chance  that  a C is  not  a 
B is  hence  if  the  thing  be  both  an  A and  a C,  the  chance  is  4 of 

* Rationale  of  Judicial  Evidence , vol.  iii. , p.  22L 

t The  evaluation  of  the  chances  in  this  statement  has  been  objected  to  by  a mathematical 
friend.  The  correct  mode,  in  his  opinion,  of  setting  out  the  possibilities  is  as  follows.  If 
the  thing  (let  us  call  it  T)  which  is  both  an  A and  a C,  is  a B,  something  is  true  which  is 
only  true  twice  in  every  thrice,  and  something  else  which  is  only  true  thrice  in  every  four 


422 


INDUCTION. 


In  this  computation  it  is  of  course  supposed  that  the  probabilities  arising 
from  A and  C are  independent  of  each  other.  There  must  not  be  any  such 
connection  between  A and  C,  that  when  a tiling  belongs  to  the  one  class  it 
will  therefore  belong  to  the  other,  or  even  have  a greater  chance  of  doing 
so.  Otherwise  the  not-Bs  which  are  Cs  may  be,  most  or  even  all  of  them, 
identical  with  the  not-Bs  which  are  As ; in  which  last  case  the  probability 
arising  from  A and  C together  will  be  no  greater  than  that  arising  from  A 
alone. 

When  approximate  generalizations  are  joined  together  in  the  other  mode, 
that  of  deduction,  the  degree  of  probability  of  the  inference,  instead  of  in- 
creasing, diminishes  at  each  step.  From  two  such  premises  as  Most  A are 
B,  Most  B are  C,  we  can, not  with  certainty  conclude  that  even  a single  A 
is  C ; for  the  whole  of  the  portion  of  A which  in  any  way  falls  under  B, 
may  perhaps  be  comprised  in  the  exceptional  part  of  it.  Still,  the  two 
propositions  in  question  afford  an  appreciable  probability  that  any  given  A 
is  C,  provided  the  average  on  which  the  second  proposition  is  grounded 
was  taken  fairly  with  reference  to  the  first;  provided  the  proposition,  Most 

times.  The  first  fact  being  true  eight  times  in  twelve,  and  the  second  being  true  six  times  in 
every  eight,  and  consequently  six  times  in  those  eight;  both  facts  will  be  true  only  six  times 
in  twelve.  On  the  other  hand,  if  T,  although  it  is  both  an  A and  a C,  is  not  a B,  something 
is  true  which  is  only  true  once  in  every  thrice,  and  something  else  which  is  only  true  once  in 
every  four  times.  The  former  being  true  four  times  out  of  twelve,  and  the  latter  once  in 
every  four,  and  therefore  once  in  those  four  ; both  are  only  true  in  one  case  out  of  twelve.  So 
that  T is  a B six  times  in  twelve,  and  T is  not  a B,  only  once  : making  the  comparative  prob- 
abilities, not  eleven  to  one,  as  I had  previously  made  them,  but  six  to  one. 

In  the  last  edition  I accepted  this  reasoning  as  conclusive.  More  attentive  consideration, 
however,  has  convinced  me  that  it  contains  a fallacy. 

The  objector  argues,  that  the  fact  of  A’s  being  a B is  true  eight  times  in  twelve,  and  the 
fact  of  C’s  being  a B six  times  in  eight,  and  consequently  six  times  in  those  eight ; both  facts, 
therefore,  are  true  only  six  times  in  every  twelve.  That  is,  he  concludes  that  because  among  As 
taken  indiscriminately  only  eight  out  of  twelve  are  Bs  and  the  remaining  four  are  not,  it  must 
equally  hold  that  four  out  of  twelve  are  not  Bs  when  the  twelve  are  taken  from  the  select  por- 
tion of  As  which  are  also  Cs.  And  by  this  assumption  he  arrives  at  the  strange  result,  that 
there  are  fewer  Bs  among  things  which  are  both  As  and  Cs  than  there  are  among  either  As 
or  Cs  taken  indiscriminately ; so  that  a thing  which  has  both  chances  of  being  a B,  is  less 
likely  to  be  so  than  if  it  had  only  the  one  chance  or  only  the  other. 

The  objector  (as  has  been  acutely  remarked  by  another  correspondent)  applies  to  the  prob- 
lem under  consideration,  a mode  of  calculation  only  suited  to  the  reverse  problem.  Had 
the  question  been — If  two  of  every  three  Bs  are  As  and  three  out  of  every  four  Bs  are  Cs, 
how  many  Bs  will  be  both  As  and  Cs,  his  reasoning  would  have  been  correct.  For  the  Bs 
that  are  both  As  and  Cs  must  be  fewer  than  either  the  Bs  that  are  As  or  the  Bs  that  are  Cs, 
and  to  find  their  number  we  must  abate  either  of  these  numbers  in  the  ratio  due  to  the  other. 
But  when  the  problem  is  to  find,  not  how  many  Bs  are  both  As  and  Cs,  but  how  many  things 
that  are  both  As  and  Cs  are  Bs,  it  is  evident  that  among  these  the  proportion  of  Bs  must  be 
not  less,  but  greater,  than  among  things  which  are  only  A,  or  among  things  which  are  only  B. 

The  true  theory  of  the  chances  is  best  found  by  going  back  to  the  scientific  grounds  on 
which  the  proportions  rest.  The  degree  of  frequency  of  a coincidence  depends  on,  and  is  a 
measure  of,  the  frequency,  combined  with  the  efficacy,  of  the  causes  in  operation  that  are  fa- 
vorable to  it.  If  out  of  every  twelve  As  taken  indiscriminately  eight  are  Bs  and  four  are  not, 
it  is  implied  that  there  are  causes  operating  on  A which  tend  to  make  it  a B,  and  that  these 
causes  are  sufficiently  constant  and  sufficiently  powerful  to  succeed  in  eight  out  of  twelve 
cases,  but  fail  in  the  remaining  four.  So  if  of  twelve  Cs,  nine  are  Bs  and  three  are  not,  there 
must  be  causes  of  the  same  tendency  operating  on  C,  which  succeed  in  nine  cases  and  fail  in 
three.  Now  suppose  twelve  cases  which  are  both  As  and  Cs.  The  whole  twelve  are  now 
under  the  operation  of  both  sets  of  causes.  One  set  is  sufficient  to  prevail  in  eight  of  the 
twelve  cases,  the  other  in  nine.  The  analysis  of  the  cases  shows  that  six  of  the  twelve  will  he 
Bs  through  the  operation  of  both  sets  of  causes ; two  more  in  virtue  of  the  causes  operating 
on  A ; and  three  more  through  those  operating  on  C,  and  that  there  will  be  only  one  case  in 
which  all  the  causes  will  be  inoperative.  The  total  number,  therefore,  which  are  Bs  will  be 
eleven  in  twelve,  and  the  evaluation  in  the  text  is  correct. 


APPROXIMATE  GENERALIZATIONS. 


423 


B are  C,  was  arrived  at  in  a manner  leaving  no  suspicion  that  the  probabili- 
ty arising- from  it  is  otherwise  than  fairly  distributed  over  the  section  of  B 
which  belongs  to  A.  For  though  the  instances  which  are  A may  be  all  in 
the  minority,  they  may,  also,  be  all  in  the  majority ; and  the  one  possibility 
is  to  be  set  against  the  other.  On  the  whole,  the  probability  arising  from 
the  two  propositions  taken  together,  will  be  correctly  measured  by  the  prob- 
ability arising  from  the  one,  abated  in  the  ratio  of  that  arising  from  the 
other.  If  nine  out  of  ten  Swedes  have  light  hair,  and  eight  out  of  nine  in- 
habitants of  Stockholm  are  Swedes,  the  probability  arising  from  these  two 
propositions,  that  any  given  inhabitant  of  Stockholm  is  light-haired,  will 
amount  to  eight  in  ten ; though  it  is  rigorously  possible  that  the  whole 
Swedish  population  of  Stockholm  might  belong  to  that  tenth  section  of  the 
people  of  Sweden  who  are  an  exception  to  the  rest. 

if  the  premises  are  known  to  be  true  not  of  a bare  majority,  but  of  near- 
ly the  whole,  of  their  respective  subjects,  we  may  go  on  joining  one  such 
proposition  to  another  for  several  steps,  before  we  reach  a conclusion  not 
presumably  true  even  of  a majority.  The  error  of  the  conclusion  will 
amount  to  the  aggregate  of  the  errors  of  all  the  premises.  Let  the  prop- 
osition, most  A are  B,  be  true  of  nine  in  ten;  Most  B are  C,  of  eight  in 
nine ; then  not  only  will  one  A in  ten  not  be  C,  because  not  B,  but  even  of 
the  nine-tenths  which  are  B,  only  eight-ninths  will  be  C;  that  is,  the  cases 
of  A which  are  C will  be  only  f-  of  or  four-fifths.  Let  us  now  add 
Most  C are  D,  and  suppose  this  to  be  true  of  seven  cases  out  of  eight ; 
the  proportion  of  A which  is  D will  be  only  X of  of  -j^-,  or  -yL.  Thus  the 
probability  progressively  dwindles.  The  experience,  however,  on  which  our 
approximate  generalizations  are  grounded,  has  so  rarely  been  subjected  to, 
or  admits  of,  accurate  numerical  estimation,  that  we  can  not  in  general  ap- 
ply any  measurement  to  the  diminution  of  probability  which  takes  place  at 
each  illation ; but  must  be  content  with  remembering  that  it  does  diminish 
at  every  step,  and  that  unless  the  premises  approach  very  nearly  indeed  to 
being  universally  true,  the  conclusion  after  a very  few  steps  is  worth  noth- 
ing. A hearsay  of  a hearsay,  or  an  argument  from  presumptive  evidence 
depending  not  on  immediate  marks  but  on  marks  of  marks,  is  worthless  at 
a very  few  removes  from  the  first  stage. 

§ 7.  There  are,  however,  two  cases  in  which  reasonings  depending  on  ap- 
proximate generalizations  may  be  carried  to  any  length  we  please  with  as 
much  assurance,  and  are  as  strictly  scientific,  as  if  they  were  composed  of 
universal  laws  of  nature.  But  these  cases  are  exceptions  of  the  sort  which 
are  currently  said  to  prove  the  rule.  The  approximate  generalizations  are 
as  suitable,  in  the  cases  in  question,  for  purposes  of  ratiocination,  as  if  they 
were  complete  generalizations,  because  they  are  capable  of  being  transform- 
ed into  complete  generalizations  exactly  equivalent. 

First : If  the  approximate  generalization  is  of  the  class  in  which  our  rea- 
son for  stopping  at  the  approximation  is  not  the  impossibility,  but  only  the 
inconvenience,  of  going  further;  if  we  are  cognizant  of  the  character  which 
distinguishes  the  cases  that  accord  with  the  generalization  from  those 
which  are  exceptions  to  it;  we  may  then  substitute  for  the  approximate 
proposition,  a universal  proposition  with  a proviso.  The  proposition, 
Most  persons  who  have  uncontrolled  power  employ  it  ill,  is  a generalization 
of  this  class,  and  may  be  transformed  into  the  following : All  persons  who 
have  uncontrolled  power  employ  it  ill,  provided  they  are  not  persons  of  un- 
usual strength  of  judgment  and  rectitude  of  purpose.  The  proposition, 


424 


INDUCTION. 


carrying  the  hypothesis  or  proviso  with  it,  may  then  be  dealt  with  no  longer 
as  an  approximate,  but  as  a universal  proposition;  and  to  whatever  num- 
ber of  steps  the  reasoning  may  reach,  the  hypothesis,  being  carried  forward 
to  the  conclusion,  will  exactly  indicate  how  far  that  conclusion  is  from  be- 
ing  applicable  universally.  If  in  the  course  of  the  argument  other  approx- 
imate generalizations  are  introduced,  each  of  them  being  in  like  manner 
expressed  as  a universal  proposition  with  a condition  annexed,  the  sum  of 
all  the  conditions  will  appear  at  the  end  as  the  sum  of  all  the  errors  which 
affect  the  conclusion.  Thus,  to  the  proposition  last  cited,  let  us  add  the 
following:  All  absolute  monarehs  have  uncontrolled  power,  unless  their  po- 
sition is  such  that  they  need  the  active  support  of  their  subjects  (as  was 
the  case  with  Queen  Elizabeth,  Frederick  of  Prussia,  and  others).  Com- 
bining these  two  propositions,  we  can  deduce  from  them  a universal  con- 
clusion, which  will  be  subject  to  both  the  hypotheses  in  the  premises;  All 
absolute  monarehs  employ  their  power  ill,  unless  their  position  makes  them 
need  the  active  support  of  their  subjects,  or  unless  they  are  persons  of  un- 
usual strength  of  judgment  and  rectitude  of  purpose.  It  is  of  no  conse- 
quence how  rapidly  the  errors  in  our  premises  accumulate,  if  we  are  able 
in  this  manner  to  record  each  error,  and  keep  an  account  of  the  aggregate 
as  it  swells  up. 

Secondly:  there  is  a case  in  which  approximate  propositions,  even  with- 
out our  taking  note  of  the  conditions  under  which  they  are  not  true  of  indi- 
vidual cases,  are  yet,  for  the  purposes  of  science,  universal  ones  ; namely,  in 
the  inquiries  which  relate  to  the  properties  not  of  individuals,  but  of  multi- 
tudes. The  principal  of  these  is  the  science  of  politics,  or  of  human  soci- 
ety. This  science  is  principally  concerned  with  the  actions  not  of  solitary 
individuals,  but  of  masses;  with  the  fortunes  not  of  single  persons,  but 
of  communities.  For  the  statesman,  therefore,  it  is  generally  enough  to 
know  that  most  persons  act  or  are  acted  upon  in  a particular  way;  since 
his  speculations  and  his  practical  arrangements  refer  almost  exclusively 
to  cases  in  which  the  whole  community,  or  some  large  portion  of  it,  is 
acted  upon  at  once,  and  in  which,  therefore,  what  is  done  or  felt  by  most 
persons  determines  the  result  produced  by  or  upon  the  body  at  large.  He 
can  get  on  well  enough  with  approximate  generalizations  on  human  nature, 
since  what  is  true  approximately  of  all  individuals  is  true  absolutely  of  all 
masses.  And  even  when  the  operations  of  individual  men  have  a part  to 
play  in  his  deductions,  as  when  he  is  reasoning  of  kings,  or  other  single 
rulers,  still,  as  he  is  providing  for  indefinite  duration,  involving  an  indefinite 
succession  of  such  individuals,  he  must  in  general  both  reason  and  act  as 
if  what  is  true  of  most  persons  were  true  of  all. 

The  two  kinds  of  considerations  above  adduced  are  a sufficient  refuta- 
tion of  the  popular  error,  that  speculations  on  society  and  government,  as 
resting  on  merely  probable  evidence,  must  be  inferior  in  certainty  and 
scientific  accuracy  to  the  conclusions  of  what  are  called  the  exact  sciences, 
and  less  to  be  relied  on  in  practice.  There  are  reasons  enough  why  the 
moral  sciences  must  remain  inferior  to  at  least  the  more  perfect  of  the  phys- 
ical ; why  the  laws  of  their  more  complicated  phenomena  can  not  be  so 
completely  deciphered,  nor  the  phenomena  predicted  with  the  same  degree 
of  assurance.  But  though  we  can  not  attain  to  so  many  truths,  there  is  no 
reason  that  those  wo  can  attain  should  deserve  less  reliance,  or  have  less 
of  a scientific  character.  Of  this  topic,  however,  I shall  treat  more  system- 
atically in  the  concluding  Book,  to, which  place  any  further  consideration 
of  it  must  be  deferred. 


REMAINING  LAWS  OF  NATURE. 


425 


CHAPTER  XXIV. 

OF  THE  REMAINING  LAWS  OF  NATURE. 

§ 1.  In  the  First  Book  we  found  that  all  the  assertions  which  can  be 
conveyed  by  language,  express  some  one  or  more  of  five  different  things: 
Existence;  Order  in  Place ; Order  in  Time ; Causation;  and  Resemblance.* 
Of  these,  Causation,  in  our  view  of  the  subject,  not  being  fundamentally 
different  from  Order  in  Time,  the  five  species  of  possible  assertions  are 
reduced  to  four.  The  propositions  which  affirm  Order  in  Time  in  either 
of  its  two  modes,  Co-existence  and  Succession,  have  formed,  thus  far,  the 
subject  of  the  present  Book.  And  we  have  now  concluded  the  exposition, 
so  far  as  it  falls  within  the  limits  assigned  to  this  work,  of  the  nature  of 
the  evidence  on  which  these  propositions  rest,  and  the  processes  of  investi- 
gation by  which  they  are  ascertained  and  proved.  There  remain  three 
classes  of  facts:  Existence,  Order  in  Place,  and  Resemblance;  in  regard  to 
which  the  same  questions  are  now  to  be  resolved. 

Regarding  the  first  of  these,  very  little  needs  be  said.  Existence  in 
general,  is  a subject  not  for  our  science,  but  for  metaphysics.  To  deter- 
mine what  things  can  be  recognized  as  really  existing,  independently  of  ou« 
own  sensible  or  other  impressions,  and  in  what  meaning  the  term  is,  in  that 
case,  predicated  of  them,  belongs  to  the  consideration  of  “Things  in  them- 
selves,” from  which,  throughout  this  work,  we  have  as  much  as  possible 
kept  aloof.  Existence,  so  far  as  Logic  is  concerned  about  it,  has  reference 
only  to  phenomena;  to  actual,  or  possible,  states  of  external  or  internal 
consciousness,  in  ourselves  or  others.  Feelings  of  sensitive  beings,  or  pos- 
sibilities of  having  such  feelings,  are  the  only  things  the  existence  of  which 
can  be  a subject  of  logical  induction,  because  the  only  things  of  which  the 
existence  in  individual  cases  can  be  a subject  of  experience. 

It  is  true  that  a thing  is  said  by  us  to  exist,  even  when  it  is  absent,  and 
therefore  is  not  and  can  not  be  perceived.  But  even  then,  its  existence  is 
to  us  only  another  word  for  our  conviction  that  we  should  perceive  it  on  a 
certain  supposition  ; namely,  if  we  were  in  the  needful  circumstances  of 
time  and  place,  and  endowed  with  the  needful  perfection  of  organs.  My 
belief  that  the  Emperor  of  China  exists,  is  simply  my  belief  that  if  I were 
transported  to  the  imperial  palace  or  some  other  locality  in  Pekin,  I should 
see  him.  My  belief  that  Julius  Caesar  existed,  is  my  belief  that  I should 
have  seen  him  if  I had  been  present  in  the  field  of  Pharsalia,  or  in  the 
senate-house  at  Rome.  When  I believe  that  stars  exist  beyond  the  utmost 
range  of  my  vision,  though  assisted  by  the  most  powerful  telescopes  yet 
invented,  my  belief,  philosophically  expressed,  is,  that  with  still  better  tele- 
scopes, if  such  existed,  I could  see  them,  or  that  they  may  be  perceived  by 
beings  less  remote  from  them  in  space,  or  whose  capacities  of  perception 
are  superior  to  mine. 

The  existence,  therefore,  of  a phenomenon,  is  but  another  word  for  its 
being  perceived,  or  for  the  inferred  possibility  of  perceiving  it.  When  the 
phenomenon  is  within  the  range  of  present  observation,  by  present  obser- 


Supra,  book  i.,  chap.  v. 


426 


INDUCTION. 


vation  we  assure  ourselves  of  its  existence;  when  it  is  beyond  that  range, 
and  is  therefore  said  to  be  absent,  we  infer  its  existence  from  marks  or  evi- 
dences. But  what  can  these  evidences  be  ? Other  phenomena ; ascertain- 
ed by  induction  to  be  connected  with  the  given  phenomenon,  either  in  the 
way  of  succession  or  of  co-existence.  The  simple  existence,  therefore,  of  an 
individual  phenomenon,  when  not  directly  perceived,  is  inferred  from  some 
inductive  law  of  succession  or  co-existence;  and  is  consequently  not  amen- 
able to  any  peculiar  inductive  principles.  We  prove  the  existence  of  a 
thing,  by  proving  that  it  is  connected  by  succession  or  co-existence  with 
some  known  thing. 

With  respect  to  general  propositions  of  this  class,  that  is,  which  affirm  the 
bare  fact  of  existence,  they  have  a peculiarity  which  renders  the  logical 
treatment  of  them  a very  easy  matter  ; they  are  generalizations  which  are 
sufficiently  proved  by  a single  instance.  That  ghosts,  or  unicorns,  or  sea- 
serpents  exist,  would  be  fully  established  if  it  could  be  ascertained  posi- 
tively that  such  things  had  been  even  ones  seen.  Whatever  lias  once  hap- 
pened, is  capable  of  happening  again;  the  only  question  relates  to  the  con- 
ditions under  which  it  happens. 

So  far,  therefore,  as  relates  to  simple  existence,  the  Inductive  Logic  has 
no  knots  to  untie.  And  we  may  proceed  to  the  remaining  two  of  the  great 
classes  into  which  facts  have  been  divided ; Resemblance,  and  Order  in 
Place. 

§ 2.  Resemblance  and  its  opposite,  except  in  the  case  in  which  they  as- 
sume the  names  of  Equality  and  Inequality,  are  seldom  regarded  as  sub- 
jects of  science;  they  are  supposed  to  be  perceived  by  simple  apprehen- 
sion ; by  merely  applying  our  senses  or  directing  our  attention  to  the  two 
objects  at  once,  or  in  immediate  succession.  And  this  simultaneous,  or 
virtually  simultaneous,  application  of  our  faculties  to  the  two  things  which 
are  to  be  compared,  does  necessarily  constitute  the  ultimate  appeal,  wher- 
ever such  application  is  practicable.  But,  in  most  cases,  it  is  not  practica- 
ble: the  objects  can  not  be  brought  so  close  together  that  the  feeling  of 
their  resemblance  (at  least  a complete  feeling  of  it)  directly  arises  in  the 
mind.  We  can  only  compare  each  of  them  with  some  third  object,  capa- 
ble of  being  transported  from  one  to  the  other.  And  besides,  even  when 
the  objects  can  be  brought  into  immediate  juxtaposition,  their  resemblance 
or  difference  is  but  imperfectly  known  to  us,  unless  we  have  compared 
them  minutely,  part  by  part.  Until  this  has  been  done,  things  in  reality 
very  dissimilar  often  appear  undistinguish  ably  alike.  Two  lines  of  very 
unequal  length  will  appear  about  equal  when  lying  in  different  directions ; 
but  place  them  parallel  with  their  farther  extremities  even,  and  if  we  look 
at  the  nearer  extremities,  their  inequality  becomes  a matter  of  direct  per- 
ception. 

To  ascertain  whether,  and  in  what,  two  phenomena  resemble  or  differ,  is 
not  always,  therefore,  so  easy  a thing  as  it  might  at  first  appear.  When 
the  two  can  not  be  brought  into  juxtaposition,  or  not  so  that  the  observer 
is  able  to  compare  their  several  parts  in  detail,  lie  must  employ  the  indi- 
rect means  of  reasoning  and  general  propositions.  When  we  can  not  bring 
two  straight  lines  together,  to  determine  whether  they  are  equal,  we  do  it 
by  the  physical  aid  of  a foot-rule  applied  first  to  one  and  then  to  the  other, 
and  the  logical  aid  of  the  general  proposition  or  formula,  “Things  which 
are  equal  to  the  same  thing  are  equal  to  one  another.”  The  comparison 
of  two  things  through  the  intervention  of  a third  thing,  when  their  direct 


REMAINING  LAWS  OF  NATURE. 


427 


comparison  is  impossible,  is  the  appropriate  scientific  process  for  ascertain- 
ing resemblances  and  dissimilarities,  and  is  the  sum  total  of  what  Logic 
lias  to  teach  on  the  subject. 

An  undue  extension  of  this  remark  induced  Locke  to  consider  reasoning 
itself  as  nothing  but  the  comparison  of  two  ideas  through  the  medium  of 
a third,  and  knowledge  as  the  perception  of  the  agreement  or  disagreement 
of  two  ideas  ; doctrines  which  the  Condillac  school  blindly  adopted,  with- 
out the  qualifications  and  distinctions  with  which  they  were  studiously 
guarded  by  their  illustrious  author.  Where,  indeed,  the  agreement  or  dis- 
agreement (otherwise  called  resemblance  or  dissimilarity)  of  any  two  things 
is  the  very  matter  to  be  determined,  as  is  the  case  particularly  in  the  sci- 
ences of  quantity  and  extension;  there,  the  process  by  which  a solution,  if 
not  attainable  by  direct  perception,  must  be  indirectly  sought,  consists  in 
comparing  these  two  things  through  the  medium  of  a third.  But  this  is 
far  from  being  true  of  all  inquiries.  The  knowledge  that  bodies  fall  to  the 
ground  is  not  a perception  of  agreement  or  disagreement,  but  of  a series 
of  physical  occurrences,  a succession  of  sensations.  Locke’s  definitions  of 
knowledge  and  of  reasoning  required  to  be  limited  to  our  knowledge  of, 
and  reasoning  about,  resemblances.  Nor,  even  when  thus  restricted,  are  the 
propositions  strictly  correct;  since  the  comparison  is  not  made,  as  he  rep- 
resents, between  the  ideas  of  the  two  phenomena, but  between  the  phenome- 
na themselves.  This  mistake  has  been  pointed  out  in  an  earlier  part  of  our 
inquiry,*  and  we  traced  it  to  an  imperfect  conception  of  what  takes  place  in 
mathematics,  where  very  often  the  comparison  is  really  made  between  the 
ideas,  without  any  appeal  to  the  outward  senses ; only,  however,  because 
in  mathematics  a comparison  of  the  ideas  is  strictly  equivalent  to  a com- 
parison of  the  phenomena  themselves.  Where,  as  in  the  case  of  numbers, 
lines,  and  figures,  our  idea  of  an  object  is  a complete  picture  of  the  object, 
so  far  as  respects  the  matter  in  hand;  we  can,  of  course,  learn  from  the 
picture,  whatever  could  be  learned  from  the  object  itself  by  mere  contem- 
plation of  it  as  it  exists  at  the  particular  instant  when  the  picture  is  taken. 
No  mere  contemplation  of  gunpowder  would  ever  teach  us  that  a spark 
would  make  it  explode,  nor,  consequently,  would  the  contemplation  of  the 
idea  of  gunpowder  do  so;  but  the  mere  contemplation  of  a straight  line 
shows  that  it  can  not  inclose  a space ; accordingly  the  contemplation  of  the 
idea  of  it  will  show  the  same.  What  takes  place  in  mathematics  is  thus 
no  argument  that  the  comparison  is  between  the  ideas  only.  It  is  always, 
either  indirectly  or  directly,  a comparison  of  the  phenomena. 

In  cases  in  which  we  can  not  bring  the  phenomena  to  the  test  of  direct 
inspection  at  all,  or  not  in  a manner  sufficiently  precise, but  must  judge  of 
their  resemblance  by  inference  from  other  resemblances  or  dissimilarities 
more  accessible  to  observation,  we  of  course  require,  as  in  all  cases  of  ra- 
tiocination, generalizations  or  formulae  applicable  to  the  subject.  We  must 
reason  from  laws  of  nature;  from  the  uniformities  which  are  observable  in 
the  fact  of  likeness  or  unlikeness. 

§ 3.  Of  these  laws  or  uniformities,  the  most  comprehensive  are  those  sup- 
plied by  mathematics  ; the  axioms  relating  to  equality,  inequality,  and  pro- 
portionality, and  the  various  theorems  thereon  founded.  And  these  are  the 
only  Laws  of  Resemblance  which  require  to  be,  or  which  can  be,  treated  apart. 
It  is  true  there  are  innumerable  other  theorems  which  affirm  resemblances 


* Supra,  book  i.,  chap,  v.,  § 1,  and  book  ii. , chap,  v.,  § 5. 


428 


INDUCTION. 


among  phenomena;  as  that  the  angle  of  the  reflection  of  light  is  equal 
to  its  angle  of  incidence  (equality  being  merely  exact  resemblance  in  mag- 
nitude). Again,  that  the  heavenly  bodies  describe  equal  areas  in  equal 
rimes;  and  that  their  periods  of  revolution  ar  e proportional  (another  spe- 
cies of  resemblance)  to  the  sesquiplicate  powers  of  their  distances  from  the 
centre  of  force.  These  and  similar  propositions  affirm  resemblances,  of  the 
same  nature  with  those  asserted  in  the  theorems  of  mathematics ; but  the 
distinction  is,  that  the  propositions  of  mathematics  are  true  of  all  phe- 
nomena whatever,  or  at  least  without  distinction  of  origin  ; while  the  truths 
in  question  are  affirmed  only  of  special  phenomena,  which  originate  in  a 
certain  way  ; and  the  equalities,  proportionalities,  or  other  resemblances, 
which  exist  between  such  phenomena,  must  necessarily  be  either  derived 
from,  or  identical  with,  the  law  of  their  origin  — the  law  of  causation  on 
which  they  depend.  The  equality  of  the  areas  described  in  equal  times  by 
the  planets,  is  derived  from  the  laws  of  the  causes ; and,  until  its  derivation 
was  shown,  it  was  an  empirical  law.  The  equality  of  the  angles  of  reflec- 
tion and  incidence  is  identical  with  the  law  of  the  cause;  for  the  cause  is 
the  incidence  of  a ray  of  light  upon  a reflecting  surface,  and  the  equality 
in  question  is  the  very  law  according  to  which  that  cause  produces  its  ef- 
fects. This  class,  therefore,  of  the  uniformities  of  resemblance  between 
phenomena,  are  inseparable,  in  fact  and  in  thought,  from  the  laws  of  the 
production  of  those  phenomena ; and  the  principles  of  induction  applicable 
to  them  are  no  other  than  those  of  which  we  have  treated  in  the  preceding 
chapters  of  this  Book. 

It  is  otherwise  with  the  truths  of  mathematics.  The  laws  of  equality 
and  inequality  between  spaces,  or  between  numbers,  have  no  connection 
with  laws  of  causation.  That  the  angle  of  reflection  is  equal  to  the  angle 
of  incidence,  is  a statement  of  the  mode  of  action  of  a particular  cause  ; but 
that  when  two  straight  lines  intersect  each  other  the  opposite  angles  are 
equal,  is  true  of  all  such  lines  and  angles,  by  whatever  cause  produced. 
That  the  squares  of  the  periodic  times  of  the  planets  are  proportional  to 
the  cubes  of  their  distances  from  the  sun,  is  a uniformity  derived  from 
the  laws  of  the  causes  (or  forces)  which  produce  the  planetary  motions; 
but  that  the  square  of  any  number  is  four  times  the  square  of  half  the 
number,  is  true  independently  of  any  cause.  The  only  laws  of  resemblance, 
therefore,  which  we  are  called  upon  to  consider  independently  of  causation, 
belong  to  the  province  of  mathematics. 

§ 4.  The  same  thing  is  evident  with  respect  to  the  only  one  remaining 
of  our  five  categories,  Order  in  Place.  The  order  in  place,  of  the  effects 
of  a cause,  is  (like  every  thing  else  belonging  to  the  effects)  a consequence 
of  the  laws  of  that  cause.  The  order  in  place,  or,  as  we  have  termed  it, 
the  collocation,  of  the  primeval  causes,  is  (as  well  as  their  resemblance)  in 
each  instance  an  ultimate  fact,  in  which  no  laws  or  uniformities  are  trace- 
able. The  only  remaining  general  propositions  respecting  order  in  place, 
and  the  only  ones  which  have  nothing  to  do  with  causation,  are  some  of 
the  truths  of  geometry;  laws  through  which  we  are  able,  from  the  order 
in  place  of  certain  points,  lines,  or  spaces,  to  infer  the  order  in  place  of 
others  which  are  connected  Avith  the  former  in  some  known  mode;  quite 
independently  of  the  particular  nature  of  those  points,  lines,  or  spaces,  in 
any  other  respect  than  position  or  magnitude,  as  well  as  independently  of 
the  physical  cause  from  which  in  any  particular  case  they  happen  to  de- 
rive their  origin. 


REMAINING  LAWS  OF  NATURE. 


429 


It  thus  appears  that  mathematics  is  the  only  department  of  science  into 
the  methods  of  which  it  still  remains  to  inquire.  And  there  is  the  less  ne- 
cessity that  this  inquiry  should  occupy  us  long,  as  we  have  already,  in  the 
Second  Book,  made  considerable  progress  in  it.  We  there  remarked,  that 
the  directly  inductive  truths  of  mathematics  are  few  in  number ; consist- 
ing of  the  axioms,  together  with  certain  propositions  concerning  existence, 
tacitly  involved  in  most  of  the  so-called  definitions.  And  we  gave  what 
appeared  conclusive  reasons  for  affirming  that  these  original  premises,  from 
which  the  remaining  truths  of  the  science  are  deduced,  are,  notwithstand- 
ing all  appearances  to  the  contrary,  results  of  observation  and  experience; 
founded,  in  short,  on  the  evidence  of  the  senses.  That  things  equal  to  the 
same  thing  are  equal  to  one  another,  and  that  two  straight  lines  which 
have  once  intersected  one  another  continue  to  diverge,  are  inductive  truths  ; 
resting,  indeed,  like  the  law  of  universal  causation,  only  on  induction  per 
enumerationem  simplicem;  on  the  fact  that  they  have  been  perpetually 
perceived  to  be  true,  and  never  once  found  to  be  false.  But,  as  we  have 
seen  in  a recent  chapter  that  this  evidence,  in  the  case  of  a law  so  complete- 
ly universal  as  the  law  of  causation,  amounts  to  the  fullest  proof,  so  is  this 
even  more  evidently  true  of  the  general  propositions  to  which  we  are  now 
adverting;  because,  as  a perception  of  their  truth  in  any  individual  case 
whatever,  requires  only  the  simple  act  of  looking  at  the  objects  in  a proper 
position,  there  never  could  have  been  in  their  case  (what,  for  a long  period, 
there  were  in  the  case  of  the  law  of  causation)  instances  which  were  appar- 
ently, though  not  really,  exceptions  to  them.  Their  infallible  truth  was 
recognized  from  the  very  dawn  of  speculation ; and  as  their  extreme  famil- 
iarity made  it  impossible  for  the  mind  to  conceive  the  objects  under  any 
other  law,  they  were,  and  still  are,  generally  considered  as  truths  recog- 
nized by  their  own  evidence,  or  by  instinct. 

§ 5.  There  is  something  which  seems  to  require  explanation,  in  the  fact 
that  the  immense  multitude  of  truths  (a  multitude  still  as  far  from  being 
exhausted  as  ever)  comprised  in  the  mathematical  sciences,  can  be  elicited 
from  so  small  a number  of  elementary  laws.  One  sees  not,  at  first,  how  it 
is  that  there  can  be  room  for  such  an  infinite  variety  of  true  propositions, 
on  subjects  apparently  so  limited. 

To  begin  with  the  science  of  number.  The  elementary  or  ultimate  truths 
of  this  science  are  the  common  axioms  concerning  equality,  namely,  “ Things 
which  are  equal  to  the  same  thing  are  equal  to  one  another,”  and  “Equals 
added  to  equals  make  equal  sums”  (no  other  axioms  are  required),*  to- 
gether with  the  definitions  of  the  various  numbers.  Like  other  so-called 
definitions,  these  are  composed  of  two  things,  the  explanation  of  a name, 
and  the  assertion  of  a fact;  of  which  the  latter  alone  can  form  a first  prin- 

* The  axiom,  “Equals  subtracted  from  equals  leave  equal  differences,”  may  be  demon- 
strated from  the  two  axioms  in  the  text.  If  A=«  and  B=6,  A — B=a  — b.  For  if  not,  let  A 
— B =a  — b+e.  Then  since  B —b,  adding  equals  to  equals,  A=a-|-r.  ButA=a.  Therefore 
a = a+c,  which  is  impossible. 

This  proposition  having  been  demonstrated,  we  may,  by  means  of  it,  demonstrate  the  fol- 
lowing: “If  equals  be  added  to  unequals,  the  sums  are  unequal.”  If  A=a  and  B not=6, 
A+B  is  not  = a + 6.  For  suppose  it  to  be  so.  Then,  since  A =a  and  A + B=a  + 6,  sub- 
tracting equals  from  equals,  B = 6;  which  is  contrary  to  the  hypothesis. 

So  again,  it  may  be  proved  that  two  things,  one  of  which  is  equal  and  the  other  unequal  to 
a third  thing,  are  unequal  to  one  another.  If  A — a and  A not=B.  neither  is  a=B.  For 
suppose  it  to  be  equal.  Then  since  A =a  and  a = B,  and  since  things  equal  to  the  same 
thing  are  equal  to  one  another  A=B  ; which  is  contrary  to  the  hypothesis. 


430 


INDUCTION. 


eiple  or  premise  of  a science.  The  fact  asserted  in  the  definition  of  a num- 
ber is  a physical  fact.  Each  of  the  numbers  two,  three,  four,  etc.,  denotes 
physical  phenomena,  and  connotes  a physical  property  of  those  phenomena. 
Two,  for  instance,  denotes  all  pairs  of  things,  and  twelve  all  dozens  of 
things,  connoting  what  makes  them  pairs,  or  dozens;  and  that  which 
makes  them  so  is  something  physical;  since  it  can  not  be  denied  that  two 
apples  are  physically  distinguishable  from  three  apples,  two  horses  from 
one  horse,  and  so  forth  ; that  they  are  a different  visible  and  tangible  phe- 
nomenon. I am  not  undertaking  to  say  what  the  difference  is  ; it  is 
enough  that  there  is  a difference  of  which  the  senses  can  take  cognizance. 
And  although  a hundred  and  two  horses  are  not  so  easily  distinguished 
from  a hundred  and  three,  as  two  horses  are  from  three — though  in  most 
positions  the  senses  do  not  perceive  any  difference — yet  they  may  be  so 
placed  that  a difference  will  be  perceptible,  or  else  we  should  never  have 
distinguished  them,  and  given  them  different  names.  Weight  is  confess- 
edly a physical  property  of  things;  yet  small  differences  between  great 
weights  are  as  imperceptible  to  the  senses  in  most  situations,  as  small  dif- 
ferences between  great  numbers;  and  are  only  put  in  evidence  by  placing 
the  two  objects  in  a peculiar  position — namely,  in  the  opposite  scales  of  a 
delicate  balance. 

What,  then,  is  that  which  is  connoted  by  a name  of  number?  Of 
course,  some  property  belonging  to  the  agglomeration  of  things  which  we 
call  by  the  name;  and  that  property  is,  the  characteristic  manner  in  which 
the  agglomeration  is  made  up  of,  and  may  be  separated  into,  parts.  I will 
endeavor  to  make  this  more  intelligible  by  a few  explanations. 

When  we  call  a collection  of  objects  two , three,  or  four , they  are  not 
two,  three,  or  four  in  the  abstract;  they  are  two,  three,  or  four  things  of 
some  particular  kind  ; pebbles,  horses,  inches,  pounds’  weight.  What  the 
name  of  number  connotes  is,  the  manner  in  which  single  objects  of  the 
given  kind  must  be  put  together,  in  order  to  produce  that  particular  aggre- 
gate. If  the  aggregate  be  of  pebbles,  and  we  call  it  tico,  the  name  implies 
that,  to  compose  the  aggregate,  one  pebble  must  be  joined  to  one  pebble. 
If  we  call  it  three,  one  and  one  and  one  pebble  must  be  brought  together 
to  produce  it,  or  else  one  pebble  must  be  joined  to  an  aggregate  of  the 
kind  called  two,  already  existing.  The  aggregate  which  we  call  four , has 
a still  greater  number  of  characteristic  modes  of  formation.  One  and  one 
and  one  and  one  pebble  may  be  brought  together;  or  two  aggregates  of  the 
kind  called  two  may  be  united ; or  one  pebble  may  be  added  to  an  aggre- 
gate of  the  kind  called  three.  Every  succeeding  number  in  the  ascending 
series,  may  be  formed  by  the  junction  of  smaller  numbers  in  a progressive- 
ly greater  variety  of  ways.  Even  limiting  the  parts  to  two,  the  number 
may  be  formed,  and  consequently  may  be  divided,  in  as  many  different 
ways  as  there  are  numbers  smaller  than  itself;  and,  if  we  admit  of  threes, 
fours,  etc.,  in  a still  greater  variety.  Other  modes  of  arriving  at  the  same 
aggregate  present  themselves,  not  by  the  union  of  smaller,  but  by  the  dis- 
memberment of  larger  aggregates.  Thus , three  pebbles  may  be  formed  by 
taking  away  one  pebble  from  an  aggregate  of  four ; two  pebbles,  by  an 
equal  division  of  a similar  aggregate;  and  so  on. 

Every  arithmetical  proposition ; every  statement  of  the  result  of  an 
arithmetical  operation  ; is  a statement  of  one  of  the  modes  of  formation 
of  a given  number.  It  affirms  that  a certain  aggregate  might  have  been 
formed  by  putting  together  certain  other  aggregates,  or  by  withdrawing 
certain  portions  of  some  aggregate.;  and  that,  by  consequence,  we  might 
reproduce  those  aggregates  from  it,  by  reversing  the  process. 


REMAINING  LAWS  OF  NATURE. 


431 


Thus,  when  we  say  that  the  cube  of  12  is  1728,  what  we  affirm  is  this: 
that  if,  having  a sufficient  number  of  pebbles  or  of  any  other  objects,  we 
put  them  together  into  the  particular  sort  of  parcels  or  aggregates  called 
twelves ; and  put  together  these  twelves  again  into  similar  collections ; 
and,  finally,  make  up  twelve  of  these  largest  parcels;  the  aggregate  thus 
formed  will  be  such  a one  as  we  call  1728;  namely,  that  which  (to  take 
the  most  familiar  of  its  modes  of  formation)  may  be  made  by  joining  the 
parcel  called  a thousand  pebbles,  the  parcel  called  seven  hundred  pebbles, 
the  parcel  called  twenty  pebbles,  and  the  parcel  called  eight  pebbles. 

The  converse  proposition  that  the  cube  root  of  1728  is  12,  asserts  that 
this  large  aggregate  may  again  be  decomposed  into  the  twelve  twelves  of 
twelves  of  pebbles  which  it  consists  of. 

The  modes  of  formation  of  any  number  are  innumerable ; but  when  we 
know  one  mode  of  formation  of  each,  all  the  rest  may  be  determined  de- 
ductively. If  we  know  that  a is  formed  from  b and  c,  b from  a and  e,  c 
from  cl  and  j\  and  so  forth,  until  we  have  included  all  the  numbers  of  any 
scale  we  choose  to  select  (taking  care  that  for  each  number  the  mode  of 
formation  be  really  a distinct  one,  not  bringing  us  round  again  to  the  for- 
mer numbers,  but  introducing  a new  number),  we  have  a set  of  propositions 
from  which  we  may  reason  to  all  the  other  modes  of  formation  of  those 
numbers  from  one  another.  Having  established  a chain  of  inductive  truths 
connecting  together  all  the  numbers  of  the  scale,  we  can  ascertain  the  forma- 
tion of  any  one  of  those  numbers  from  any  other  by  merely  traveling  from 
one  to  the  other  along  the  chain.  Suppose  that  we  know  only  the  follow- 
ing modes  of  formation  : 6 = 4 + 2, 4 = 7 — 3,  7 = 5 + 2,  5 = 9 — 4.  We  could 
determine  how  6 may  be  formed  from  9.  For  6=4  + 2 = 7 — 3+2=5+2— 
3 + 2 = 9 — 4 + 2 — 3 + 2.  It  may  therefore  be  formed  by  taking  away  4 and 
3,  and  adding  2 and  2.  If  we  know  besides  that  2 + 2 = 4,  we  obtain  6 from 
9 in  a simpler  mode,  by  merely  taking  away  3. 

It  is  sufficient,  therefore,  to  select  one  of  the  various  modes  of  formation 
of  each  number,  as  a means  of  ascertaining  all  the  rest.  And  since  things 
which  are  uniform,  and  therefore  simple,  are  most  easily  received  and  re- 
tained by  the  understanding,  there  is  an  obvious  advantage  in  selecting  a 
mode  of  formation  which  shall  be  alike  for  all ; in  fixing  the  connotation 
of  names  of  number  on  one  uniform  principle.  The  mode  in  which  our 
existing  numerical  nomenclature  is  contrived  possesses  this  advantage,  with 
the  additional  one,  that  it  happily  conveys  to  the  mind  two  of  the  modes 
of  formation  of  every  number.  Each  number  is  considered  as  formed  by 
the  addition  of  a unit  to  the  number  next  below  it  in  magnitude,  and  this 
mode  of  formation  is  conveyed  bv  the  place  which  it  occupies  in  the  series. 
And  each  is  also  considered  as  formed  by  the  addition  of  a number  of 
units  less  than  ten,  and  a number  of  aggregates  each  equal  to  one  of  the 
successive  powers  of  ten;  and  this  mode  of  its  formation  is  expressed  by 
its  spoken  name,  and  by  its  numerical  character. 

What  renders  arithmetic  the  type  of  a deductive  science,  is  the  fortunate 
applicability  to  it  of  a law  so  comprehensive  as  “The  sums  of  equals  are 
equals or  (to  express  the  same  principle  in  less  familiar  but  more  charac- 
teristic language),  Whatever  is  made  up  of  parts,  Is  made  up  of  the  parts 
of  those  parts.  This  truth,  obvious  to  the  senses  in  all  cases  which  can  be 
fairly  referred  to  their  decision,  and  so  general  as  to  be  co-extensive  with 
nature  itself,  being  true  of  all  sorts  of  phenomena  (for  all  admit  of  being 
numbered),  must  be  considered  an  inductive  truth,  or  law  of  nature,  of  the 
highest  order.  And  every  arithmetical  operation  is  an  application  of  this 


432 


INDUCTION. 


law,  or  of  other  laws  capable  of  being  deduced  from  it.  This  is  our  war- 
rant for  all  calculations.  We  believe  that  five  and  two  are  equal  to  seven, 
on  the  evidence  of  this  inductive  law,  combined  with  the  definitions  of  those 
numbers.  We  arrive  at  that  conclusion  (as  all  know  who  remember  how 
they  first  learned  it)  by  adding  a single  unit  at  a time:  5 + 1 = 6,  therefore 
5 + l + l = G + l=  l7 ; and  again  2 = 1 + 1,  therefore  5 + 2 = 5 + l + l = 7. 

§ 6.  Innumerable  as  are  the  true  propositions  which  can  be  formed  con- 
cerning particular  numbers,  no  adequate  conception  could  be  gained,  from 
these  alone,  of  the  extent  of  the  truths  composing  the  science  of  number. 
Such  propositions  as  we  have  spoken  of  are  the  least  general  of  all  numer- 
ical truths.  It  is  true  that  even  these  are  co-extensive  with  all  nature;  the 
properties  of  the  number  four  are  true  of  all  objects  that  are  divisible  into 
four  equal  parts,  and  all  objects  are  either  actually  or  ideally  so  divisible. 
But  the  propositions  which  compose  the  science  of  algebra  are  true,  not  of 
a particular  number,  but  of  all  numbers  ; not  of  all  things  under  the  condi- 
tion of  being  divided  in  a particular  way,  but  of  all  things  under  the  condi- 
tion of  being  divided  in  any  way — of  being  designated  by  a number  at  all. 

Since  it  is  impossible  for  different  numbers  to  have  any  of  their  modes 
of  formation  completely  in  common,  it  is  a kind  of  paradox  to  say,  that  all 
propositions  which  can  be  made  concerning  numbers  relate  to  their  modes 
of  formation  from  other  numbers,  and  yet  that  there  are  propositions  which 
are  true  of  all  numbers.  But  this  very  paradox  leads  to  the  real  principle 
of  generalization  concerning  the  properties  of  numbers.  Two  different 
numbers  can  not  be  formed  in  the  same  manner  from  the  same  numbers; 
but  they  may  be  formed  in  the  same  manner  from  different  numbers ; as 
nine  is  formed  from  three  by  multiplying  it  into  itself,  and  sixteen  is  form- 
ed from  four  by  the  same  process.  Thus  there  arises  a classification  of 
modes  of  formation,  or  in  the  language  commonly  used  by  mathematicians, 
a classification  of  Functions.  Any  number,  considered  as  formed  from  any 
other  number,  is  called  a function  of  it;  and  there  are  as  many  kinds  of 
functions  as  there  are  modes  of  formation.  The  simple  functions  are  by  no 
means  numerous,  most  functions  being  formed  by  the  combination  of  sever- 
al of  the  operations  which  form  simple  functions,  or  by  successive  repeti- 
tions of  some  one  of  those  operations.  The  simple  functions  of  any  num- 



ber  x are  all  reducible  to  the  following  forms:  x-\-a , x—a,  ax,  -,  xa,  y/x, 

log.  x (to  the  base  a),  and  the  same  expressions  varied  by  putting  x for  a 
and  a for  x,  wherever  that  substitution  would  alter  the  value:  to  which, 
perhaps,  ought  to  be  added  sin  x,  and  arc  (sin=a;).  All  other  functions 
of  x are  formed  by  putting  some  one  or  more  of  the  simple  functions  in 
the  place  of  x or  a,  and  subjecting  them  to  the  same  elementary  operations. 

In  order  to  carry  on  general  reasonings  on  the  subject  of  Functions,  we 
require  a nomenclature  enabling  us  to  express  any  two  numbers  by  names 
which,  without  specifying  what  particular  numbers  they  are,  shall  show 
what  function  each  is  of  the  other;  or,  in  other  words,  shall  put  in  evi- 
dence their  mode  of  formation  from  one  another.  The  system  of  general 
language  called  algebraical  notation  does  this.  The  expressions  a and 
a2  + 3«  denote,  the  one  any  number,  the  other  the  number  formed  from  it 
in  a particular  manner.  The  expressions  a,  b,  n,  and  (a+Z>)n,  denote  any 
three  numbers,  and  a fourth  which  is  formed  from  them  in  a certain  mode. 

The  following  may  be  stated  as  the  general  problem  of  the  algebraical 
calculus:  F being  a certain  function  of  a given  number,  to  find  what  func- 


REMAINING  LAWS  OF  NATURE. 


433 


tion  5'  will  be  of  any  function  of  that  number.  For  example,  a binomial 
a-\-b  is  a function  of  its  two  parts  a and  b,  and  the  parts  are,  in  their 
turn,  functions  of  a-\-b:  now  ( a-\-b)n  is  a certain  function  of  the  binomial; 
what  function  will  this  be  of  a and  b,  the  two  parts?  The  answer  to  this 

question  is  the  binomial  theorem.  The  formula  (a+6)’1=an+- an_16  + 

JUl 1 

— an~2b‘2  + , etc.,  shows  in  what  manner  the  number  which  is  formed  bv 

multiplying  a-\-b  into  itself  n times,  might  be  formed  without  that  process, 
directly  from  a,  b,  and  n.  And  of  this  nature  are  all  the  theorems  of  the 
science  of  number.  They  assert  the  identity  of  the  result  of  different 
modes  of  formation.  They  affirm  that  some  mode  of  formation  from  x , 
and  some  mode  of  formation  from  a certain  function  of  x,  produce  the 
same  number. 

Besides  these  general  theorems  or  formulae,  what  remains  in  the  algebra- 
ical calculus  is  the  resolution  of  equations.  But  the  resolution  of  an  equa- 
tion is  also  a theorem.  If  the  equation  be  x*  + ctx=b,  the  resolution  of  this 
equation,  viz.,  x=  a±  -y/^  d2 + b,  is  a general  proposition,  which  may  be 
regarded  as  an  answer  to  the  question,  If  b is  a certain  function  of  x and  a 
(namely  x2-\-ax),  what  function  is  x of  b and  a?  The  resolution  of  equa- 
tions is,  therefore,  a mere  variety  of  the  general  problem  as  above  stated. 
The  problem  is — Given  a function,  what  function  is  it  of  some  other  func- 
tion? And  in  the  resolution  of  an  equation,  the  question  is,  to  find  what 
function  of  one  of  its  own  functions  the  number  itself  is. 

Such,  as  above  described,  is  the  aim  and  end  of  the  calculus.  As  for  its 
processes,  every  one  knows  that  they  are  simply  deductive.  In  demon- 
strating an  algebraical  theorem,  or  in  resolving  an  equation,  we  travel  from 
the  datum  to  the  qucesitum  by  pure  ratiocination  ; in  which  the  only  prem- 
ises introduced,  besides  the  original  hypotheses,  are  the  fundamental  ax- 
ioms already  mentioned — that  things  equal  to  the  same  thing  are  equal  to 
one  another,  and  that  the  sums  of  equal  things  are  equal.  At  each  step  in 
the  demonstration  or  in  the  calculation,  we  apply  one  or  other  of  these 
truths,  or  truths  deducible  from  them,  as,  that  the  differences,  products, 
etc.,  of  equal  numbers  are  equal. 

It  would  be  inconsistent  with  the  scale  of  this  work,  and  not  necessary 
to  its  design,  to  carry  the  analysis  of  the  truths  and  processes  of  algebra 
any  further;  which  is  also  the  less  needful,  as  the  task  has  been,  to  a very 
great  extent,  performed  by  other  writers.  Peacock’s  Algebra,  and  Dr. 
Whewell’s  Doctrine  of  Limits,  are  full  of  instruction  on  the  subject.  The 
profound  treatises  of  a truly  philosophical  mathematician,  Professor  De 
Morgan,  should  be  studied  by  every  one  who  desires  to  comprehend  the 
evidence  of  mathematical  truths,  and  the  meaning  of  the  obscurer  proc- 
esses of  the  calculus,  and  the  speculations  of  M.  Comte,  in  his  Cours  de 
Philosophic  Positive,  on  the  philosophy  of  the  higher  branches  of  mathe- 
matics, are  among  the  many  valuable  gifts  for  which  philosophy  is  indebted 
to  that  eminent  thinker. 

§ 7.  If  the  extreme  generality,  and  remoteness  not  so  much  from  sense 
as  from  the  visual  and  tactual  imagination,  of  the  laws  of  number,  renders 
it  a somewhat  difficult  effort  of  abstraction  to  conceive  those  laws  as  being 
in  reality  physical  truths  obtained  by  observation  ; the  same  difficulty  does 
not  exist  with  regard  to  the  laws  of  extension.  The  facts  of  which  those 

28 


434 


INDUCTION. 


laws  are  expressions,  are  ol'  a kind  peculiarly  accessible  to  the  senses,  and 
suggesting  eminently  distinct  images  to  the  fancy.  That  geometry  is  a 
strictly  physical  science  would  doubtless  have  been  recognized  in  all  ages, 
had  it  not  been  for  the  illusions  produced  by  two  circumstances.  One  of 
these  is  the  characteristic  property,  already  noticed,  of  the  facts  of  geom- 
etry, that  they  may  be  collected  from  our  ideas  or  mental  pictures  of  ob- 
jects as  effectually  as  from  the  objects  themselves.  The  other  is,  the  de- 
monstrative character  of  geometrical  truths  ; which  was  at  one  time  sup- 
posed to  constitute  a radical  distinction  between  them  and  physical  truths; 
the  latter,  as  resting  on  merely  probable  evidence,  being  deemed  essentially 
uncertain  and  imprecise.  The  advance  of  knowledge  has,  however,  made 
it  manifest  that  physical  science,  in  its  better  understood  branches,  is  quite 
as  demonstrative  as  geometry.  The  task  of  deducing  its  details  from  a 
few  comparatively  simple  principles  is  found  to  be  any  thing  but  the  im- 
possibility it  was  once  supposed  to  be ; and  the  notion  of  the  superior  cer- 
tainty of  geometry  is  an  illusion,  arising  from  the  ancient  prejudice  which, 
in  that  science,  mistakes  the  ideal  data  from  which  we  reason,  for  a pecul- 
iar class  of  realities,  while  the  corresponding  ideal  data  of  any  deductive 
physical  science  are  recognized  as  what  they  really  are,  hypotheses. 

Every  theorem  in  geometry  is  a law  of  external  nature,  and  might  have 
been  ascertained  by  generalizing  from  observation  and  experiment,  which 
in  this  case  resolve  themselves  into  comparison  and  measurement.  But  it 
was  found  practicable,  and,  being  practicable,  was  desirable,  to  deduce  these 
truths  by  ratiocination  from  a small  number  of  general  laws  of  nature,  the 
certainty  and  universality  of  which  are  obvious  to  the  most  careless  ob- 
server, and  which  compose  the  first  principles  and  ultimate  premises  of  the 
science.  Anions  these  areneral  laws  must  be  included  the  same  two  which 
we  have  noticed  as  ultimate  principles  of  the  Science  of  Number  also,  and 
which  are  applicable  to  every  description  of  quantity;  viz.,  The  sums  of 
equals  are  equal,  and  Things  which  are  equal  to  the  same  thing  are  equal 
to  one  another;  the  latter  of  which  may  be  expressed  in  a manner  more 
suggestive  of  the  inexhaustible  multitude  of  its  consequences,  by  the  fol- 
lowing terms:  Whatever  is  equal  to  any  one  of  a number  of  equal  magni- 
tudes, is  equal  to  any  other  of  them.  To  these  two  must  be  added,  in  ge- 
ometry, a third  law  of  equality,  namely,  that  lines,  surfaces,  or  solid  spaces, 
which  can  be  so  applied  to  one  another  as  to  coincide,  are  equal.  Some 
writers  have  asserted  that  this  law  of  nature  is  a mere  verbal  definition; 
that  the  expression  “equal  magnitudes ” means  nothing  but  magnitudes 
which  can  be  so  applied  to  one  another  as  to  coincide.  But  in  this  opinion 
I can  not  agree.  The  equality  of  two  geometrical  magnitudes  can  not  dif- 
fer fundamentally  in  its  nature  from  the  equality  of  two  weights,  two  de- 
grees of  heat,  or  two  portions  of  duration,  to  none  of  which  would  this 
definition  of  equality  be  suitable.  None  of  these  things  can  be  so  applied 
to  one  another  as  to  coincide,  yet  we  perfectly  understand  what  we  mean 
when  we  call  them  equal.  Things  are  equal  in  magnitude,  as  things  are 
equal  in  weight,  when  they  are  felt  to  be  exactly  similar  in  respect  of  the 
attribute  in  which  we  compare  them : and  the  application  of  the  objects  to 
each  other  in  the  one  case,  like  the  balancing  them  with  a pair  of  scales  in 
the  other,  is  but  a mode  of  bringing  them  into  a position  in  which  our 
senses  can  recognize  deficiencies  of  exact  resemblance  that  would  otherwise 
escape  our  notice. 

Along  with  these  three  general  principles  or  axioms,  the  remainder  of 
the  premises  of  geometry  consists  of  the  so-called  definitions:  that  is  to 


REMAINING  LAWS  OF  NATURE. 


435 


say,  propositions  asserting  the  real  existence  of  the  various  objects  therein 
designated,  together  with  some  one  property  of  each.  In  some  cases  more 
than  one  property  is  commonly  assumed,  but  in  no  case  is  more  than  one 
necessary.  It  is  assumed  that  there  are  such  things  in  nature  as  straight 
lines,  and  that  any  two  of  them  setting  out  from  the  same  point,  diverge 
more  and  more  without  limit.  This  assumption  (which  includes  and  goes 
beyond  Euclid’s  axiom  that  two  straight  lines  can  not  inclose  a space)  is 
as  indispensable  in  geometry,  and  as  evident,  resting  on  as  simple,  familiar, 
and  universal  observation,  as  any  of  the  other  axioms.  It  is  also  assumed 
that  straight  lines  diverge  from  one  another  in  different  degrees;  in  other 
words,  that  there  are  such  things  as  angles,  and  that  they  are  capable  of 
being  equal  or  unequal.  It  is  assumed  that  there  is  such  a thing  as  a 
circle,  and  that  all  its  radii  are  equal;  such  things  as  ellipses,  and  that 
the  sums  of  the  focal  distances  are  equal  for  every  point  in  an  ellipse ; 
such  things  as  parallel  lines,  and  that  those  lines  are  everywhere  equally 
distant.* 

.§  8.  It  is  a matter  of  more  than  curiosity  to  consider,  to  what  peculiarity 
of  the  physical  truths  which  are  the  subject  of  geometry,  it  is  owing  that 
they  can  all  be  deduced  from  so  small  a number  of  original  premises ; why 
it  is  that  we  can  set  out  from  only  one  characteristic  property  of  each  kind 
of  phenomenon,  and  with  that  and  two  or  three  general  truths  relating  to 
equality,  can  travel  from  mark  to  mark  until  we  obtain  a vast  body  of  de- 
rivative truths,  to  all  appearance  extremely  unlike  those  elementary  ones. 

The  explanation  of  this  remarkable  fact  seems  to  lie  in  the  following  cir- 
cumstances. In  the  first  place,  all  questions  of  position  and  figure  may  be 
resolved  into  questions  of  magnitude.  The  position  and  figure  of  any  ob- 
ject are  determined  by  determining  the  position  of  a sufficient  number  of 
points  in  it;  and  the  position  of  any  point  may  be  determined  by  the  mag- 
nitude of  three  rectangular  co-ordinates,  that  is,  of  the  perpendiculars  drawn 
from  the  point  to  three  planes  at  right  angles  to  one  another,  arbitrarily 
selected.  By  this  transformation  of  all  questions  of  quality  into  questions 
only  of  quantity,  geometry  is  reduced  to  the  single  problem  of  the  meas- 
urement of  magnitudes,  that  is,  the  ascertainment  of  the  equalities  which 
exist  between  them.  Now  when  we  consider  that  by  one  of  the  general 
axioms,  any  equality,  when  ascertained,  is  proof  of  as  many  other  equalities 
as  there  are  other  things  equal  to  either  of  the  two  equals;  and  that  by 
another  of  those  axioms,  any  ascertained  equality  is  proof  of  the  equality 
of  as  many  pairs  of  magnitudes  as  can  be  formed  by  the  numerous  opera- 

* Geometers  have  usually  preferred  to  define  parallel  lines  by  the  property  of  being  in  the 
same  plane  and  never  meeting.  This,  however,  has  rendered  it  necessary  for  them  to  assume, 
as  an  additional  axiom,  some  other  property  of  parallel  lines ; and  the  unsatisfactory  manner 
in  which  properties  for  that  purpose  have  been  selected  by  Euclid  and  others  has  always  been 
deemed  the  opprobrium  of  elementary  geometry.  Even  as  a verbal  definition,  equidistance  is 
a fitter  property  to  characterize  parallels  by,  since  it  is  the  attribute  really  involved  in  the  sig- 
nification of  the  name.  If  to  be  in  the  same  plane  and  never  to  meet  were  all  that  is  meant 
by  being  parallel,  we  should  feel  no  incongruity  in  speaking  of  a curve  as  parallel  to  its 
asymptote.  The  meaning  of  parallel  lines  is,  lines  which  pursue  exactly  the  same  direction, 
and  which,  therefore,  neither  draw  nearer  nor  go  farther  from  one  another ; a conception 
suggested  at  once  by  the  contemplation  of  nature.  That  the  lines  will  never  meet  is  of  course 
included  in  the  more  comprehensive  proposition  that  they  are  everywhere  equally  distant. 
And  that  any  straight  lines  which  are  in  the  same  plane  and  not  equidistant  will  certainly 
meet,  may  be  demonstrated  in  the  most  rigorous  manner  from  the  fundamental  property  of 
straight  lines  assumed  in  the  text,  viz.,  that  if  they  set  out  from  the  same  point,  they  diverge 
more  and  more  without  limit. 


436 


INDUCTION. 


lions  which  resolve  themselves  into  the  addition  of  the  equals  to  them- 
selves or  to  other  equals  ; we  cease  to  wonder  that  in  proportion  as  a sci- 
ence is  conversant  about  equality,  it  should  afford  a more  copious  supply 
of  marks  of  marks ; and  that  the  sciences  of  number  and  extension,  which 
are  conversant  with  little  else  than  equality,  should  be  the  most  deductive 
of  all  the  sciences. 

There  are  also  two  or  three  of  the  principal  laws  of  space  or  extension 
which  are  unusually  fitted  for  rendering  one  position  or  magnitude  a mark 
of  another,  and  thereby  contributing  to  render  the  science  largely  deduc- 
tive. First,  the  magnitudes  of  inclosed  spaces,  whether  superficial  or  solid, 
are  completely  determined  by  the  magnitudes  of  the  lines  and  angles  which 
bound  them.  Secondly,  the  length  of  any  line,  whether  straight  or  curve, 
is  measured  (certain  other  things  being  given)  by  the  angle  which  it  sub- 
tends, and  vick  versa.  Lastly,  the  angle  which  any  two  straight  lines  make 
with  each  other  at  an  inaccessible  point,  is  measured  by  the  angles  they 
severally  make  with  any  third  line  we  choose  to  select.  By  means  of  these 
general  laws,  the  measurement  of  all  lines,  angles,  and  spaces  whatsoever 
might  be  accomplished  by  measuring  a single  straight  line  and  a sufficient 
number  of  angles;  which  is  the  plan  actually  pursued  in  the  trigonometrical 
survey  of  a country ; and  fortunate  it  is  that  this  is  practicable,  the  exact 
measurement  of  long  straight  lines  being  always  difficult,  and  often  impos- 
sible, but  that  of  angles  very  easy.  Three  such  generalizations  as  the  fore- 
going afford  such  facilities  for  the  indirect  measurement  of  magnitudes 
(by  supplying  us  with  known  lines  or  angles  which  are  marks  of  the  mag- 
nitude of  unknown  ones,  and  thereby  of  the  spaces  which  they  inclose), 
that  it  is  easily  intelligible  how  from  a few  data  we  can  go  on  to  ascertain 
the  magnitude  of  an  indefinite  multitude  of  lines,  angles,  and  spaces,  which 
we  could  not  easily,  or  could  not  at  all,  measure  by  any  more  direct  process. 

§ 9.  Such  are  the  remarks  which  it  seems  necessary  to  make  in  this 
place,  respecting  the  laws  of  nature  which  are  the  peculiar  subject  of  the 
sciences  of  number  and  extension.  The  immense  part  which  those  laws 
take  in  giving  a deductive  character  to  the  other  departments  of  physical 
science,  is  well  known ; and  is  not  surprising,  when  we  consider  that  all 
causes  operate  according  to  mathematical  laws.  The  effect  is  always  de- 
pendent on,  or  is  a function  of,  the  quantity  of  the  agent ; and  generally  of 
its  position  also.  We  can  not,  therefore,  reason  respecting  causation,  with- 
out introducing  considerations  of  quantity  and  extension  at  every  step; 
and  if  the  nature  of  the  phenomena  admits  of  our  obtaining  numerical  data 
of  sufficient  accuracy,  the  laws  of  quantity  become  the  grand  instrument  for 
calculating  forward  to  an  effect,  or  backward  to  a cause.  That  in  all  other 
sciences,  as  well  as  in  geometry,  questions  of  quality  are  scarcely  ever  inde- 
pendent of  questions  of  quantity,  may  be  seen  from  the  most  familiar  phe- 
nomena. Even  when  several  colors  are  mixed  on  a painter’s  palette,  the 
comparative  quantity  of  each  entirely  determines  the  color  of  the  mixture. 

With  this  mere  suggestion  of  the  general  causes  which  render  mathe- 
matical  principles  and  processes  so  predominant  in  those  deductive  sciences 
which  afford  precise  numerical  data,  I must,  on  the  present  occasion,  con- 
tent myself ; referring  the  reader  who  desires  a more  thorough  acquaint- 
ance with  the  subject,  to  the  first  two  volumes  of  M.  Comte’s  systematic 
work. 

In  the  same  work,  and  more  particularly  in  the  third  volume,  are  also 
fully  discussed  the  limits  of  the  applicability  of  mathematical  principles  to 


REMAINING  LAWS  OF  NATURE. 


437 


the  improvement  of  other  sciences.  Such  principles  are  manifestly  inap- 
plicable, where  the  causes  on  which  any  class  of  phenomena  depend  are  so 
imperfectly  accessible  to  our  observation,  that  we  can  not  ascertain,  by  a 
proper  induction,  their  numerical  laws ; or  where  the  causes  are  so  numer- 
ous, and  intermixed  in  so  complex  a manner  with  one  another,  that  even 
supposing  their  laws  known,  the  computation  of  the  aggregate  effect  tran- 
scends the  powers  of  the  calculus  as  it  is,  or  is  likely  to  be;  or, lastly,  where 
the  causes  themselves  are  in  a state  of  perpetual  fluctuation ; as  in  physiol- 
ogy, and  still  more,  if  possible,  in  the  social  science.  The  mathematical  so- 
lutions of  physical  questions  become  progressively  more  difficult  and  im- 
perfect, in  proportion  as  the  questions  divest  themselves  of  their  abstract 
and  hypothetical  character,  and  approach  nearer  to  the  degree  of  complica- 
tion actually  existing  in  nature;  insomuch  that  beyond  the  limits  of  astro- 
nomical phenomena,  and  of  those  most  nearly  analogous  to  them,  mathe- 
matical accuracy  is  generally  obtained  “ at  the  expense  of  the  reality  of  the 
inquiry while  even  in  astronomical  questions,  “ notwithstanding  the  ad- 
mirable simplicity  of  their  mathematical  elements,  our  feeble  intelligence 
becomes  incapable  of  following  out  effectually  the  logical  combinations  of 
the  laws  on  which  the  phenomena  are  dependent,  as  soon  as  we  attempt  to 
take  into  simultaneous  consideration  more  than  two  or  three  essential  influ- 
ences.”* Of  this,  the  problem  of  the  Three  Bodies  has  already  beerr  cited, 
more  than  once,  as  a remarkable  instance ; the  complete  solution  of  so  com- 
paratively simple  a question  having  vainly  tried  the  skill  of  the  most  pro- 
found mathematicians.  We  may  conceive,  then,  how  chimerical  would  be 
the  hope  that  mathematical  principles  could  be  advantageously  applied  to 
phenomena  dependent  on  the  mutual  action  of  the  innumerable  minute  par- 
ticles of  bodies,  as  those  of  chemistry,  and  still  more,  of  physiology ; and 
for  similar  reasons  those  principles  remain  inapplicable  to  the  still  more 
complex  inquiries,  the  subjects  of  which  are  phenomena  of  society  and 
government. 

The  value  of  mathematical  instruction  as  a preparation  for  those  more 
difficult  investigations,  consists  in  the  applicability  not  of  its  doctrines,  but 
of  its  method.  Mathematics  will  ever  remain  the  most  perfect  type  of  the 
Deductive  Method  in  general;  and  the  applications  of  mathematics  to  the 
deductive  branches  of  physics,  furnish  the  only  school  in  which  philosophers 
can  effectually  learn  the  most  difficult  and  important  portion  of  their  art, 
the  employment  of  the  laws  of  simpler  phenomena  for  explaining  and  pre- 
dicting those  of  the  more  complex.  These  grounds  are  quite  sufficient  for 
deeming  mathematical  training  an  indispensable  basis  of  real  scientific  ed- 
ucation, and  regarding  (according  to  the  dictum  which  an  old  but  unau- 
thentic  tradition  ascribes  to  Plato)  one  who  is  ayeuipi-priTOQ,  as  wanting  in 
one  of  the  most  essential  qualifications  for  the  successful  cultivation  of  the 
higher  branches  of  philosophy. 

* Philosophie  Positive , iii.,  414-416. 


438 


INDUCTION. 


CHAPTER  XXV. 

OP  THE  GROUNDS  OP  DISBELIEF. 

§ 1.  The  method  of  arriving  at  general  truths,  or  general  propositions 
fit  to  be  believed,  and  the  nature  of  the  evidence  on  which  they  are  ground- 
ed, have  been  discussed,  as  far  as  space  and  the  writer’s  faculties  permit- 
ted, in  the  twenty-four  preceding  chapters.  But  the  result  of  the  exami- 
nation of  evidence  is  not  always  belief,  nor  even  suspension  of  judgment; 
it  is  sometimes  disbelief.  The  philosophy,  therefore,  of  induction  and  ex- 
perimental inquiry  is  incomplete,  unless  the  grounds  not  only  of  belief,  but 
of  disbelief,  are  treated  of;  and  to  this  topic  we  shall  devote  one,  and  the 
final,  chapter. 

By  disbelief  is  not  here  to  be  understood  the  mere  absence  of  belief. 
The  ground  for  abstaining  from  belief  is  simply  the  absence  or  insufficiency 
of  proof ; and  in  considering  what  is  sufficient  evidence  to  support  any 
given  conclusion,  we  have  already,  by  implication,  considered  what  evidence 
is  not  sufficient  for  the  same  purpose.  By  disbelief  is  here  meant,  not  the 
state  of  mind  in  which  we  form  no  opinion  concerning  a subject,  but  that 
in  which  we  are  fully  persuaded  that  some  opinion  is  not  true;  insomuch 
that  if  evidence,  even  of  great  apparent  strength  (whether  grounded  on 
the  testimony  of  others  or  on  our  own  supposed  perceptions),  were  pro- 
duced in  favor  of  the  opinion,  we  should  believe  that  the  witnesses,  spoke 
falsely,  or  that  they,  or  we  ourselves  if  we  were  the  direct  percipients,  were 
mistaken. 

That  there  are  such  cases,  no  one  is  likely  to  dispute.  Assertions  for 
which  there  is  abundant  positive  evidence  are  often  disbelieved,  on  account 
of  what  is  called  their  improbability,  or  impossibility.  And  the  question 
for  consideration  is  what,  in  the  present  case,  these  words  mean,  and  how 
far  and  in  what  circumstances  the  properties  which  they  express  are  suffi- 
cient grounds  for  disbelief. 

§ 2.  It  is  to  be  remarked,  in  the  first  place,  that  the  positive  evidence 
produced  in  support  of  an  assertion  which  is  nevertheless  rejected  on  the 
score  of  impossibility  or  improbability,  is  never  such  as  amounts  to  full 
proof.  It  is  always  grounded  on  some  approximate  generalization.  The 
fact  may  have  been  asserted  by  a hundred  witnesses  ; but  there  are  many 
exceptions  to  the  universality  of  the  generalization  that  what  a hundred 
witnesses  affirm  is  true.  We  may  seem  to  ourselves  to  have  actually  seen 
the  fact ; but  that  we  really  see  what  we  think  we  see,  is  by  no  means  a 
universal  truth;  our  organs  may  have  been  in  a morbid  state;  or  we  may 
have  inferred  something,  and  imagined  that  we  perceived  it.  The  evi- 
dence, then,  in  the  affirmative  being  never  more  than  an  approximate  gen- 
eralization, all  will  depend  on  what  the  evidence  in  the  negative  is.  If  that 
also  rests  on  an  approximate  generalization,  it  is  a case  for  comparison  of 
probabilities.  If  the  approximate  generalizations  leading  to  the  affirmative 
are,  when  added  together,  less  strong,  or,  in  other  words,  farther  from  be- 
ing universal,  than  the  approximate  generalizations  which  support  the  neg- 
ative side  of  the  question,  the  proposition  is  said  to  be  improbable,  and  is 


GROUNDS  OF  DISBELIEF. 


439 


to  be  disbelieved  provisionally.  If,  however,  an  alleged  fact  be  in  contra- 
diction, not  to  any  number  of  approximate  generalizations,  but  to  a com- 
pleted generalization  grounded  on  a rigorous  induction,  it  is  said  to  be  im- 
possible, and  is  to  be  disbelieved  totally. 

This  last  principle,  simple  and  evident  as  it  appears,  is  the  doctrine 
which,  on  the  occasion  of  an  attempt  to  apply  it  to  the  question  of  the  cred- 
ibility of  miracles,  excited  so  violent  a controversy.  Hume’s  celebrated 
doctrine,  that  nothing  is  credible  which  is  contradictory  to  experience,  or 
at  variance  with  laws  of  nature,  is  merely  this  very  plain  and  harmless 
proposition,  that  whatever  is  contradictory  to  a complete  induction  is  in- 
credible. That  such  a maxim  as  this  should  either  be  accounted  a danger- 
ous heresy,  or  mistaken  for  a great  and  recondite  truth,  speaks  ill  for  the 
state  of  philosophical  speculation  on  such  subjects. 

But  does  not  (it  may  be  asked)  the  very  statement  of  the  proposition 
imply  a contradiction  ? An  alleged  fact,  according  to  this  theory,  is  not  to 
be  believed  if  it  contradict  a complete  induction.  But  it  is  essential  to 
the  completeness  of  an  induction  that  it  shall  not  contradict  any  known 
fact.  Is  it  not,  then,  a petitio  principii  to  say,  that  the  fact  ought  to  be 
disbelieved  because  the  induction  opposed  to  it  is  complete?  IIow  can 
we  have  a right  to  declare  the  induction  complete,  while  facts,  supported 
by  credible  evidence,  present  themselves  in  opposition  to  it? 

I answer,  we  have  that  right  whenever  the  scientific  canons  of  induction 
give  it  to  us;  that  is,  whenever  the  induction  can  be  complete.  We  have 
it,  for  example,  in  a case  of  causation  in  which  there  has  been  an  experi- 
mentum  crucis.  If  an  antecedent  A,  superadded  to  a set  of  antecedents  in 
all  other  respects  unaltered,  is  followed  by  an  effect  B which  did  not  exist 
before,  A is,  in  that  instance  at  least,  the  cause  of  B,  or  an  indispensable 
part  of  its  cause;  and  if  A be  tried  again  with  many  totally  different  sets 
of  antecedents  and  B still  follows,  then  it  is  the  whole  cause.  If  these  ob- 
servations or  experiments  have  been  repeated  so  often,  and  by  so  many 
persons,  as  to  exclude  all  supposition  of  error  in  the  observer,  a law  of  na- 
ture is  established  ; and  so  long  as  this  law  is  received  as  such,  the  asser- 
tion that  on  any  particular  occasion  A took  place,  and  yet  B did  not  follow, 
without  any  counteracting  cause , must  be  disbelieved.  Such  an  assertion 
is  not  to  be  credited  on  any  less  evidence  than  what  would  suffice  to  over- 
turn the  law.  The  general  truths,  that  whatever  has  a beginning  has  a 
cause,  and  that  when  none  but  the  same  causes  exist,  the  same  effects  fol- 
low, rest  on  the  strongest  inductive  evidence  possible;  the  proposition  -that 
things  affirmed  by  even  a crowd  of  respectable  witnesses  are  true,  is  but  an 
approximate  generalization ; and — even  if  we  fancy  we  actually  saw  or  felt 
the  fact  which  is  in  contradiction  to  the  law — what  a human  being  can  see 
is  no  more  than  a set  of  appearances;  from  which  the  real  nature  of  the 
phenomenon  is  merely  an  inference,  and  in  this  inference  approximate  gen- 
eralizations usually  have  a large  share.  If,  therefore,  we  make  our  election 
to  hold  by  the  law,  no  quantity  of  evidence  whatever  ought  to  persuade  us 
that  there  has  occurred  any  thing  in  contradiction  to  it.  If,  indeed,  the 
evidence  produced  is  such  that  it  is  more  likely  that  the  set  of  observations 
and  experiments  on  which  the  law  rests  should  have  been  inaccurately  per- 
formed or  incorrectly  interpreted,  than  that  the  evidence  in  question  should 
be  false,  we  may  believe  the  evidence  ; but  then  we  must  abandon  the  law. 
And  since  the  law  was  received  on  what  seemed  a complete  induction,  it 
can  only  be  rejected  on  evidence  equivalent;  namely,  as  being  inconsistent 
not  with  any  number  of  approximate  generalizations,  but  with  some  other 


440 


INDUCTION. 


and  better  established  law  of  nature.  This  extreme  case,  of  a conflict  be- 
tween two  supposed  laws  of  nature,  has  probably  never  actually  occurred 
where,  in  the  process  of  investigating  both  the  laws,  the  true  canons  of 
scientific  induction  had  been  kept  in  view;  but  if  it  did  occur,  it  must  ter- 
minate in  the  total  rejection  of  one  of  the  supposed  laws.  It  would  prove 
that  there  must  be  a flaw  in  the  logical  process  by  which  either  one  or  the 
other  was  established ; and  if  there  be  so,  that  supposed  general  truth  is 
no  truth  at  all.  We  can  not  admit  a proposition  as  a law  of  nature,  and 
yet  believe  a fact  in  real  contradiction  to  it.  We  must  disbelieve  the  al- 
leged fact,  or  believe  that  we  were  mistaken  in  admitting  the  supposed  law. 

But  in  order  that  any  alleged  fact  should  be  contradictory  to  a law  of 
causation,  the  allegation  must  be,  not  simply  that  the  cause  existed  with 
out  being  followed  by  the  effect,  for  that  would  be  no  uncommon  occur- 
rence ; but  that  this  happened  in  the  absence  of  any  adequate  counteract- 
ing cause.  Now  in  the  case  of  an  alleged  miracle,  the  assertion  is  the  ex- 
act opposite  of  this.  It  is,  that  the  effect  was  defeated,  not  in  the  absence, 
but  in  consequence  of  a counteracting  cause,  namely,  a direct  interposit  ion 
of  an  act  of  the  will  of  some  being  who  has  power  over  nature;  and  in 
particular  of  a Being,  whose  will  being  assumed  to  have  endowed  all  the 
causes  with  the  powers  by  which  they  produce  their  effects,  may  well  be 
supposed  able  to  counteract  them.  * A miracle  (as  was  justly  remarked  by 
Brown)*  is  no  contradiction  to  the  law  of  cause  and  effect;  it  is  a new  ef- 
fect, supposed  to  be  produced  by  the  introduction  of  a new  cause.  Of  the 
adequacy  of  that  cause,  if  present,  there  can  be  no  doubt;  and  the  only 
antecedent  improbabilty  which  can  be  ascribed  to  the  miracle,  is  the  im- 
probability that  any  such  cause  existed. 

All,  therefore,  which  Hume  has  made  out,  and  this  he  must  be  consider- 
ed to  have  made  out,  is,  that  (at  least  in  the  imperfect  state  of  our  knowl- 
edge of  natural  agencies,  which  leaves  it  always  possible  that  some  of  the 
physical  antecedents  may  have  been  hidden  from  us)  no  evidence  can  prove 
a miracle  to  any  one  who  did  not  previously  believe  the  existence  of  a be- 
ing or  beings  with  supernatural  power;  or  who  believes  himself  to  have 
full  proof  that  the  character  of  the  Being  whom  he  recognizes  is  inconsist- 
ent with  his  having  seen  fit  to  interfere  on  the  occasion  in  question. 

If  we  do  not  already  believe  in  supernatural  agencies,  no  miracle  can 
prove  to  us  their  existence.  The  miracle  itself,  considered  merely  as  an 
extraordinary  fact,  may  be  satisfactorily  certified  bv  our  senses  or  by  testi- 
mony; but  nothing  can  ever  prove  that  it  is  a miracle;  there  is  still  anoth- 
er possible  hypothesis,  that  of  its  being  the  result  of  some  unknown  nat- 
ural cause ; and  this  possibility  can  not  be  so  completely  shut  out,  as  to 
leave  no  alternative  but  that  of  admitting  the  existence  and  intervention  of 
a being  superior  to  nature.  Those,  however,  who  already  believe  in  such 
a being  have  two  hypotheses  to  choose  from,  a supernatural  and  an  un- 
known natural  agency;  and  they  have  to  judge  which  of  the  two  is  the 
most  probable  in  the  particular  case.  In  forming  this  judgment,  an  im- 
portant element  of  the  question  will  be  the  conformity  of  the  result  to  the 
laws  of  the  supposed  agent,  that  is,  to  the  character  of  the  Deity  as  they 
conceive  it.  But  with  the  knowledge  which  we  now  possess  of  the  gen- 
eral uniformity  of  the  course  of  nature,  religion,  following  in  the  wake  of 
science,  has  been  compelled  to  acknowledge  the  government  of  the  uni- 
verse as  being  on  the  whole  carried  on  by  general  laws,  and  not  by  special 

* See  the  two  remarkable  notes  (A)  and  (F),  appended  to  his  Inquiry  into  the  Relation  of 
Cause  and  Effect. 


GROUNDS  OF  DISBELIEF. 


441 


interpositions.  To  whoever  holds  this  belief,  there  is  a general  presump- 
tion against  any  supposition  of  divine  agency  not  operating  through  gen- 
eral laws,  or,  in  other  words,  there  is  an  antecedent  improbability  in  every 
miracle,  which,  in  order  to  outweigh  it,  requires  an  extraordinary  strength 
of  antecedent  probability  derived  from  the  special  circumstances  of  the  case. 

§ 3.  It  appears  from  what  has  been  said,  that  the  assertion  that  a cause 
has  been  defeated  of  an  effect  which  is  connected  with  it  by  a completely 
ascertained  law  of  causation,  is  to  be  disbelieved  or  not,  according  to  the 
probability  or  improbability  that  there  existed  in  the  particular  instance  an 
adequate  counteracting  cause.  To  form  an  estimate  of  this,  is  not  more 
difficult  than  of  other  probabilities.  With  regard  to  all  knoxcn  causes  ca- 
pable of  counteracting  the  given  causes,  we  have  generally  some  previous 
knowledge  of  the  frequency  or  rarity  of  their  occurrence,  from  which  we 
may  draw  an  inference  as  to  the  antecedent  improbability  of  their  having 
been  present  in  any  particular  case.  And  neither  in  respect  to  known  nor 
unknown  causes  are  we  required  to  pronounce  on  the  probability  of  their 
existing  in  nature,  but  only  of  their  having  existed  at  the  time  and  place  at 
which  the  transaction  is  alleged  to  have  happened.  We  are  seldom,  there- 
fore, without  the  means  (when  the  circumstances  of  the  case  are  at  all 
known  to  us)  of  judging  how  far  it  is  likely  that  such  a cause,  should  have 
existed  at  that  time  and  place  without  manifesting  its.  presence  by  some 
other  marks,  and  (in  the  case  of  an  unknown  cause)  without  having  hither- 
to manifested  its  existence  in  any  other  instance.  According  as  this  cir- 
cumstance, or  the  falsity  of  the  testimony,  appears  more  improbable — that 
is,  conflicts  with  an  approximate  generalization  of  a higher  order — we  be- 
lieve the  testimony,  or  disbelieve  it ; with  a stronger  or  a weaker  degree  of 
conviction,  according  to  the  preponderance;  at  least  until  we  have  sifted 
the  matter  further. 

So  much,  then,  for  the  case  in  which  the  alleged  fact  conflicts,  or  appears 
to  conflict,  with  a real  law  of  causation.  But  a more  common  case,  per- 
haps, is  that  of  its  conflicting  with  uniformities  of  mere  co-existence,  not 
proved  to  be  dependent  on  causation ; in  other  words,  with  the  properties 
of  Kinds.  It  is  with  these  uniformities  principally  that  the  marvelous 
stories  related  by  travelers  are  apt  to  be  at  variance ; as  of  men  with  tails, 
or  with  wings,  and  (until  confirmed  by  experience)  of  flying  fish  ; or  of  ice, 
in  the  celebrated  anecdote  of  the  Dutch  travelers  and  the  King  of  Siam. 
Facts  of  this  description,  facts  previously  unheard  of,  but  which  could  not 
from  any  known  law  of  causation  be  pronounced  impossible,  are  what 
Hume  characterizes  as  not  contrary  to  experience,  but  merely  unconforma- 
ble  to  it ; and  Bentham,  in  his  treatise  on  Evidence,  denominates  them  facts 
disconformable  in  specie , as  distinguished  from  such  as  are  diseonformable 
in  toto  or  in  decree. 

In  a case  of  this  description,  the  fact  asserted  is  the  existence  of  a new 
Kind ; which  in  itself  is  not  in  the  slightest  degree  incredible,  and  only  to  be 
rejected  if  the  improbability  that  any  variety  of  object  existing  at  the  par- 
ticular place  and  time  should  not  have  been  discovered  sooner,  be  greater 
than  that  of  error  or  mendacity  in  the  'witnesses.  Accordingly,  such  asser- 
tions, when  made  by  credible  persons,  and  of  unexplored  places,  are  not  dis- 
believed, but  at  most  regarded  as  requiring  confirmation  from  subsequent 
observers ; unless  the  alleged  properties  of  the  supposed  new  Kind  are  at 
variance  with  known  properties  of  some  larger  kind  which  includes  it;  or, 
in  other  words,  unless,  in  the  new  Kind  which  is  asserted  to  exist,  some 


INDUCTION. 


442 

properties  are  said  to  have  been  found  disjoined  from  others  which  have 
always  been  known  to  accompany  them;  as  in  the  case  of  Pliny’s  men, or 
any  other  kind  of  animal  of  a structure  different  from  that  which  has  al- 
ways been  found  to  co-exist  with  animal  life.  On  the  mode  of  dealing  with 
any  such  case,  little  needs  be  added  to  what  has  been  said  on  the  same  top- 
ic in  the  twenty-second  chapter.*  When  the  uniformities  of  co-existence 
which  the  alleged  fact  would  violate,  are  such  as  to  raise  a strong  presump- 
tion of  their  being  the  result  of  causation,  the  fact  which  conflicts  with 
them  is  to  be  disbelieved;  at  least  provisionally, and  subject  to  further  in- 
vestigation. When  the  presumption  amounts  to  a virtual  certainty,  as  in 
the  case  of  the  general  structure  of  organized  beings,  the  only  question  re- 
quiring consideration  is  whether,  in  phenomena  so  little  understood,  there 
may  not  be  liabilities  to  counteraction  from  causes  hitherto  unknown ; or 
whether  the  phenomena  may  not  be  capable  of  originating  in  some  other 
way,  which  would  produce  a different  set  of  derivative  uniformities.  Where 
(as  in  the  case  of  the  flying  fish,  or  the  ornithorhynclnis)  the  generalization 
to  which  the  alleged  fact  would  be  an  exception  is  very  special  and  of  lim- 
ited range,  neither  of  the  above  suppositions  can  be  deemed  very  improba- 
ble; and  it  is  generally,  in  the  case  of  such  alleged  anomalies,  wise  to  sus- 
pend our  judgment,  pending  the  subsequent  inquiries  which  will  not  fail 
to  confirm  the  assertion  if  it  be  true.  But  when  the  generalization  is  very 
comprehensive,  embracing  a vast  number  and  variety  of  observations,  and 
covering  a considerable  province  of  the  domain  of  nature  ; then,  for  reasons 
which  have  been  fully  explained,  such  an  empirical  law  comes  near  to  the 
certainty  of  an  ascertained  law  of  causation  ; and  any  alleged  exception  to 
it  can  not  be  admitted,  unless  on  the  evidence  of  some  law  of  causation 
proved  by  a still  more  complete  induction. 

Such  uniformities  in  the  course  of  nature  as  do  not  bear  marks  of  be- 
ing the  results  of  causation  are,  as  we  have  already  seen,  admissible  as 
universal  truths  wjth  a degree  of  credence  proportioned  to  their  general- 
ity. Those  which  are  true  of  all  things  whatever,  or  at  least  which  are 
totally  independent  of  the  varieties  of  Kinds,  namely,  the  laws  of  number 
and  extension,  to  which  we  may  add  the  law  of  causation  itself,  are  proba- 
bly the  only  ones,  an  exception  to  which  is  absolutely  and  permanently  in- 
credible. Accordingly,  it  is  to  assertions  supposed  to  be  contradictory  to 
these  laws,  or  to  some  others  coming  near  to  them  in  generality,  that  the 
word  impossibility  (at  least  total  impossibility)  seems  to  be  generally  con- 
fined. Violations  of  other  laws,  of  special  laws  of  causation,  for  instance, 
are  said,  by  persons  studious  of  accuracy  in  expression,  to  be  impossible 
in  the  circumstances  of  the  case • or  impossible  unless  some  cause  had  ex- 
isted which  did  not  exist  in  the  particular  case.f  Of  no  assertion,  not  in 

* Supra,  p.  413. 

+ A writer  to  whom  I have  several  times  referred,  gives  as  the  definition  of  an  impossibility, 
that  which  there  exists  in  the  world  no  cause  adequate  to  produce.  This  definition  does  not 
take  in  such  impossibilities  as  these — that  two  and  two  should  make  five  ; that  two  straight 
lines  should  inclose  a space ; or  that  any  thing  should  begin  to  exist  without  a cause.  I can 
think  of  no  definition  of  impossibility  comprehensive  enough  to  include  all  its  varieties,  ex- 
cept the  one  which  I have  given  : viz.,  An  impossibility  is  that,  the  truth  of  which  would  con- 
flict with  a complete  induction,  that  is,  with  the  most  conclusive  evidence  which  we  possess 
of  universal  truth. 

As  to  the  reputed  impossibilities  which  rest  on  no  other  grounds  than  our  ignorance  of  any 
cause  capable  of  producing  the  supposed  effects  ; very  few  of  them  are  certainly  impossible,  or 
permanently  incredible.  The  facts  of  traveling  seventy  miles  an  hour,  painless  surgical  oper- 
ations, and  conversing  by  instantaneous  signals  between  London  and  New  York,  held  a high 
place,  not  many  years  ago,  among  such  impossibilities. 


GROUNDS  OF  DISBELIEF. 


443 


contradiction  to  some  of  these  very  general  laws,  will  more  than  improb- 
ability be  asserted  by  any  cautious  person ; and  improbability  not  of  the 
highest  degree,  unless  the  time  and  place  in  which  the  fact  is  said  to  have 
occurred,  render  it  almost  certain  that  the  anomaly,  if  real,  could  not  have 
been  overlooked  by  other  observers.  Suspension  of  judgment  is  in  all 
other  cases  the  resource  of  the  judicious  inquirer;  provided  the  testimony 
in  favor  of  the  anomaly  presents,  when  well  sifted,  no  suspicious  circum- 
stances. 

But  the  testimony  is  scarcely  ever  found  to  stand  that  test,  in  cases  in 
which  the  anomaly  is  not  real.  In  the  instances  on  record  in  which  a great 
number  of  witnesses,  of  good  reputation  and  scientific  acquirements,  have 
testified  to  the  truth  of  something  which  has  turned  out  untrue,  there  have 
almost  always  been  circumstances  which,  to  a keen  observer  who  had  taken 
due  pains  to  sift  the  matter,  would  have  rendered  the  testimony  untrust- 
worthy. There  have  generally  been  means  of  accounting  for  the  impres- 
sion on  the  senses  or  minds  of  the  alleged  percipients,  by  fallacious  appear- 
ances ; or  some  epidemic  delusion,  propagated  by  the  contagious  influence 
of  popular  feeling,  has  been  concerned  in  the  case;  or  some  strong  interest 
has  been  implicated — religious  zeal,  party  feeling,  vanity,  or  at  least  the 
passion  for  the  marvelous,  in  persons  strongly  susceptible  of  it.  When 
none  of  these  or  similar  circumstances  exist  to  account  for  the  apparent 
strength  of  the  testimony ; and  where  the  assertion  is  not  in  contradiction 
either  to  those  universal  laws  which  know  no  counteraction  or  anomaly,  or 
to  the  generalizations  next  in  comprehensiveness  to  them,  but  would  only 
amount,  if  admitted,  to  the  existence  of  an  unknown  cause  or  an  anomalous 
Kind,  in  circumstances  not  so  thoroughly  explored  but  that  it  is  credible 
that  things  hitherto  unknown  may  still  come  to  light;  a cautious  person 
will  neither  admit  nor  reject  the  testimony,  but  will  wait  for  confirmation 
at  other  times  and  from  other  unconnected  sources.  Such  ought  to  have 
been  the  conduct  of  the  King  of  Siam  when  the  Dutch  travelers  aftirmed 
to  him  the  existence  of  ice.  But  an  ignorant  person  is  as  obstinate  in  his 
contemptuous  incredulity  as  he  is  unreasonably  credulous.  Any  thing  un- 
like his  own  narrow  experience  he  disbelieves,  if  it  flatters  no  propensity ; 
any  nursery  tale  is  swallowed  implicitly  by  him  if  it  does. 

§ 4.  I shall  now  advert  to  a very  serious  misapprehension  of  the  princi- 
ples of  the  subject,  which  has  been  committed  by  some  of  the  writers 
against  Hume’s  Essay  on  Miracles,  and  by  Bishop  Butler  before  them,  in 
their  anxiety  to  destroy  what  appeared  to  them  a formidable  weapon  of 
assault  against  the  Christian  religion ; and  the  effect  of  which  is  entirely 
to  confound  the  doctrine  of  the  Grounds  of  Disbelief.  The  mistake  con- 
sists in  overlooking  the  distinction  between  (what  may  be  called)  improba- 
bility before  the  fact  and  improbability  after  it;  or  (since,  as  Mr.  Venn 
remarks,  the  distinction  of  past  and  future  is  not  the  material  circumstance) 
between  the  improbability  of  a mere  guess  being  right,  and  the  improbabil- 
ity of  an  alleged  fact  being  true. 

Many  events  are  altogether  improbable  to  us,  before  they  have  happened, 
or  before  we  are  informed  of  their  happening,  which  are  not  in  the  least 
incredible  when  we  are  informed  of  them,  because  not  contrary  to  any, 
even  approximate,  induction.  In  the  cast  of  a perfectly  fair  die,  the 
chances  are  five  to  one  against  throwing  ace,  that  is,  ace  will  be  thrown 
on  an  average  only  once  in  six  throws.  But  this  is  no  reason  against  be- 
lieving that  ace  was  thrown  on  a given  occasion,  if  any  credible  witness 


444 


INDUCTION. 


asserts  it ; since  though  ace  is  only  thrown  once  in  six  times,  some  number 
which  is  only  thrown  once  in  six  times  must  have  been  thrown  if  the  die 
was  thrown  at  all.  The  improbability,  then,  or,  in  other  words,  the  unusu- 
alness, of  any  fact,  is  no  reason  for  disbelieving  it,  if  the  nature  of  the  case 
renders  it  certain  that  either  that  or  something  equally  improbable,  that 
is,  equally  unusual,  did  happen.  Nor  is  this  all;  for  even  if  the  other  five 
sides  of  the  die  were  all  twos,  or  all  threes,  yet  as  ace  would  still,  on  the 
average,  come  up  once  in  every  six  throws,  its  coming  up  in  a given  throw 
would  be  not  in  any  way  contradictory  to  experience.  If  we  disbelieved 
all  facts  which  had  the  chances  against  them  beforehand,  we  should  believe 
hardly  any  thing.  We  are  told  that  A.  B.  died  yesterday;  the  moment 
before  we  were  so  told,  the  chances  against  his  having  died  on  that  day 
may  have  been  ten  thousand  to  one ; but  since  he  was  certain  to  die  at 
some  time  or  other,  and  when  he  died  must  necessarily  die  on  some  par- 
ticular day,  while  the  preponderance  of  chances  is  very  great  against  every 
day  in  particular,  experience  affords  no  ground  for  discrediting  any  testi- 
mony which  may  be  produced  to  the  event’s  having  taken  place  on  a given 
day. 

Yet  it  has  been  considered  by  Dr.  Campbell  and  others,  as  a complete 
answer  to  Hume’s  doctrine  (that  things  are  incredible  which  are  contrary 
to  the  uniform  course  of  experience),  that  we  do  not  disbelieve,  merely 
because  the  chances  were  against  them,  things  in  strict  conformity  to  the 
uniform  course  of  experience ; that  we  do  not  disbelieve  an  alleged  fact 
merely  because  the  combination  of  causes  on  which  it  depends  occurs  only 
once  in  a certain  number  of  times.  It  is  evident  that  whatever  is  shown 
by  observation,  or  can  be  proved  from  laws  of  nature,  to  occur  in  a certain 
proportion  (however  small)  of  the  whole  number  of  possible  cases,  is  not 
contrary  to  experience;  though  we  are  right  in  disbelieving  it,  if  some 
other  supposition  respecting  the  matter  in  question  involves,  on  the  whole, 
a less  departure  from  the  ordinary  course  of  events.  Yet  on  such  grounds 
as  this  have  able  writers  been  led  to  the  extraordinary  conclusion,  that 
nothing  supported  by  credible  testimony  ought  ever  to  be  disbelieved. 

§ 5.  We  have  considered  two  species  of  events,  commonly  said  to  be  im- 
probable ; one  kind  which  are  in  no  way  extraordinary,  but  which,  having 
an  immense  preponderance  of  chances  against  them,  are  improbable  until 
they  are  affirmed,  but  no  longer ; another  kind  which,  being  contrary  to 
some  recognized  law  of  nature,  are  incredible  on  any  amount  of  testimony 
except  such  as  would  be  sufficient  to  shake  our  belief  in  the  law  itself. 
But  between  these  two  classes  of  events,  there  is  an  intermediate  class,  con- 
sisting of  what  are  commonly  termed  Coincidences : in  other  words,  those 
combinations  of  chances  which  present  some  peculiar  and  unexpected  reg- 
ularity, assimilating  them,  in  so  far,  to  the  results  of  law.  As  if,  for  exam- 
ple, in  a lottery  of  a thousand  tickets,  the  numbers  should  be  drawn  in  the 
exact  order  of  what  are  called  the  natural  numbers,  1,  2,  3,  etc.  We  have 
still  to  consider  the  principles  of  evidence  applicable  to  this  case : whether 
there  is  any  difference  between  coincidences  and  ordinary  events,  in  the 
amount  of  testimony  or  other  evidence  necessary  to  render  them  credible. 

It  is  certain  that  on  every  rational  principle  of  expectation,  a combina- 
tion of  this  peculiar  sort  may  be  expected  quite  as  often  as  any  other  given 
series  of  a thousand  numbers  ; that  with  perfectly  fair  dice,  sixes  will  be 
thrown  twice,  thrice,  or  any  number  of  times  in  succession,  quite  as  often 
in  a thousand  or  a million  throws,  as  any  other  succession  of  numbers  fixed 


GROUNDS  OF  DISBELIEF. 


445 


upon  beforchnnd;  and  that  no  judicious  player  would  give  greater  odds 
against  the  one  series  than  against  the  other.  Notwithstanding  this,  there 
is  a general  disposition  to  regard  the  one  as  much  more  improbable  than 
the  other,  and  as  requiring  much  stronger  evidence  to  make  it  credible. 
Such  is  the  force  of  this  impression,  that  it  has  led  some  thinkers  to  the 
conclusion,  that  nature  has  greater  difficulty  in  producing  regular  combi- 
nations than  irregular  ones;  or  in  other  words,  that  there  is  some  general 
tendency  of  things,  some  law,  which  prevents  regular  combinations  from 
occurring,  or  at  least  from  occurring  so  often  as  others.  Among  these 
thinkers  may  be  numbered  D’Alembert;  who,  in  an  Essay  on  Probabilities 
to  be  found  in  the  fifth  volume  of  his  Melanges,  contends  that  regular 
combinations,  though  equally  probable  according  to  the  mathematical  theo- 
ry with  any  others,  are  physically  less  probable.  He  appeals  to  common 
sense,  or,  in  other  words,  to  common  impressions ; saying,  if  dice  thrown 
repeatedly  in  our  presence  gave  sixes  every  time,  should  we  not,  before  the 
number  of  throws  had  reached  ten  (not  to  speak  of  thousands  of  millions), 
be  ready  to  affirm,  with  the  most  positive  conviction,  that  the  dice  were 
false? 

The  common  and  natural  impression  is  in  favor  of  D’Alembert : the  reg- 
ular series  would  be  thought  much  more  unlikely  than  an  irregular.  But 
this  common  impression  is,  I apprehend,  merely  grounded  on  the  fact,  that 
scarcely  any  body  remembers  to  have  ever  seen  one  of  these  peculiar  coin- 
cidences : the  reason  of  which  is  simply  that  no  one’s  experience  extends  to 
any  thing  like  the  number  of  trials,  within  which  that  or  any  other  given 
combination  of  events  can  be  expected  to  happen.  The  chance  of  sixes  on 
a single  throw  of  two  dice  being  gL-,  the  chance  of  sixes  ten  times  in  suc- 
cession is  1 divided  by  the  tenth  power  of  36;  in  other  words,  such  a con- 
currence is  only  likely  to  happen  once  in  3,656,158,440,062,976  trials,  a 
number  which  no  dice-player’s  experience  comes  up  to  a millionth  part  of. 
But  if,  instead  of  sixes  ten  times,  any  other  given  succession  of  ten  throws 
had  been  fixed  upon,  it  would  have  been  exactly  as  unlikely  that  in  any 
individual’s  experience  that  particular  succession  had  ever  occurred;  al- 
though this  does  not  seem  equally  improbable,  because  no  one  would  be 
likely  to  have  remembered  whether  it  had  occurred  or  not,  and  because  the 
comparison  is  tacitly  made,  not  between  sixes  ten  times  and  any  oue  par- 
ticular series  of  throws,  but  between  all  regular  and  all  irregular  succes- 
sions taken  together. 

That  (as  D’Alembert  says)  if  the  succession  of  sixes  was  actually  thrown 
before  our  eyes,  we  should  ascribe  it  not  to  chance,  but  to  unfairness  in  the 
dice,  is  unquestionably  true.  But  this  arises  from  a totally  different  prin- 
ciple. We  should  then  be  considering,  not  the  probability  of  the  fact  in 
itself,  but  the  comparative  probability  with  which,  when  it  is  known  to 
have  happened,  it  may  be  referred  to  one  or  to  another  cause.  The  regu- 
lar series  is  not  at  all  less  likely  than  the  irregular  one  to  be  brought  about 
by  chance,  but  it  is  much  more  likely  than  the  irregular  oue  to  be  pro- 
duced by  design ; or  by  some  general  cause  operating  through  the  struc- 
ture of  the  dice.  It  is  the  nature  of  casual  combinations  to  produce  a 
repetition  of  the  same  event,  as  often  and  no  oftener  than  any  other  series 
of  events.  But  it  is  the  nature  of  general  causes  to  reproduce,  in  the  same 
circumstances,  always  the  same  event.  Common  sense  and  science  alike 
dictate  that,  all  other  things  being  the  same,  we  should  rather  attribute  the 
effect  to  a cause  which  if  real  would  be  very  likely  to  produce  it,  than  to  a 
cause  which  would  be  very  unlikely  to  produce  it.  According  to  Laplace’s 


446 


INDUCTION. 


sixth  theorem,  which  we  demonstrated  in  a former  chapter,  the  difference 
of  probability  arising  from  the  superior  efficacy  of  the  constant  cause,  un- 
fairness in  the  dice,  would  after  a very  few  throws  far  outweigh  any  ante- 
cedent probability  which  there  could  be  against  its  existence. 

D’Alembert  should  have  put  the  question  in  another  manner.  He  should 
have  supposed  that  we  had  ourselves  previously  tried  the  dice,  and  knew 
by  ample  experience  that  they  were  fair.  Another  person  then  tries  them 
:n  our  absence,  and  assures  us  that  he  threw  sixes  ten  times  in  succession. 
Is  the  assertion  credible  or  not?  Here  the  effect  to  be  accounted  for  is 
not  the  occurrence  itself,  but  the  fact  of  the  witness’s  asserting  it.  This 
may  arise  either  from  its  having  really  happened,  or  from  some  other 
cause.  What  we  have  to  estimate  is  the  comparative  probability  of  these 
two  suppositions. 

If  the  witness  affirmed  that  he  had  thrown  any  other  series  of  numbers, 
supposing  him  to  be  a person  of  veracity,  and  tolerable  accuracy,  and  to 
profess  that  lie  took  particular  notice,  we  should  believe  him.  But  the 
ten  sixes  are  exactly  as  likely  to  have  been  really  thrown  as  the  other  se- 
ries. If,  therefore,  this  assertion  is  less  credible  than  the  other,  the  reason 
must  be,  not  that  it  is  less  likely  than  the  other  to  be  made  truly,  but  that 
it  is  more  likely  than  the  other  to  be  made  falsely. 

One  reason  obviously  presents  itself  why  what  is  called  a coincidence, 
should  be  oftener  asserted  falsely  than  an  ordinary  combination.  It  ex- 
cites wonder.  It  gratifies  the  love  of  the  marvelous.  The  motives,  there- 
fore, to  falsehood,  one  of  the  most  frequent  of  which  is  the  desire  to  aston- 
ish, operate  more  strongly  in  favor  of  this  kind  of  assertion  than  of  the 
other  kind.  Thus  far  there  is  evidently  more  reason  for  discrediting  an 
alleged  coincidence,  than  a statement  in  itself  not  more  probable,  but 
which  if  made  would  not  be  thought  remarkable.  There  are  cases,  how- 
ever, in  which  the  presumption  on  this  ground  would  be  the  other  way. 
There  are  some  witnesses  who,  the  more  extraordinary  an  occurrence 
might  appear,  would  be  the  more  anxious  to  verify  it  by  the  utmost  care- 
fulness of  observation  before  they  would  venture  to  believe  it,  and  still 
more  before  they  would  assert  it  to  others. 

§ 6.  Independently,  however,  of  any  peculiar  chances  of  mendacity  aris- 
ing from  the  nature  of  the  assertion,  Laplace  contends,  that  merely  on  the 
general  ground  of  the  fallibility  of  testimony,  a coincidence  is  not  credible 
on  the  same  amount  of  testimony  on  which  we  should  be  warranted  in  be- 
lieving an  ordinary  combination  of  events.  In  order  to  do  justice  to  his 
argument,  it  is  necessary  to  illustrate  it  by  the  example  chosen  by  himself. 

If,  says  Laplace,  there  were  one  thousand  tickets  in  a box,  and  one  only 
has  been  drawn  out,  then  if  an  eye-witness  affirms  that  the  number  drawn 
was  79,  this,  though  the  chances  were  999  in  1000  against  it,  is  not  on  that 
account  the  less  credible;  its  credibility  is  equal  to  the  antecedent  proba- 
bility of  the  witness’s  veracity.  But  if  there  were  in  the  box  999  black 
balls  and  only  one  white,  and  the  witness  affirms  that  the  white  ball  was 
drawn,  the  case  according  to  Laplace  is  very  different:  the  credibility  of 
his  assertion  is  but  a small  fraction  of  what  it  was  in  the  former  case;  the 
reason  of  the  difference  being  as  follows : 

The  witnesses  of  whom  we  are  speaking  must,  from  the  nature  of  the 
case,  be  of  a kind  whose  credibility  falls  materially  short  of  certainty;  let 
us  suppose,  then,  the  credibility  of  the  witness  in  the  case  in  question  to 
be  ytj- ; that  is,  let  us  suppose  that  in  every  ten  statements  which  the  wit- 


GROUNDS  OF  DISBELIEF. 


447 


ness  makes,  nine  on  an  average  are  correct,  and  one  incorrect.  Let  us 
now  suppose  that  there  have  taken  place  a sufficient  number  of  drawings 
to  exhaust  all  the  possible  combinations,  the  witness  deposing  in  every  one. 
In  one  case  out  of  every  ten  in  all  these  drawings  he  will  actually  have 
made  a false  announcement.  But  in  the  case  of  the  thousand  tickets  these 
false  announcements  will  have  been  distributed  impartially  over  all  the 
numbers,  and  of  the  999  cases  in  which  No.  79  was  not  drawn,  there  will 
have  been  only  one  case  in  which  it  was  announced.  On  the  contrary,  in 
the  case  of  the  thousand  balls  (the  announcement  being  always  either 
“ black  ” or  “ white),”  if  white  was  not  drawn,  and  there  was  a false  an- 
nouncement, that  false  announcement  must  have  been  white;  and  since  by 
the  supposition  there  was  a false  announcement  once  in  every  ten  times, 
white  will  have  been  announced  falsely  in  one-tenth  part  of  all  the  cases  in 
which  it  was  not  drawn,  that  is,  in  one-tenth  part  of  999  cases  out  of  ev- 
ery thousand.  White,  then,  is  drawn,  on  an  average,  exactly  as  often  as 
No.  79,  but  it  is  announced,  without  having  been  really  drawn,  999  times 
as  often  as  No.  79;  the  announcement,  therefore,  requires  a much  greater 
amount  of  testimony  to  render  it  credible.* 

To  make  this  argument  valid  it  must  of  course  be  supposed,  that  the 
announcements  made  by  the  witness  are  average  specimens  of  his  general 
veracity  and  accuracy ; or,  at  least,  that  they  are  neither  more  nor  less  so 
in  the  case  of  the  black  and  white  balls,  than  in  the  case  of  the  thousand 
tickets.  This  assumption,  however,  is  not  warranted.  A person  is  far  less 
likely  to  mistake,  who  has  only  one  form  of  error  to  guard  against,  than  if 
he  had  999  different  errors  to  avoid.  For  instance,  in  the  example  chosen, 
a messenger  who  might  make  a mistake  once  in  ten  times  in  reporting  the 
number  drawn  in  a lottery,  might  not  err  once  in  a thousand  times  if  sent 
simply  to  observe  whether  a ball  was  black  or  white.  Laplace’s  argument, 
therefore,  is  faulty  even  as  applied  to  his  own  case.  Still  less  can  that  case 
be  received  as  completely  representing  all  cases  of  coincidence.  Laplace 
has  so  contrived  his  example,  that  though  black  answers  to  999  distinct 
possibilities,  and  white  only  to  one,  the  witness  has  nevertheless  no  bias 
which  can  make  him  prefer  black  to  white.  The  witness  did  not  know 
that  there  were  999  black  balls  in  the  box  and  only  one  white ; or  if  he 
did,  Laplace  has  taken  care  to  make  all  the  999  cases  so  undistinguishably 
alike,  that  there  is  hardly  a possibility  of  any  cause  of  falsehood  or  error 
operating  in  favor  of  any  of  them,  which  would  not  operate  in  the  same 
manner  if  there  were  only  one.  Alter  this  supposition,  and  the  whole  ar- 
gument falls  to  the  ground.  Let  the  balls,  for  instance,  be  numbered,  and 
let  the  white  ball  be  No.  79.  Considered  in  respect  of  their  color,  there 
are  but  two  things  which  the  witness  can  be  interested  in  asserting,  or  can 
have  dreamed  or  hallucinated,  or  has  to  choose  from  if  he  answers  at  ran- 
dom, viz.,  black  and  white;  but  considered  in  respect  of  the  numbers  at- 
tached to  them,  there  are  a thousand ; and  if  his  interest  or  error  happens 
to  be  connected  with  the  numbers,  though  the  only  assertion  he  makes  is 
about  the  color,  the  case  becomes  precisely  assimilated  to  that  of  the  thou- 

* Not,  however,  as  might  at  first  sight  appear,  999  times  as  much.  A complete  analysis  of 
the  cases  shows  that  (always  assuming  the  veracity  of  the  witness  to  be  JV)  in  10,000  draw- 
ings, the  drawing  of  No.  79  will  occur  nine  times,  and  be  announced  incorrectly  once  ; the 
credibility,  therefore,  of  the  announcement  of  No.  79  is  ^ ; while  the  drawing  of  a white  ball 
will  occur  nine  times,  and  be  announced  incorrectly  999  times.  The  credibility,  therefore,  of 
the  announcement  of  white  is  and  the  ratio  of  the  two  1008:  10  ; the  one  announcement 
being  thus  only  about  a hundred  times  more  credible  than  the  other,  instead  of  999  times. 


448 


INDUCTION. 


sand  tickets.  Or  instead  of  the  balls  suppose  a lottery,  with  1000  tickets 
- and  but  one  prize,  and  that  I hold  No.  79,  and  being  interested  only  in  that, 
ask  the  witness  not  what  was  the  number  drawn,  but  whether  it  was  79  or 
some  other.  There  are  now  only  two  cases,  as  in  Laplace’s  example;  yet 
he  surely  would  not  say  that  if  the  witness  answered  79,  the  assertion 
would  be  in  an  enormous  proportion  less  credible,  than  if  he  made  the  same 
answer  to  the  same  question  asked  in  the  other  way.  If,  for  instance  (to 
put  a case  supposed  by  Laplace  himself),  he  has  staked  a large  sum  on  one 
of  the  chances,  and  thinks  that  by  announcing  its  occurrence  he  shall  in- 
crease  his  credit;  he  is  equally  likely  to  have  betted  on  any  one  of  the  999 
numbers  which  are  attached  to  black  balls,  and  so  far  as  the  chances  of 
mendacity  from  this  cause  are  concerned,  there  will  be  999  times  as  many 
chances  of  his  announcing  black  falsely  as  white. 

Or  suppose  a regiment  of  1000  men,  999  Englishmen  and  one  French- 
man, and  that  of  these  one  man  has  been  killed,  and  it  is  not  known 
which.  I ask  the  question,  and  the  witness  answers,  the  Frenchman.  This 
was  not  only  as  improbable  a priori , but  is  in  itself  as  singular  a circum- 
stance, as  remarkable  a coincidence,  as  the  drawing  of  the  white  ball;  yet 
we  should  believe  the  statement  as  readily,  as  if  the  answer  had  been  John 
Thompson.  Because,  though  the  999  Englishmen  were  all  alike  in  the 
point  in  which  they  differed  from  the  Frenchman,  they  were  not,  like  the 
999  black  balls,  undistinguishable  in  every  other  respect ; but  being  all  dif- 
ferent, they  admitted  as  many  chances  of  interest  or  error,  as  if  each  man 
had  been  of  a different  nation  ; and  if  a lie  was  told  or  a mistake  made,  the 
misstatement  was  as  likely  to  fall  on  any  Jones  or  Thompson  of  the  set,  as 
on  the  Frenchman. 

The  example  of  a coincidence  selected  by  D’Alembert,  that  of  sixes 
thrown  on  a pair  of  dice  ten  times  in  succession,  belongs  to  this  sort  of 
cases  rather  than  to  such  as  Laplace’s.  The  coincidence  is  here  far  more 
remarkable,  because  of  far  rarer  occurrence,  than  the  drawing  of  the  white 
ball.  But  though  the  improbability  of  its  really  occurring  is  greater,  the 
superior  probability  of  its  being  announced  falsely  can  not  be  establish- 
ed with  the  same  evidence.  The  announcement  “black”  represented  999 
cases,  but  the  witness  may  not  have  known  this,  and  if  he  'did,  the  999 
cases  are  so  exactly  alike,  that  there  is  really  only  one  set  of  possible  causes 
of  mendacity  corresponding  to  the  whole.  The  announcement  “ sixes  not 
drawn  ten  times,”  represents,  and  is  known  by  the  witness  to  represent, 
a great  multitude  of  contingencies,  every  one  of  which  being  unlike  every 
other,  there  may  be  a different  and  a fresh  set  of  causes  of  mendacity  cor- 
responding to  each. 

It  appears  to  me,  therefore,  that  Laplace’s  doctrine  is  not  strictly  true  of 
any  coincidences,  and  is  wholly  inapplicable  to  most;  and  that  to  know 
whether  a coincidence  does  or  does  not  require  more  evidence  to  render  it 
credible  than  an  ordinary  event,  we  must  refer,  in  every  instance,  to  first 
principles,  and  estimate  afresh  what  is  the  probability  that  the  given  testi- 
mony would  have  been  delivered  in  that  instance,  supposing  the  fact  which 
it  asserts  not  to  be  true. 

With  these  remarks  we  close  the  discussion  of  the  Grounds  of  Disbelief; 
and  along  with  it,  such  exposition  as  space  admits,  and  as  the  writer  has  it 
in  his  power  to  furnish,  of  the  Logic  of  Induction. 


BOOK  IV 


OF  OPERATIONS  SUBSIDIARY  TO  INDUCTION 


“Clear  and  distinct  ideas  are  terms  which,  though  familiar  and  frequent  in  men's  mouths, 
I have  reason  to  think  every  one  who  uses  does  not  perfectly  understand.  And  possibly  it  is 
but  here  and  there  one  who  gives  himself  the  trouble  to  consider  them  so  far  as  to  know  what 
he  himself  or  others  precisely  mean  by  them  ; I have,  therefore,  in  most  places,  chose  to  put 
determinate  or  determined,  instead  of  clear  and  distinct,  as  more  likely  to  direct  men’s  thoughts 
to  my  meaning  in  this  matter.” — Locke’s  Essay  on  the  Human  Understanding ; Epistle  to 
the  Reader. 

“II  ne  pent  y avoir  qu’une  methode  parfaite,  qui  est  la  methode  naturelle ; on  nomme 
ainsi  un  arrangement  dans  lequel  les  etres  du  meme  genre  seraient  plus  voisins  entre  eux  que 
ceux  de  tons  les  autres  genres ; les  genres  du  meme  ordre,  plus  que  ceux  de  tous  les  autres 
ordres  ; et  ainsi  de  suite.  Cette  methode  est  l'ideal  auquel  l’histoire  naturelle  doit  tendre ; 
car  il  est  evident  que  si  Ton  v parvenait,  Ton  aurait  l’expression  exacte  et  complete  de  la  na- 
ture entiere. ” — Cuvier,  Regne  Animal,  Introduction. 

“Deux  grandes  notions  philosophiques  dominent  la  the'orie  fondamentale  de  la  methode 
naturelle  proprement  dite,  savoir  la  formation  des  groupes  naturels,  et  ensuite  leur  succession 
hierarchique. ” — Cosite,  Cours  de  rhilosophie  Positive,  42me  le<;on. 


CHAPTER  I. 

OF  OBSERVATION  AND  DESCRIPTION. 

§ 1.  Tiie  inquiry  which  occupied  us  in  the  two  preceding  Books,  has 
conducted  us  to  what  appears  a satisfactory  solution  of  the  principal  prob- 
lem of  Logic,  according  to  the  conception  I have  formed  of  the  science. 
We  have  found,  that  the  mental  process  with  which  Logic  is  conversant, 
the  operation  of  ascertaining  truths  by  means  of  evidence,  is  always,  even 
when  appearances  point  to  a different  theory  of  it,  a process  of  induction. 
And  we  have  particularized  the  various  modes  of  induction,  and  obtained 
a clear  view  of  the  principles  to  which  it  must  conform,  in  order  to  lead  to 
results  which  can  be  relied  on. 

The  consideration  of  Induction,  however,  does  not  end  with  the  direct 
rules  for  its  performance.  Something  must  be  said  of  those  other  opera- 
tions of  the  mind,  which  are  either  necessarily  presupposed  in  all  induction, 
or  are  instrumental  to  the  more  difficult  and  complicated  inductive  process- 
es. The  present  Book  will  be  devoted  to  the  consideration  of  these  sub- 
sidiary operations ; among  which  our  attention  must  first  be  given  to  those, 
which  are  indispensable  preliminaries  to  all  induction  whatsoever. 

Induction  being  merely  the  extension  to  a class  of  cases,  of  something 
which  has  been  observed  to  be  true  in  certain  individual  instances  of  the 
class ; the  first  place  among  the  operations  subsidiary  to  induction,  is 
claimed  by  Observation.  This  is  not,  however,  the  place  to  lay  down  rules 
for  making  good  observers;  nor  is  it  within  the  competence  of  Logic  to  do 
so,  but  of  the  art  of  intellectual  Education.  Our  business  with  observation 

29 


450 


OPERATIONS  SUBSIDIARY  TO  INDUCTION. 


is  only  in  its  connection  with  the  appropriate  problem  of  logic,  the  estima- 
tion of  evidence.  We  have  to  consider,  not  how  or  what  to  observe,  but 
under  what  conditions  observation  is  to  be  relied  on;  what  is  needful, in 
order  that  the  fact,  supposed  to  be  observed,  may  safely  be  received  as 
true. 

§ 2.  The  answer  to  this  question  is  very  simple,  at  least  in  its  first  as- 
pect. The  sole  condition  is,  that  what  is  supposed  to  have  been  observed 
shall  really  have  been  observed  ; that  it  be  an  observation,  not  an  inference. 
For  in  almost  every  act  of  our  perceiving  faculties,  observation  and  infer- 
ence are  intimately  blended.  What  we  are  said  to  observe  is  usually  a 
compound  result,  of  which  one-tenth  may  be  observation,  and  the  remain- 
ing nine-tenths  inference. 

I affirm,  for  example,  that  I hear  a man’s  voice.  This  would  pass,  in  com- 
mon language,  for  a direct  perception.  All,  however,  which  is  really  per- 
ception, is  that  I hear  a sound.  That  the  sound  is  a voice,  and  that  voice 
the  voice  of  a man,  are  not  perceptions  but  inferences.  I affirm,  again,  that 
I saw  my  brother  at  a certain  hour  this  morning.  If  any  proposition  con- 
cerning a matter  of  fact  would  commonly  be  said  to  be  known  by  the  di- 
rect testimony  of  the  senses,  this  surely  would  be  so.  The  truth,  however, 
is  far  otherwise.  I only  saw  a certain  colored  surface ; or  rather  I had  the 
kind  of  visual  sensations  which  are  usually  produced  by  a colored  surface; 
and  from  these  as  marks,  known  to  be  such  by  previous  experience,  I con- 
cluded that  I saw  my  brother.  I might  have  had  sensations  precisely  sim- 
ilar, when  my  brother  was  not  there.  I might  have  seen  some  other  per- 
son so  nearly  resembling  him  in  appearance,  as,  at  the  distance,  and,  with 
the  degree  of  attention  which  I bestowed,  to  be  mistaken  for  him.  I might 
have  been  asleep,  and  have  dreamed  that  I saw  him ; or  in  a state  of  nerv- 
ous disorder,  which  brought  his  image  before  me  in  a waking  hallucina- 
tion. In  all  these  modes,  many  have  been  led  to  believe  that  they  saw  per- 
sons well  known  to  them,  who  were  dead  or  far  distant.  If  any  of  these 
suppositions  had  been  true,  the  affirmation  that  I saw  my  brother  would 
have  been  erroneous;  but  whatever  was  matter  of  direct  perception,  name- 
ly the  visual  sensations,  would  have  been  real.  The  inference  only  would 
have  been  ill  grounded;  I should  have  ascribed  those  sensations  to  a wrong 
cause. 

Innumerable  instances  might  be  given,  and  analyzed  in  the  same  manner, 
of  what  are  vulgarly  called  errors  of  sense.  There  are  none  of  them  prop- 
erly errors  of  sense;  they  are  erroneous  inferences  from  sense.  When  I 
look  at  a candle  through  a multiplying  glass,  I see  what  seems  a dozen 
candles  instead  of  one;  and  if  the  real  circumstances  of  the  case  were  skill- 
fully disguised,  I might  suppose  that  there  were  really  that  number  ; there 
would  be  what  is  called  an  optical  deception.  In  the  kaleidoscope  there 
really  is  that  deception;  when  I look  through  the  instrument,  instead  of 
what  is  actually  there,  namely  a casual  arrangement  of  colored  fragments, 
the  appearance  presented  is  that  of  the  same  combination  several  times  re- 
peated in  symmetrical  arrangement  round  a point.  The  delusion  is  of  course 
effected  by  giving  me  the  same  sensations  which  I should  have  had  if  such  a 
symmetrical  combination  had  really  been  presented  to  me.  If  I cross  two 
of  my  fingers,  and  bring  any  small  object,  a marble  for  instance,  into  con 
tact  with  both,  at  points  not  usually  touched  simultaneously  by  one  object, 
I can  hardly,  if  my  eyes  are  shut,  help  believing  that  there  are  two  marbles 
instead  of  one.  But  it  is  not  my  touch  in  this  case,  nor  my  sight  in  the 


V 


OBSERVATION  AND  DESCRIPTION.  451 

other,  which  is  deceived ; the  deception, whether  durable  or  only  momentary, 
is  in  my  judgment.  From  my  senses  I have  only  the  sensations,  and  those 
are  genuine.  Being  accustomed  to  have  those  or  similar  sensations  when, 
and  only  when,  a certain  arrangement  of  outward  objects  is  present  to  my 
organs,  I have  the  habit  of  instantly,  when  I experience  the  sensations,  in- 
ferring the  existence  of  that  state  of  outward  things.  This  habit  has  be- 
come so  powerful,  that  the  inference,  performed  with  the  speed  and  certainty 
of  an  instinct,  is  confounded  with  intuitive  perceptions.  When  it  is  cor- 
rect, I am  unconscious  that  it  ever  needed  proof ; even  when  I know  it  to 
be  incorrect,  I can  not  without  considerable  effort  abstain  from  making  it. 
In  order  to  be  aware  that  it  is  not  made  by  instinct  but  by  an  acquired  hab- 
it, I am  obliged  to  reflect  on  the  slow  process  through  which  I learned  to 
judge  by  the  eye  of  many  things  which  I now  appear  to  perceive  directly 
by  sight;  and  on  the  reverse  operation  performed  by  persons  learning  to 
draw,  who  with  difficulty  and  labor  divest  themselves  of  their  acquired 
perceptions,  and  learn  afresh  to  see  things  as  they  appear  to  the  eye. 

It  would  be  easy  to  prolong  these  illustrations,  were  there  any  need  to  ex- 
patiate on  a topic  so  copiously  exemplified  in  various  popular  works.  From 
the  examples  already  given,  it  is  seen  sufficiently,  that  the  individual  facts 
from  which  we  collect  our  inductive  generalizations  are  scarcely  ever  obtaiued 
by  observation  alone.  Observation  extends  only  to  the  sensations  by  which 
wc  recognize  objects;  but  the  propositions  which  we  make  use  of,  either 
in  science  or  in  common  life,  relate  mostly  to  the  objects  themselves.  In 
every  act  of  what  is  called  observation,  there  is  at  least  one  inference — from 
the  sensations  to  the  presence  of  the  object;  from  the  marks  or  diagnos- 
tics, to  the  entire  phenomenon.  And  hence,  among  other  consequences,  fol- 
lows the  seeming  paradox,  that  a general  proposition  collected  from  par- 
ticulars is  often  more  certainly  true  than  any  one  of  the  particular  propo- 
sitions from  which,  by  an  act  of  induction,  it  was  inferred.  For,  each  of 
those  particular  (or  rather  singular)  propositions  involved  an  inference, 
from  the  impression  on  the  senses  to  the  fact  which  caused  that  impression  ; 
and  this  inference  may  have  been  erroneous  in  any  one  of  the  instances, 
but  can  not  well  have  been  erroneous  in  all  of  them,  provided  their  number 
was  sufficient  to  eliminate  chance.  The  conclusion,  therefore,  that  is,  the 
general  proposition,  may  deserve  more  complete  reliance  than  it  would  be 
safe  to  repose  in  any  one  of  the  inductive  premises. 

The  logic  of  observation,  then,  consists  solely  in  a correct  discrimination 
between  that,  in  a result  of  observation,  which  has  really  been  perceived, 
and  that  which  is  an  inference  from  the  perception.  Whatever  portion  is 
inference,  is  amenable  to  the  rules  of  induction  already  treated  of,  and  re- 
quires no  further  notice  here  ; the  question  for  us  in  this  place  is,  when  all 
which  is  inference  is  taken  away  what  remains  ? There  remains,  in  the  first 
place,  the  mind’s  own  feelings  or  states  of  consciousness,  namely,  its  outward 
feelings  or  sensations,  and  its  inward  feelings — its  thoughts,  emotions,  and 
volitions.  Whether  any  thing  else  remains,  or  all  else  is  inference  from 
this ; whether  the  mind  is  capable  of  directly  perceiving  or  apprehending 
any  thing  except  states  of  its  own  consciousness  — is  a problem  of  meta- 
physics not  to  be  discussed  in  this  place.  But  after  excluding  all  questions 
on  which  metaphysicians  differ,  it  remains  true,  that  for  most  purposes  the 
discrimination  we  are  called  upon  practically  to  exercise  is  that  between 
sensations  or  other  feelings,  of  our  own  or  of  other  people,  and  inferences 
drawn  from  them.  And  on  the  theory  of  Observation  this  is  all  which 
seems  necessary  to  be  said  for  the  purposes  of  the  present  work. 


452\ 


OPERATIONS  SUBSIDIARY  TO  INDUCTION. 


§ 3.  If,  in  the  simplest  observation,  or  in  what  passes  for  such,  there  is  a 
large  part  which  is  not  observation  but  something  else;  so  in  the  simplest 
description  of  an  observation,  there  is,  and  must  always  be,  much  more  as- 
serted than  is  contained  in  the  perception  itself.  We  can  not  describe  a 
fact,  without  implying  more  than  the  fact.  The  perception  is  only  of  one 
individual  thing;  but  to  describe  it  is  to  affirm  a connection  between  it 
and  every  other  thing  which  is  either  denoted  or  connoted  by  any  of  the 
terms  used.  To  begin  with  an  example,  than  which  none  can  be  conceived 
more  elementary : I have  a sensation  of  sight,  and  I endeavor  to  describe 
it  by  saying  that  I see  something  white.  In  saying  this,  I do  not  solely  af- 
firm my  sensation;  I also  class  it.  I assert  a resemblance  between  the 
thing  I see,  and  all  things  which  I and  others  are  accustomed  to  call  white. 
I assert  that  it  resembles  them  in  the  circumstance  in  which  they  all 
resemble  one  another,  in  that  which  is  the  ground  of  their  being  called  by 
the  name.  This  is  not  merely  one  way  of  describing  an  observation,  but 
the  only  way.  If  I would  either  register  my  observation  for  my  own  fu- 
ture use,  or  make  it  known  for  the  benefit  of  others,  I must  assert  a resem- 
blance between  the  fact  which  I have  observed  and  something  else.  It  is 
inherent  in  a description,  to  be  the  statement  of  a resemblance,  or  resem- 
blances. 

We  thus  see  that  it  is  impossible  to  express  in  words  any  result  of  ob- 
servation, without  performing  an  act  possessing  what  Dr.  Whewell  consid- 
ers to  be  characteristic  of  Induction.  There  is  always  something  intro- 
duced which  was  not  included  in  the  observation  itself;  some  conception 
common  to  the  phenomenon  with  other  phenomena  to  which  it  is  com- 
pared. An  observation  can  not  be  spoken  of  in  language  at  all  without 
declaring  more  than  that  one  observation ; without  assimilating  it  to  other 
phenomena  already  observed  and  classified.  But  this  identification  of  an 
object — this  recognition  of  it  as  possessing  certain  known  characteristics — 
has  never  been  confounded  with  Induction.  It  is  an  operation  which  pre- 
cedes all  induction,  and  supplies  it  with  its  materials.  It  is  a perception  of 
resemblances,  obtained  by  comparison. 

These  resemblances  are  not  always  apprehended  directly,  by  merely  com- 
paring the  object  observed  with  some  other  present  object,  or  with  our 
recollection  of  an  object  which  is  absent.  They  are  often  ascertained 
through  intermediate  marks,  that  is,  deductively.  In  describing  some  new 
kind  of  animal,  suppose  me  to  say  that  it  measures  ten  feet  in  length,  from 
the  forehead  to  the  extremity  of  the  tail.  I did  not  ascertain  this  by  the 
unassisted  eye.  I had  a two-foot  rule  which  I applied  to  the  object,  and, 
as  we  commonly  say,  measured  it ; an  operation  which  was  not  wholly  man- 
ual, but  partly  also  mathematical,  involving  the  two  propositions,  Five 
times  two  is  ten,  and  Things  which  are  equal  to  the  same  thing  are  equal 
to  one  another.  Hence,  the  fact  that  the  animal  is  ten  feet  long  is  not  an 
immediate  perception,  but  a conclusion  from  reasoning;  the  minor  prem- 
ises alone  being  furnished  by  observation  of  the  object.  Nevertheless,  this 
is  called  an  observation,  or  a description  of  the  animal,  not  an  induction  re- 
specting it. 

To  pass  at  once  from  a very  simple  to  a very  complex  example : I affirm 
that  the  earth  is  globular.  The  assertion  is  not  grounded  on  direct  percep- 
tion ; for  the  figure  of  the  earth  can  not,  by  us,  be  directly  perceived,  though 
the  assertion  would  not  be  true  unless  circumstances  could  be  supposed 
under  which  its  truth  could  be  so  perceived.  That  the  form  of  the  earth 
is  globular  is  inferred  from  certain  marks,  as  for  instance  from  this,  that  its 


OBSERVATION  AND  DESCRIPTION. 


453 


shadow  thrown  upon  the  moon  is  circular ; or  this,  that  on  the  sea,  or  any 
extensive  plain,  our  horizon  is  always  a circle ; either  of  which  marks  is  in- 
compatible with  any  other  than  a globular  form.  I assert  further,  that  the 
earth  is  that  particular  kind  of  a globe  which  is  termed  an  oblate  spheroid  ; 
because  it  is  found  by  measurement  in  the  direction  of  the  meridian,  that 
the  length  on  the  surface  of  the  earth  which  subtends  a given  angle  at  its 
centre,  diminishes  as  Ave  recede  from  the  equator  and  approach  the  poles. 
But  these  propositions,  that  the  earth  is  globular,  and  that  it  is  an  oblate 
spheroid,  assert,  each  of  them,  an  individual  fact;  in  its  own  nature  capa- 
ble of  being  perceived  by  the  senses  when  the  requisite  organs  and  the  nec- 
essary position  are  supposed,  and  only  not  actually  perceived  because  those 
organs  and  that  position  are  wanting.  This  identification  of  the  earth, 
first  as  a globe,  and  next  as  an  oblate  spheroid,  which,  if  the  fact  could  have 
been  seen,  would  have  been  called  a description  of  the  figure  of  the  earth, 
may  without  impropriety  be  so  called  when,  instead  of  being  seen,  it  is  in- 
ferred. But  Ave  could  not  without  impropriety  call  either  of  these  asser- 
tions an  induction  from  facts  respecting  the  earth.  They  are  not  general 
propositions  collected  from  particular  facts,  but  particular  facts  deduced 
from  general  propositions.  They  are  conclusions  obtained  deductively, 
from  premises  originating  in  induction : but  of  these  premises  some  Avere 
not  obtained  by  observation  of  the  earth,  nor  had  any  peculiar  reference 
to  it. 

If,  then,  the  truth  respecting  the  figure  of  the  earth  is  not  an  induction, 
why  should  the  truth  respecting  the  figure  of  the  earth’s  orbit  be  so  ? The 
tAvo  cases  only  differ  in  this,  that  the  form  of  the  orbit  was  not,  like  the 
form  of  the  earth  itself,  deduced  by  ratiocination  from  facts  Avhich  Avere 
marks  of  ellipticity,  but  Avas  got  at  by  boldly  guessing  that  the  path  Avas 
an  ellipse,  and  finding  aftenvard,  on  examination,  that  the  observations  Avere 
in  harmony  with  the  hypothesis.  According  to  Dr.  WheAvell,  however,  this 
process  of  guessing  and  verifying  our  guesses  is  not  only  induction,  but  the 
Avhole  of  induction : no  other  exposition  can  be  given  of  that  logical  opera- 
tion. That  he  is  wrong  in  the  latter  assertion,  the  whole  of  the  preceding- 
book  has,  I hope,  sufficiently  proved;  and  that  the  process  by  Avhich  the 
ellipticity  of  the  planetary  orbits  Avas  ascertained,  is  not  induction  at  all, 
Avas  attempted  to  be  shown  in  the  second  chapter  of  the  same  Book.*  We 
are  iioav,  however,  prepared  to  go  more  into  the  heart  of  the  matter  than  at 
that  earlier  period  of  our  inquiry,  and  to  sHoav,  not  merely  what  the  opera- 
tion in  question  is  not,  but  what  it  is. 

§ 4.  We  observed,  in  the  second  chapter,  that  the  proposition  “the  earth 
moves  in  an  ellipse,”  so  far  as  it  only  serves  for  the  colligation  or  connect- 
ing together  of  actual  observations  (that  is,  as  it  only  affirms  that  the  ob- 
served positions  of  the  earth  may  be  correctly  represented  by  as  many 
points  in  the  circumference  of  an  imaginary  ellipse),  is  not  an  induction, 
but  a description : it  is  an  induction,  only  Avhen  it  affirms  that  the  interme- 
diate positions,  of  which  there  has  been  no  direct  observation,  would  be 
found  to  correspond  to  the  remaining  points  of  the  same  elliptic  circumfer- 
ence. ISToav,  though  this  real  induction  is  one  thing,  and  the  description 
another,  Ave  are  in  a very  different  condition  for  making  the  induction  be- 
fore Ave  have  obtained  the  description,  and  after  it.  For  inasmuch  as  the 
description,  like  all  other  descriptions,  contains  the  assertion  of  a resem- 


Supra,  book  iii. , chap.  ii. , § 3,  4,  5. 


454 


OPERATIONS  SUBSIDIARY  TO  INDUCTION. 


blance  between  the  phenomenon  described  and  something  else ; in  pointing 
out  something  winch  the  series  of  observed  places  of  a planet  resembles,  it 
points  out  something  in  which  the  several  places  themselves  agree.  If  the 
series  of  places  correspond  to  as  many  points  of  an  ellipse,  the  places  them- 
selves agree  in  being  situated  in  that  ellipse.  We  have,  therefore,  by  the 
same  process  which  gave  us  the  description,  obtained  the  requisites  for  an 
induction  by  the  Method  of  Agreement.  The  successive  observed  places 
of  the  earth  being  considered  as  effects,  and  its  motion  as  the  cause  which 
produces  them,  we  find  that  those  effects,  that  is,  those  places,  agree  in  the 
circumstance  of  being  in  an  ellipse.  We  conclude  that  the  remaining  ef- 
fects, the  places  which  have  not  been  observed,  agree  in  the  same  circum- 
stance, and  that  the  law  of  the  motion  of  the  earth  is  motion  in  an  ellipse. 

The  Colligation  of  Facts,  therefore,  by  means  of  hypotheses,  or,  as  Dr. 
Whewell  prefers  to  say,  by  means  of  Conceptions,  instead  of  being,  as  he 
supposes,  Induction  itself,  takes  its  proper  place  among  operations  subsid- 
iary to  Induction.  All  Induction  supposes  that  we  have  previously  com- 
pared the  requisite  number  of  individual  instances,  and  ascertained  in  what 
circumstances  they  agree.  The  Colligation  of  Facts  is  no  other  than  this 
preliminary  operation.  When  Kepler,  after  vainly  endeavoring  to  connect 
the  observed  places  of  a planet  by  various  hypotheses  of  circular  motion, 
at  last  tried  the  hypotheses  of  an  ellipse  and  found  it  answer  to  the  phe- 
nomena; what  he  really  attempted,  first  unsuccessfully  and  at  last  success- 
fully, was  to  discover  the  circumstance  in  which  all  the  observed  positions 
of  the  planet  agreed.  And  when  he  in  like  manner  connected  another  set 
of  observed  facts,  the  periodic  times  of  the  different  planets,  by  the  propo- 
sition that  the  squares  of  the  times  are  proportional  to  the  cubes  of  the 
distances,  what  he  did  was  simply  to  ascertain  the  property  in  which  the 
periodic  times  of  all  the  different  planets  agreed. 

Since,  therefore,  all  that  is  true  and  to  the  purpose  in  Dr.  Whewell’s 
doctrine  of  Conceptions  might  be  fully  expressed  by  the  more  familiar 
term  Hypothesis;  and  since  his  Colligation  of  Facts  by  means  of  appro- 
priate Conceptions,  is  but  the  ordinary  process  of  finding  by  a comparison 
of  phenomena,  in  what  consists  their  agreement  or  resemblance  ; I would 
willingly  have  confined  myself  to  those  better  understood  expressions,  and 
persevered  to  the  end  in  the  same  abstinence  which  I have  hitherto  ob- 
served from  ideological  discussions;  considering  the  mechanism  of  our 
thoughts  to  be  a topic  distinct  from  and  irrelevant  to  the  principles  and 
rules  by  which  the  trustworthiness  of  the  results  of  thinking  is  to  be  esti- 
mated. Since,  however,  a work  of  such  high  pretensions,  and,  it  must  also 
be  said,  of  so  much  real  merit,  has  rested  the  whole  theory  of  Induction 
upon  such  ideological  considerations,  it  seems  necessary  for  others  who 
follow  to  claim  for  themselves  and  their  doctrines  whatever  position  may 
properly  belong  to  them  on  the  same  metaphysical  ground.  And  this  is 
the  object  of  the  succeeding  chapter. 


ABSTRACTION, 


455 


CHAPTER  II. 

OF  ABSTRACTION,  OR  THE  FORMATION  OF  CONCEPTIONS. 

§1.  The  metaphysical  inquiry  into  the  nature  and  composition  of  what 
have  been  called  Abstract  Ideas,  or,  in  other  words,  of  the  notions  which 
answer  in  the  mind  to  classes  and  to  general  names,  belongs  not  to  Logic, 
but  to  a different  science,  and  our  purpose  does  not  require  that  we  should 
enter  upon  it  here.  We  are  only  concerned  with  the  universally  acknowl- 
edged fact,  that  such  notions  or  conceptions  do  exist.  The  mind  can  con- 
ceive a multitude  of  individual  things  as  one  assemblage  or  class;  and  gen- 
eral names  do  really  suggest  to  us  certain  ideas  or  mental  representations, 
otherwise  we  could  not  use  the  names  with  consciousness  of  a meaning. 
Whether  the  idea  called  up  by  a general  name  is  composed  of  the  various 
circumstances  in  which  all  the  individuals  denoted  by  the  name  agree,  and 
of  no  others  (which  is  the  doctrine  of  Locke,  Brown,  and  the  Conceptual- 
ists) ; or  whether  it  be  the  idea  of  some  one  of  those  individuals,  clothed  in 
its  individualizing  peculiarities,  but  with  the  accompanying  knowledge  that 
those  peculiarities  are  not  properties  of  the  class  (which  is  the  doctrine  of 
Berkeley,  Mr.  Bailey,*  and  the  modern  Nominalists) ; or  whether  (as  held  by 
Mr.  James  Mill)  the  idea  of  the  class  is  that  of  a miscellaneous  assemblage 
of  individuals  belonging  to  the  class;  or  whether,  finally,  it  be  any  one  or 
any  other  of  all  these,  according  to  the  accidental  circumstances  of  the 
case;  certain  it  is,  that  some  idea  or  mental  conception  is  suggested  by  a 
general  name,  whenever  we  either  hear  it  or  employ  it  with  consciousness 
of  a meaning.  And  this,  which  we  may  call,  if  we  please,  a general  idea, 
represents  in  our  minds  the  whole  class  of  things  to  which  the  name  is 
applied.  Whenever  we  think  or  reason  concerning  the  class,  we  do  so  by 
means  of  this  idea..  And  the  voluntary  power  which  the  mind  has,  of  at- 
tending to  one  part  of  what  is  present  to  it  at  any  moment,  and  neglecting 
another  part,  enables  us  to  keep  our  reasonings  and  conclusions  respecting 
the  class  unaffected  by  any  thing  in  the  idea  or  mental  image  which  is  cot 
really,  or  at  least  which  we  do  not  really  believe  to  be  common,  to  the 
whole  class.f 

There  are,  then,  such  things  as  general  conceptions,  or  conceptions  by 
means  of  which  we  can  think  generally;  and  when  we  form  a set  of  phe- 
nomena into  a class,  that  is,  when  we  compare  them  with  one  another  to 
ascertain  in  what  they  agree,  some  general  conception  is  implied  in  this 

* Mr.  Bailey  has  given  the  best  statement  of  this  theory.  “The  general  name,”  he  says, 
“raises  up  the  image  sometimes  of  one  individual  of  the  class  formerly  seen,  sometimes  of 
another,  not  unfrequently  of  many  individuals  in  succession ; and  it  sometimes  suggests  an 
image  made  up  of  elements  from  several  different  objects,  by  a latent  process  of  which  I am 
not  conscious.”  (Letters  on  the  Philosophy  of  the  Human  Mind,  1st  series,  letter  22.)  But 
Mr.  Bailey  must  allow  that  we  carry  on  inductions  and  ratiocinations  respecting  the  class,  by- 
means  of  this  idea  or  conception  of  some  one  individual  in  it.  This  is  all  I require.  The 
name  of  a class  calls  up  some  idea,  through  which  we  can,  to  all  intents  and  purposes,  think 
of  the  class  as  such,  and  not  solely  of  an  individual  member  of  it. 

t I have  entered  rather  fully  into  this  question  in  chap.  xvii.  of  An  Examination  of  Sir 
William  Hamilton's  Philosophy , headed  “The  Doctrine  of  Concepts  or  General  Notions,” 
which  contains  my  last  views  on  the  subject- 


456 


OPERATIONS  SUBSIDIARY  TO  INDUCTION. 


mental  operation.  And  inasmuch  as  such  a comparison  is  a necessary  pre- 
liminary to  Induction,  it  is  most  true  that  Induction  could  not  go  on  with- 
out general  conceptions. 

§ 2.  But  it  does  not  therefore  follow  that  these  general  conceptions  must 
have  existed  in  the  mind  previously  to  the  comparison.  It  is  not  a law  of 
our  intellect,  that  in  comparing  things  with  each  other  and  taking  note 
of  their  agreement  we  merely  recognize  as  realized  in  the  outward  world 
something  that  we  already  had  in  our  minds.  The  conception  originally 
found  its  way  to  us  as  the  result  of  such  a comparison.  It  was  obtained 
(in  metaphysical  phrase)  by  abstraction  from  individual  things.  These 
things  may  be  things  which  we  perceived  or  thought  of  on  former  occa- 
sions, but  they  may  also  be  the  things  which  we  are  perceiving  or  thinking 
of  on  the  very  occasion.  When  Kepler  compared  the  observed  places  of 
the  planet  Mars,  and  found  that  they  agreed  in  being  points  of  an  elliptic 
circumference,  he  applied  a general  conception  which  was  already  in  his 
mind,  having  been  derived  from  his  former  experience.  But  this  is  by  no 
means  universally  the  case.  When  we  compare  several  objects  and  find 
them  to-  agree  in  being  white,  or  when  we  compare  the  various  species  of 
ruminating  animals  and  find  them  to  agree  in  being  cloven-footed,  we  have 
just  as  much  a general  conception  in  our  minds  as  Kepler  had  in  his:  we 
have  the  conception  of  “ a white  thing,”  or  the  conception  of  “ a cloven- 
footed  animal.”  But  no  one  supposes  that  we  necessarily  bring  these  con- 
ceptions with  us,  and  superinduce  them  (to  adopt  Dr.  Whewell’s  expres- 
sion) upon  the  facts:  because  in  these  simple  cases  every  body  sees  that 
the  very  act  of  comparison  which  ends  in  our  connecting  the  facts  by 
means  of  the  conception,  may  be  the  source  from  which  we  derive  the  con- 
ception itself.  If  we  had  never  seen  any  white  object  or  had  never  seen 
any  cloven-footed  animal  before,  we  should  at  the  same  time  and  by  the 
same  mental  act  acquire  the  idea,  and  employ  it  for  the  colligation  of  the 
observed  phenomena.  Kepler,  on  the  contrary,  really  had  to  bring  the 
idea  with  him,  and  superinduce  it  upon  the  facts;  he  could  not  evolve  it 
out  of  them:  if  he  had  not  already  had  the  idea,  he  would  not  have  been 
able  to  acquire  it  by  a comparison  of  the  planet’s  positions.  But  this  in- 
ability was  a mere  accident ; the  idea  of  an  ellipse  could  have  been  ac- 
quired from  the  paths  of  the  planets  as  effectually  as  from  any  thing  else, 
if  the  paths  had  not  happened  to  be  invisible.  If  the  planet  had  left  a 
visible  track,  and  we  had  been  so  placed  that  we  could  see  it  at  the  proper 
angle,  we  might  have  abstracted  our  original  idea  of  an  ellipse  from  the 
planetary  orbit.  Indeed,  every  conception  which  can  be  made  the  instru- 
ment for  connecting  a set  of  facts,  might  have  been  originally  evolved  from 
those  very  facts.  The  conception  is  a conception  of  something;  and  that 
which  it  is  a conception  of,  is  really  in  the  facts,  and  might,  under  some 
supposable  circumstances,  or  by  some  supposable  extension  of  the  faculties 
which  we  actually  possess,  have  been  detected  in  them.  And  not  only  is 
this  always  in  itself  possible,  but  it  actually  happens  in  almost  all  cases  in 
which  the  obtaining  of  the  right  conception  is  a matter  of  any  considera- 
ble difficulty.  For  if  there  be  no  new  conception  required  ; if  one  of  those 
already  familiar  to  mankind  will  serve  the  purpose,  the  accident  of  being 
the  first  to  whom  the  right  one  occurs,  may  happen  to  almost  any  body , 
at  least  in  the  case  of  a set  of  phenomena  which  the  whole  scientific  world 
are  engaged  in  attempting  to  connect.  The  honor,  in  Kepler’s  case,  was 
that  of  the  accurate,  patient,  and  toilsome  calculations  by  which  he  com- 


ABSTRACTION. 


451 


paved  the  results  that  followed  from  his  different  guesses,  with  the  obser- 
vations of  Tycho  Brahe ; but  the  merit  was  very  small  of  guessing  an 
ellipse;  the  only  wonder  is  that  men  had  not  guessed  it  before,  nor  could 
they  have  failed  to  do  so  if  there  had  not  existed  an  obstinate  a priori 
prejudice  that  the  heavenly  bodies  must  move,  if  not  in  a circle,  in  some 
combination  of  circles. 

The  really  difficult  cases  are  those  in  which  the  conception  destined  to 
create  light  and  order  out  of  darkness  and  confusion  has  to  be  sought  for 
among  the  very  phenomena  which  it  afterward  serves  to  arrange.  Why, 
according  to  Dr.  Whewell  himself,  did  the  ancients  fail  in  discovering  the 
laws  of  mechanics,  that  is,  of  equilibrium  and  of  the  communication  of  mo- 
tion? Because  they  had  not,  or  at  least  had  not  clearly,  the  ideas  or  con- 
ceptions of  pressure  and  resistance,  momentum,  and  uniform  and  accelera- 
ting force.  And  whence  could  they  have  obtained  these  ideas  except  from 
the  very  facts  of  equilibrium  and  motion  ? The  tardy  development  of  sev- 
eral of  the  physical  sciences,  for  example,  of  optics,  electricity,  magnetism, 
and  the  higher  generalizations  of  chemistry,  he  ascribes  to  the  fact  that 
mankind  had  not  yet  possessed  themselves  of  the  Idea  of  Polarity,  that  is, 
the  idea  of  opposite  properties  in  opposite  directions.  But  what  was  there 
to  suggest  such  an  idea,  until,  by  a separate  examination  of  several  of  these 
different  branches  of  knowledge,  it  was  shown  that  the  facts  of  each  of  them 
did  present,  in  some  instances  at  least,  the  curious  phenomenon  of  opposite 
properties  in  opposite  directions?  The  thing  was  superficially  manifest 
only  in  two  cases,  those  of  the  magnet  and  of  electrified  bodies;  and  there 
the  conception  was  encumbered  with  the  circumstance  of  material  poles, 
or  fixed  points  in  the  body  itself,  in  which  points  this  opposition  of  proper- 
ties seemed  to  be  inherent.  The  first  comparison  and  abstraction  had  led 
only  to  this  conception  of  poles  ; and  if  any  thing  corresponding  to  that  con- 
ception had  existed  in  the  phenomena  of  chemistry  or  optics,  the  difficulty 
now  justly  considered  so  great,  would  have  been  extremely  small.  The  ob- 
scurity arose  from  the  fact,  that  the  polarities  in  chemistry  and  optics  were 
distinct  species,  though  of  the  same  genus,  with  the  polarities  in  electricity 
and  magnetism  ; and  that  in  order  to  assimilate  the  phenomena  to  one  anoth- 
er, it  was  necessary  to  compare  a polarity  without  poles,  such  for  instance  as 
is  exemplified  in  the  polarization  of  light,  and  the  polarity  with  (apparent) 
poles,  which  we  see  in  the  magnet;  and  to  recognize  that  these  polarities, 
while  different  in  many  other  respects,  agree  in  the  one  character  which  is 
expressed  by  the  phrase,  opposite  properties  in  opposite  directions.  From 
the  result  of  such  a comparison  it  was  that  the  minds  of  scientific  men 
formed  this  new  general  conception  ; between  which,  and  the  first  confused 
feeling  of  an  analogy  between  some  of  the  phenomena  of  light  and  those  of 
electricity  and  magnetism,  there  is  a long  interval,  filled  up  by  the  labors 
and  more  or  less  sagacious  suggestions  of  many  superior  minds. 

The  conceptions,  then,  which  we  employ  for  the  colligation  and  methodi- 
zation  of  facts,  do  not  develop  themselves  from  within,  but  are  impressed 
upon  the  mind  from  without;  they  are  never  obtained  otherwise  than  by 
way  of  comparison  and  abstraction,  and,  in  the  most  important  and  the 
most  numerous  cases,  are  evolved  by  abstraction  from  the  very  phenomena 
which  it  is  their  office  to  colligate.  I am  far,  however,  from  wishing  to  im- 
ply that  it  is  not  often  a very  difficult  thing  to  perform  this  process  of  ab- 
straction well,  or  that  the  success  of  an  inductive  operation  does  not,  in  many 
cases,  principally  depend  on  the  skill  with  which  we  perform  it.  Bacon 
was  quite  justified  in  designating  as  one  of  the  principal  obstacles  to  good 


45S 


OPERATIONS  SUBSIDIARY  TO  INDUCTION. 


induction,  general  conceptions  wrongly  formed,  “ notiones  temere  a rebus 
abst  racts) to  which  Dr.  Whewell  adds,  that  not  only  does  bad  abstraction 
make  bad  induction,  but  that,  in  order  to  perform  induction  well,  we  must 
have  abstracted  well;  our  general  conceptions  must  be  “clear”  and  “ap- 
propriate” to  the  matter  in  hand. 

§ 3.  In  attempting  to  show  what  the  difficulty  in  this  matter  really  is, 
and  how  it  is  surmounted,  I must  beg  the  reader,  once  for  all,  to  bear  this 
in  mind;  that  although,  in  discussing  the  opinions  of  a different  school  of 
philosophy,  I am  willing  to  adopt  their  language,  and  to  speak,  therefore, 
of  connecting  facts  through  the  instrumentality  of  a conception,  this  tech- 
nical phraseology  means  neither  more  nor  less  than  what  is  commonly  call- 
ed comparing  the  facts  with  one  another  and  determining  in  what  they 
agree.  Nor  has  the  technical  expression  even  the  advantage  of  being  met- 
aphysically correct.  The  facts  are  not  connected , except  in  a merely  met- 
aphorical acceptation  of  the  term.  The  ideas  of  the  facts  may  become 
connected,  that  is,  we  may  be  led  to  think  of  them  together;  but  this  con- 
sequence is  no  more  than  what  may  be  produced  by  any  casual  association. 
What  really  takes  place,  is,  I conceive,  more  philosophically  expressed  by 
the  common  word  Comparison,  than  by  the  phrases  “to  connect”  or  “to 
superinduce.”  For,  as  the  general  conception  is  itself  obtained  by  a com- 
parison of  particular  phenomena,  so,  when  obtained,  the  mode  in  which  we 
apply  it  to  other  phenomena  is  again  by  comparison.  We  compare  phe- 
nomena with  each  other  to  get  the  conception,  and  we  then  compare  those 
and  other  phenomena  with  the  conception.  We  get  the  conception  of  an 
animal  (for  instance)  by  comparing  different  animals,  and  when  we  after- 
ward see  a creature  resembling  an  animal,  we  compare  it  with  our  general 
conception  of  an  animal ; and  if  it  agrees  with  that  general  conception,  wc 
include  it  in  the  class.  The  conception  becomes  the  type  of  comparison. 

And  we  need  only  consider  what  comparison  is,  to  see  that  where  the 
objects  are  more  than  two,  and  still  more  when  they  are  an  indefinite  num- 
ber, a type  of  some  sort  is  an  indispensable  condition  of  the  comparison. 
When  we  have  to  arrange  and  classify  a great  number  of  objects  according 
to  their  agreements  and  differences,  we  do  not  make  a confused  attempt  to 
compare  all  with  all.  We  know  that  two  things  are  as  much  as  the  mind 
can  easily  attend  to  at  a time,  and  we  therefore  fix  upon  one  of  the  objects, 
either  at  hazard  or  because  it  offers  in  a peculiarly  striking  manner  some 
important  character,  and,  taking  this  as  our  standard,  compare  it  with  one 
object  after  another.  If  we  find  a second  object  which  presents  a remark- 
able agreement  with  the  first,  inducing  us  to  class  them  together,  the  ques- 
tion instantly  arises,  in  what  particular  circumstances  do  they  agree?  and 
to  take  notice  of  these  circumstances  is  already  a first  stage  of  abstraction, 
giving  rise  to  a general  conception.  Having  advanced  thus  far,  when  we 
now  take  in  hand  a third  object  we  naturally  ask  ourselves  the  question, 
not  merely  whether  this  third  object  agrees  with  the  first,  but  whether  it 
agrees  with  it  in  the  same  circumstances  in  which  the  second  did?  in  other 
words,  whether  it  agrees  with  the  general  conception  which  has  been  ob- 
tained by  abstraction  from  the  first  and  second  ? Thus  we  see  the  tenden- 
cy of  general  conceptions,  as  soon  as  formed,  to  substitute  themselves  ns 
types,  for  whatever  individual  objects  previously  answered  that  purpose  in 
our  comparisons.  We  may,  perhaps,  find  that  no  considerable  number  of 
other  objects  agree  with  this  first  general  conception ; and  that  we  must 
drop  the  conception,  and  beginning  again  with  a different  individual  case, 


ABSTRACTION. 


459 


proceed  by  fresh  comparisons  to  a different  general  conception.  Some- 
times, again,  we  find  that  the  same  conception  will  serve,  by  merely  leaving 
ont  some  of  its  circumstances ; and  by  this  higher  effort  of  abstraction,  we 
obtain  a still  more  general  conception ; as  in  the  case  formerly  referred  to, 
the  scientific  world  rose  from  the  conception  of  poles  to  the  general  concep- 
tion of  opposite  properties  in  opposite  directions ; or  as  those  South-Sea 
islanders,  whose  conception  of  a quadruped  had  been  abstracted  from  hogs 
(the  only  animals  of  that  description  which  they  had  seen),  when  they  after- 
ward compared  that  conception  with  other  quadrupeds,  dropped  some  of 
the  circumstances,  and  arrived  at  the  more  general  conception  which  Eu- 
ropeans associate  with  the  term. 

These  brief  remarks  contain,  I believe,  all  that  is  well  grounded  in  the 
doctrine,  that  the  conception  by  which  the  mind  arranges  and  gives  unity 
to  phenomena  must  be  furnished  by  the  mind  itself,  and  that  we  find  the 
right  conception  by  a tentative  process,  trying  first  one  and  then  another 
until  we  hit  the  mark.  The  conception  is  not  furnished  by  the  mind  until 
it  has  been  furnished  to  the  mind;  and  the  facts  which  supply  it  are  some- 
times extraneous  facts,  but  more  often  the  very  facts  which  we  are  attempt- 
ing to  arrange  by  it.  It  is  quite  true,  however,  that  in  endeavoring  to 
arrange  the  facts,  at  whatever  point  we  begin,  we  never  advance  three 
steps  without  forming  a general  conception,  more  or  less  distinct  and  pre- 
cise; and  that  this  general  conception  becomes  the  clue  which  we  instant- 
ly endeavor  to  trace  through  the  rest  of  the  facts,  or  rather,  becomes  the 
standard  with  which  we  thenceforth  compare  them.  If  we  are  not  satis- 
fied with  the  agreements  which  we  discover  among  the  phenomena  by  com- 
paring them  with  this  type,  or  with  some  still  more  general  conception 
which  by  an  additional  stage  of  abstraction  we  can  form  from  the  type; 
we  change  our  path,  and  look  out  for  other  agreements ; we  recommence 
the  comparison  from  a different  starting-point,  and  so  generate  a different 
set  of  general  conceptions.  This  is  the  tentative  process  which  Dr.  Whe- 
well  speaks  of;  and  which  has  not  unnaturally  suggested  the  theory,  that 
the  conception  is  supplied  by  the  mind  itself ; since  the  different  concep- 
tions which  the  mind  successively  tries,  it  either  already  possessed  from 
its  previous  experience,  or  they  were  supplied  to  it  in  the  first  stage  of  the 
corresponding  act  of  comparison  ; so  that,  in  the  subsequent  part  of  the 
process,  the  conception  manifested  itself  as  something  compared  with  the 
phenomena,  not  evolved  from  them. 

§ 4.  If  this  be  a correct  account  of  the  instrumentality  of  general  con- 
ceptions in  the  comparison  which  necessarily  precedes  Induction,  we  are 
now  able  to  translate  into  our  own  language  what  Dr.  Whewell  means  by 
saying  that  conceptions,  to  be  subservient  to  Induction,  must  be  “clear” 
and  “ appropriate.” 

If  the  conception  corresponds  to  a real  agreement  among  the  phenome- 
na; if  the  comparison  which  we  have  made  of  a set  of  objects  has  led  us  to 
class  them  according  to  real  resemblances  and  differences ; the  conception 
which  does  this  can  not  fail  to  be  appropriate,  for  some  purpose  or  other. 
The  question  of  appropriateness  is  relative  to  the  particular  object  we 
have  in  view.  As  soon  as,  by  our  comparison,  we  have  ascertained  some 
agreement,  something  which  can  be  predicated  in  common  of  a number  of 
objects;  we  have  obtained  a basis  on  which  an  inductive  process  is  capa- 
ble of  being  founded.  But  the  agreements,  or  the  ulterior  consequences 
to  which  those  agreements  lead,  may  be  of  very  different  degrees  of  impor- 


460 


OPERATIONS  SUBSIDIARY  TO  INDUCTION. 


tance.  If,  for  instance,  we  only  compare  animals  according  to  their  color, 
and  class  those  together  which  are  colored  alike,  we  form  the  general  con- 
ceptions of  a white  animal,  a black  animal,  etc.,  which  are  conceptions  le- 
gitimately formed ; and  if  an  induction  were  to  be  attempted  concerning 
the  causes  of  the  colors  of  animals,  this  comparison  would  be  the  proper 
and  necessary  preparation  for  such  an  induction,  but  would  not  help  us  to- 
ward a knowledge  of  the  laws  of  any  other  of  the  properties  of  animals; 
while  if,  with  Cuvier,  we  compare  and  class  them  according  to  the  struc- 
ture of  the  skeleton,  or,  with  Blainville,  according  to  the  nature  of  their 
outward  integuments,  the  agreements  and  differences  which  are  observable 
in  these  respects  are  not  only  of  much  greater  importance  in  themselves, 
but  are  marks  of  agreements  and  differences  in  many  other  important  par- 
ticulars of  the  structure  and  mode  of  life  of  the  animals.  If,  therefore,  the 
study  of  their  structure  and  habits  be  our  object,  the  conceptions  gener- 
ated by  these  last  comparisons  are  far  more  “ appropriate  ” than  those  gen- 
erated by  the  former.  Nothing,  other  than  this,  can  be  meant  by  the  ap- 
propriateness of  a conception. 

When  Dr.  Whewell  says  that  the  ancients,  or  the  school-men,  or  any 
modern  inquirers,  missed  discovering  the  real  law  of  a phenomenon  because 
they  applied  to  it  an  inappropriate  instead  of  an  appropriate  conception; 
he  can  only  mean  that  in  comparing  various  instances  of  the  phenomenon, 
to  ascertain  in  what  those  instances  agreed,  they  missed  the  important 
points  of  agreement;  and  fastened  upon  such  as  were  either  imaginary, 
and  not  agreements  at  all,  or,  if  real  agreements,  were  comparatively  tri- 
fling, and  had  no  connection  with  the  phenomenon,  the  law  of  which  was 
sought. 

Aristotle,  philosophizing  on  the  subject  of  motion,  remarked  that  certain 
motions  apparently  take  place  spontaneously;  bodies  fall  to  the  ground, 
flame  ascends,  bubbles  of  air  rise  in  water,  etc. ; and  these  he  called  nat- 
ural motions;  while  others  not  only  never  take  place  without  external  in- 
citement, but  even  when  such  incitement  is  applied,  tend  spontaneously  to 
cease ; which,  to  distinguish  them  from  the  former,  he  called  violent  mo- 
tions. Now,  in  comparing  the  so-called  natural  motions  with  one  another, 
it  appeared  to  Aristotle  that  they  agreed  in  one  circumstance,  namely,  that 
the  body  which  moved  (or  seemed  to  move)  spontaneously,  rvas  moving 
toward  its  own  place ; meaning  thereby  the  place  from  whence  it  originally 
came,  or  the  place  where  a great  quantity  of  matter  similar  to  itself  was 
assembled.  In  the  other  class  of  motions,  as  when  bodies  are  thrown  up  in 
the  air,  they  are,  on  the  contrary,  moving  from  their  own  place.  Now, 
this  conception  of  a body  moving  toward  its  own  place  may  justly  be  con- 
sidered inappropriate ; because,  though  it  expresses  a circumstance  really 
found  in  some  of  the  most  familiar  instances  of  motion  apparently  spon- 
taneous, yet,  first,  there  are  many  other  cases  of  such  motion,  in  which  that; 
circumstance  is  absent;  the  motion,  for  instance,  of  the  earth  and  planets. 
Secondly,  even  when  it  is  present,  the  motion,  on  closer  examination,  would 
often  be  seen  not  to  be  spontaneous ; as,  when  air  rises  in  water,  it  does 
not  rise  by  its  own  nature,  but  is  pushed  up  by  the  superior  weight  of  the 
water  which  presses  upon  it.  Finally,  there  are  many  cases  in  which  the 
spontaneous  motion  takes  place  in  the  contrary  direction  to  what  the  theory 
considers  as  the  body’s  own  place  ; for  instance,  when  a fog  rises  from  a 
lake,  or  when  water  dries  up.  The  agreement,  therefore,  which  Aristotle 
selected  as  his  principle  of  classification,  did  not  extend  to  all  cases  of  the 
phenomenon  he  wanted  to  study,  spontaneous  motion  ; while  it  did  include 


ABSTRACTION. 


461 


cases  of  the  absence  of  the  phenomenon,  cases  of  motion  not  spontaneous. 
The  conception  was  hence  “ inappropriate.”  We  may  add  that,  in  the  case 
in  question,  no  conception  would  be  appropriate ; there  is  no  agreement 
which  runs  through  all  the  cases  of  spontaneous  or  apparently  spontaneous 
motion  and  no  others  ; they  can  not  be  brought  under  one  law  ; it  is  a case 
of  Plurality  of  Causes.* 

§ 5.  So  much  for  the  first  of  Dr.  Whewell’s  conditions,  that  conceptions 
must  be  appropriate.  The  second  is,  that  they  shall  be  “clear:”  and  let  us 
consider  what  this  implies.  Unless  the  conception  corresponds  to  a real 
agreement,  it  has  a worse  defect  than  that  of  not  being  clear : it  is  not  ap- 
plicable to  the  case  at  all.  Among  the  phenomena,  therefore,  which  we  are 
attempting  to  connect  by  means  of  the  conception,  we  must  suppose  that 
there  really  is  an  agreement,  and  that  the  conception  is  a conception  of 
that  agreement.  In  order,  then,  that  it  may  be  clear,  the  only  requisite  is, 
that  we  shall  know  exactly  in  what  the  agreement  consists ; that  it  shall 
have  been  carefully  observed,  and  accurately  remembered.  We  are  said 
not  to  have  a clear  conception  of  the  resemblance  among  a set  of  objects, 
when  we  have  only  a general  feeling  that  they  resemble,  without  having 
analyzed  their  resemblance,  or  perceived  in  what  points  it  consists,  and 
fixed  in  our  memory  an  exact  recollection  of  those  points.  This  want  of 
clearness,  or,  as  it  may  be  otherwise  called,  this  vagueness  in  the  general 
conception,  may  be  owing  either  to  our  having  no  accurate  knowledge  of 
the  objects  themselves,  or  merely  to  our  not  having  carefully  compared 
them.  Thus  a person  may  have  no  clear  idea  of  a ship  because  he  has 
never  seen  one,  or  because  he  remembers  but  little,  and  that  faintly,  of 
what  he  has  seen.  Or  he  may  have  a perfect  knowledge  and  remembrance 
of  many  ships  of  various  kinds,  frigates  among  the  rest,  but  he  may  have 
no  clear  but  only  a confused  idea  of  a frigate,  because  he  has  never  been 
told,  and  has  not  compared  them  sufficiently  to  have  remarked  and  remem- 
bered, in  what  particular  points  a frigate  differs  from  some  other  kind  of 
ship. 

It  is  not,  however,  necessary,  in  order  to  have  clear  ideas,  that  we  should 
know  all  the  common  properties  of  the  things  which  we  class  together. 
That  would  be  to  have  our  conception  of  the  class  complete  as  well  as 
slear.  It  is  sufficient  if  we  never  class  things  together  without  knowing 
exactly  why  we  do  so — without  having  ascertained  exactly  what  agree- 
ments we  are  about  to  include  in  our  conception;  and  if,  after  having  thus 
fixed  our  conception,  we  never  vary  from  it,  never  include  in  the  class  any 

* Other  examples  of  inappropriate  conceptions  are  given  by  Dr.  Whewell  (Phil.  Ind.  Sc. 
ii. , 185)  as  follows:  “Aristotle  and  his  followers  endeavored  in  vain  to  account  for  the  me- 
chanical relation  of  forces  in  the  lever,  by  applying  the  inappropriate  geometrical  concep- 
tions of  the  properties  of  the  circle  : they  failed  in  explaining  the  form  of  the  luminous  spot 
made  by  the  sun  shining  through  a hole,  because  they  applied  the  inappropriate  conception 
of  a circular  quality  in  the  sun’s  light : they  speculated  to  no  purpose  about  the  elementary 
composition  of  bodies,  because  they  assumed  the  inappropriate  conception  of  likeness  between 
the  elements  and  the  compound,  instead  of  the  genuine  notion  of  elements  merely  determinin </ 
the  qualities  of  the  compound.”  But  in  these  cases  there  is  more  than  an  inappropriate  con- 
ception ; there  is  a false  conception ; one  which  has  no  prototype  in  nature,  nothing  corre- 
sponding to  it  in  facts.  This  is  evident  in  the  last  two  examples,  and  is  equally  true  in  the 
first ; the  “properties  of  the  circle”  which  were  referred  to,  being  purely  fantastical.  There 
is,  therefore,  an  error  beyond  the  wrong  choice  of  a principle  of  generalization  ; there  is  a 
false  assumption  of  matters  of  fact.  The  attempt  is  made  to  resolve  certain  laws  of  nature 
into  a more  general  law,  that  law  not  being  one  which,  though  real,  is  inappropriate,  but  one 
wholly  imaginary. 


462 


OPERATIONS  SUBSIDIARY  TO  INDUCTION. 


tiling  which  has  not  those  common  properties,  nor  exclude  from  it  any 
thing  which  has.  A clear  conception  means  a determinate  conception  ; 
one  which  does  not  fluctuate,  which  is  not  one  thing  to-day  and  another 
to-morrow,  but  remains  fixed  and  invariable,  except  when,  from  the  prog- 
ress of  our  knowledge,  or  the  correction  of  some  error,  we  consciously  add 
to  it  or  alter  it.  A person  of  clear  ideas  is  a person  who  always  knows  in 
virtue  of  what  properties  his  classes  are  constituted ; what  attributes  are 
connoted  by  his  general  names. 

The  principal  requisites,  therefore,  of  clear  conceptions,  are  habits  of  at- 
tentive observation,  an  extensive  experience,  and  a memory  which  receives 
and  retains  an  exact  image  of  what  is  observed.  And  in  proportion  as 
any  one  has  the  habit  of  observing  minutely  and  comparing  carefully  a 
particular  class  of  phenomena,  and  an  accurate  memory  for  the  results  of 
the  observation  and  comparison,  so  will  his  conceptions  of  that  class  of 
phenomena  be  clear ; provided  he  has  the  indispensable  habit  (naturally, 
however,  resulting  from  those  other  endowments),  of  never  using  general 
names  without  a precise  connotation. 

As  the  clearness  of  our  conceptions  chiefly  depends  on  the  carefulness 
and  accuracy  of  our  observing  and  comparing  faculties,  so  their  appropri- 
ateness, or  rather  the  chance  we  have  of  hitting  upon  the  appropriate  con- 
ception in  any  case,  mainly  depends  on  the  activity  of  the  same  faculties. 
He  who  by  habit,  grounded  on  sufficient  natural  aptitude,  has  acquired  a 
readiness  in  accurately  observing  and  comparing  phenomena,  will  perceive 
so  many  more  agreements,  and  will  perceive  them  so  much  more  rapidly 
than  other  people,  that  the  chances  are  much  greater  of  his  perceiving,  in 
any  instance,  the  agreement  on  which  the  important  consequences  depend. 

§ 6.  It  is  of  so  much  importance  that  the  part  of  the  process  of  investi- 
gating truth,  discussed  in  this  chapter,  should  be  rightly  understood,  that 
I think  it  is  desirable  to  restate  the  results  we  have  arrived  at,  in  a some- 
what different  mode  of  expression. 

We  can  not  ascertain  general  truths,  that  is,  truths  applicable  to  classes, 
unless  we  have  formed  the  classes  in  such  a manner  that  general  truths 
can  be  affirmed  of  them.  In  the  formation  of  any  class,  there  is  involved 
a conception  of  it  as  a class,  that  is,  a conception  of  certain  circumstances 
as  being  those  which  characterize  the  class,  and  distinguish  the  objects 
composing  it  from  all  other  things.  When  we  know  exactly  what  these 
circumstances  are,  we  have  a clear  idea  (or  conception)  of  the  class,  and  of 
the  meaning  of  the  general  name  which  designates  it.  The  primary  condi- 
tion implied  in  having  this  clear  idea,  is  that  the  class  be  really  a class; 
that  it  correspond  to  a real  distinction  ; that  the  things  it  includes  really 
do  agree  with  one  another  in  certain  particulars,  and  differ,  in  those  same 
particulars,  from  all  other  things.  A person  without  clear  ideas  is  one 
who  habitually  classes  together,  under  the  same  general  names,  things 
which  have  no  common  properties,  or  none  which  are  not  possessed  also 
by  other  things ; or  who,  if  the  usage  of  other  people  prevents  him  from 
actually  misclassing  things,  is  unable  to  state  to  himself  the  common  prop- 
erties in  virtue  of  which  he  classes  them  rightly. 

But  is  it  not  the  sole  requisite  of  classification  that  the  classes  should  be 
real  classes,  framed  by  a legitimate  mental  process  ? Some  modes  of  class- 
ing things  are  more  valuable  than  others  for  human  uses,  whether  of  spec- 
ulation or  of  practice;  and  our  classifications  are  not  well  made,  unless  the 
things  which  they  bring  together  not  only  agree  with  each  other  in  some- 


ABSTRACTION. 


463 


thing  which  distinguishes  them  from  all  other  things,  but  agree  with  each 
other  and  differ  from  other  things  in  the  very  circumstances  which  are  of 
primary  importance  for  the  purpose  (theoretical  or  practical)  which  we 
have  in  view,  and  which  constitutes  the  problem  before  us.  In  other 
words,  our  conceptions,  though  they  may  be  clear,  are  not  appropriate  for 
our  purpose,  unless  the  properties  we  comprise  in  them  are  those  which 
will  help  us  toward  what  we  wish  to  understand — i.  e.,  either  those  which  go 
deepest  into  the  nature  of  the  things,  if  our  object  be  to  understand  that, 
or  those  which  are  most  closely  connected  with  the  particular  property 
which  we  are  endeavoring  to  investigate. 

We  can  not,  therefore,  frame  good  general  conceptions  beforehand. 
That  the  conception  we  have  obtained  is  the  one  we  want,  can  only  be 
known  when  we  have  done  the  work  for  the  sake  of  which  we  wanted  it; 
when  we  completely  understand  the  general  character  of  the  phenomena, 
or  the  conditions  of  the  particular  property  with  which  we  concern  our- 
selves. General  conceptions  formed  without  this  thorough  knowledge,  are 
Bacon’s  “ notiones  temere  a rebus  abstractse.”  Yet  such  premature  con- 
ceptions we  must  be  continually  making  up,  in  our  progress  to  something 
better.  They  are  an  impediment  to  the  progress  of  knowledge,  only  when 
they  are  permanently  acquiesced  in.  When  it  has  become  our  habit  to 
group  things  in  wrong  classes — in  groups  which  either  are  not  really  class- 
es, having  no  distinctive  points  of  agreement  (absence  of  clear  ideas),  or 
which  are  not  classes  of  which  any  thing  important  to  our  purpose  can  be 
predicated  (absence  of  appropriate  ideas) ; and  when,  in  the  belief  that 
these  badly  made  classes  are  those  sanctioned  by  nature,  we  refuse  to  ex- 
change them  for  others,  and  can  not  or  will  not  make  up  our  general  con- 
ceptions from  any  other  elements;  in  that  case  all  the  evils  which  Bacon 
ascribes  to  his  “notiones  temere  abstractae”  really  occur.  This  was  what 
the  ancients  did  in  physics,  and  what  the  world  in  general  does  in  morals 
and  politics  to  the  present  day. 

It  would  thus,  in  my  view  of  the  matter,  be  an  inaccurate  mode  of  ex- 
pression to  say,  that  obtaining  appropriate  conceptions  is  a condition  pre- 
cedent to  generalization.  Throughout  the  whole  process  of  comparing 
phenomena  with  one  another  for  the  purpose  of  generalization,  the  mind  is 
trying  to  make  up  a conception;  but  the  conception  which  it  is  trying  to 
make  up  is  that  of  the  really  important  point  of  agreement  in  the  phenom- 
ena. As  we  obtain  more  knowledge  of  the  phenomena  themselves,  and  of 
the  conditions  on  which  their  important  properties  depend,  our  views  on 
this  subject  naturally  alter;  and  thus  we  advance  from  a less  to  a more 
“appropriate”  general  conception,  in  the  progress  of  our  investigations. 

We  ought  not,  at  the  same  time,  to  forget  that  the  really  important 
agreement  can  not  always  be  discovered  by  mere  comparison  of  the  very 
phenomena  in  question,  without  the  aid  of  a conception  acquired  elsewhere; 
as  in  the  case,  so  often  referred  to,  of  the  planetary  orbits. 

The  search  for  the  agreement  of  a set  of  phenomena  is  in  truth  very 
similar  to  the  search  for  a lost  or  hidden  object.  At  first  we  place  our- 
selves in  a sufficiently  commanding  position,  and  cast  our  eyes  round  us, 
and  if  we  can  see  the  object  it  is  well;  if  not,  we  ask  ourselves  mentally 
what  are  the  places  in  which  it  may  be  hid,  in  order  that  we  may  there 
search  for  it:  and  so  on,  until  we  imagine  the  place  where  it  really  is.  And 
here  too  we  require  to  have  had  a previous  conception,  or  knowledge,  of 
those  different  places.  As  in  this  familiar  process,  so  in  the  philosophical 
operation  which  it  illustrates,  we  first  endeavor  to  find  the  lost  object  or 


464 


OPERATIONS  SUBSIDIARY  TO  INDUCTION. 


recognize  the  common  attribute,  without  conjecturally  invoking  the  aid  of 
any  previously  acquired  conception,  or,  in  other  words,  of  any  hypothesis. 
Having  failed  in  this,  we  call  upon  our  imagination  for  some  hypothesis  of 
a possible  place,  or  a possible  point  of  resemblance,  and  then  look  to  see 
whether  the  facts  agree  with  the  conjecture. 

For  such  cases  something  more  is  required  than  a mind  accustomed  to 
accurate  observation  and  comparison.  It  must  be  a mind  stored  with  gen- 
eral conceptions,  previously  acquired,  of  the  sorts  which  bear  affinity  to  the 
subject  of  the  particular  inquiry.  And  much  will  also  depend  on  the  nat- 
ural strength  and  acquired  culture  of  what  has  been  termed  the  scientific 
imagination ; on  the  faculty  possessed  of  mentally  arranging  known  ele- 
ments into  new  combinations,  such  as  have  not  yet  been  observed  in  na- 
ture, though  not  contradictory  to  any  known  laws. 

Bat  the  variety  of  intellectual  habits,  the  purposes  which  they  serve,  and 
the  modes  in  which  they  may  be  fostered  and  cultivated,  are  considerations 
belonging  to  the  Art  of  Education:  a subject  far  wider  than  Logic,  and 
which  this  treatise  does  not  profess  to  discuss.  Here,  therefore,  the  pres- 
ent chapter  may  properly  close. 


CHAPTER  III. 

OP  NAMING,  AS  SUBSIDIARY  TO  INDUCTION. 

§ 1.  It  does  not  belong  to  the  present  undertaking  to  dwell  on  the  im- 
portance of  language  as  a medium  of  human  intercourse,  whether  for  pur- 
poses of  sympathy  or  of  information.  Nor  does  our  design  admit  of  more 
than  a passing  allusion  to  that  great  property  of  names,  on  which  their  func- 
tions as  an  intellectual  instrument  are,  in  reality,  ultimately  dependent; 
their  potency  as  a means  of  forming,  and  of  riveting,  associations  among 
our  other  ideas;  a subject  on  which  an  able  thinker*  has  thus  written: 

“ Names  are  impressions  of  sense,  and  as  such  take  the  strongest  hold  on 
the  mind,  and  of  all  other  impressions  can  be  most  easily  recalled  and  re- 
tained in  view.  They  therefore  serve  to  give  a point  of  attachment  to  all 
the  more  volatile  objects  of  thought  and  feeling.  Impressions  that  when 
passed  might  be  dissipated  forever,  are,  by  their  connection  with  language, 
always  within  reach.  Thoughts,  of  themselves,  are  perpetually  slipping  out 
of  the  field  of  immediate  mental  vision ; but  the  name  abides  with  us,  and 
the  utterance  of  it  restores  them  in  a moment.  Words  are  the  custodiers 
of  every  product  of  mind  less  impressive  than  themselves.  All  extensions 
of  human  knowledge,  all  new  generalizations,  are  fixed  and  spread,  even  un- 
intentionally, by  the  use  of  words.  The  child  growing  up  learns,  along 
with  the  vocables  of  his  mother-tongue,  that  things  which  he  would  have 
believed  to  be  different  are,  in  important  points,  the  same.  Without  any 
formal  instruction,  the  language  in  which  we  grow  up  teaches  us  all  the 
common  philosophy  of  the  age.  It  directs  us  to  observe  and  know  things 
which  we  should  have  overlooked;  it  supplies  us  with  classifications  ready 
made,  by  which  things  are  arranged  (as  far  as  the  light  of  by-gone  genera- 
tions admits)  with  the  objects  to  which  they  bear  the  greatest  total  resem- 
blance. The  number  of  general  names  in  a language,  and  the  degree  of 


* Professor  Bain. 


NAMING. 


465 


generality  of  those  names,  afford  a test  of  the  knowledge  of  the  era,  and  of 
the  intellectual  insight  which  is  the  birthright  of  any  one  born  into  it.” 

It  is  not,  however,  of  the  functions  of  Names,  considered  generally,  that 
we  have  here  to  treat,  but  only  of  the  manner  and  degree  in  which  they  are 
directly  instrumental  to  the  investigation  of  truth;  in  other  words, to  the 
process  of  induction. 

§ 2.  Observation  and  Abstraction,  the  operations  which  formed  the  sub- 
ject of  the  two  foregoing  chapters,  are  conditions  indispensable  to  induc- 
tion ; there  can  be  no  induction  where  they  are  not.  It  has  been  imagined 
that  Naming  is  also  a condition  equally  indispensable.  There  are  thinkers 
who  have  held  that  language  is  not  solely,  according  to  a phrase  generally 
current,  an  instrument  of  thought,  but  the  instrument ; that  names,  or  some- 
thing equivalent  to  them,  some  species  of  artificial  signs,  are  necessary  to 
reasoning;  that  there  could  be  no  inference,  and  consequently  no  induction, 
without  them.  But  if  the  nature  of  reasoning  was  correctly  explained  in 
the  earlier  part  of  the  present  work,  this  opinion  must  be  held  to  be  an  ex- 
aggeration, though  of  an  important  truth.  If  reasoning  be  from  particulars 
to  particulars,  and  if  it,  consist  in  recognizing  one  fact  as  a mark  of  another, 
or  a mark  of  a mark  of  another,  nothing  is  required  to  render  reasoning- 
possible,  except  senses  and  association ; senses  to  perceive  that  two  facts 
are  conjoined ; association,  as  the  law  by  which  one  of  those  two  facts  raises 
up  the  idea  of  the  other.*  For  these  mental  phenomena,  as  well  as  for  the 
belief  or  expectation  which  follows,  and  by  which  we  recognize  as  having- 
taken  place,  or  as  about  to  take  place,  that  of  which  we  have  perceived  a 
mark,  there  is  evidently  no  need  of  language.  And  this  inference  of  one 
particular  fact  from  another  is  a case  of  induction.  It  is  of  this  sort  of  in- 
duction that  brutes  are  capable;  it  is  in  this  shape  that  uncultivated  minds 
make  almost  all  their  inductions,  and  that  we  all  do  so  in  the  cases  in  which 
familiar  experience  forces  our  conclusions  upon  us  without  any  active  proc- 
ess of  inquiry  on  our  part,  and  in  which  the  belief  or  expectation  follows 
the  suggestion  of  the  evidence  with  the  promptitude  and  certainty  of  an 
instinct.-) 

§ 3.  But  though  inference  of  an  inductive  character  is  possible  without 
the  use  of  signs,  it  could  never,  without  them,  be  carried  much  beyond  the 
very  simple  cases  which  we  have  just  described,  and  which  form,  in  all 
probability,  the  limit  of  the  reasonings  of  those  animals  to  whom  conven- 
tional language  is  unknown.  Without  language,  or  something  equivalent 
to  it,  there  could  only  be  as  much  reasoning  from  experience  as  can  take 
place  without  the  aid  of  general  propositions.  Now,  though  in  strictness 

* This  .sentence  having  been  erroneously  understood  as  if  I had  meant  to  assert  that  belief  is 
nothing  but  an  irresistible  association,  I think  it  necessary  to  observe  that  I express  no  theory 
respecting  the  ultimate  analysis  either  of  reasoning  or  of  belief,  two  of  the  most  obscure  points 
in  analytical  psychology.  I am  speaking  not  of  the  powers  themselves,  but  of  the  previous 
conditions  necessary  to  enable  those  powers  to  exert  themselves : of  which  conditions  I am 
contending  that  language  is  not  one,  senses  and  association  being  sufficient  without  it.  The 
irresistible  association  theory  of  belief,  and  the  difficulties  connected  with  the  subject,  have 
been  discussed  at  length  in  the  notes  to  the  new  edition  of  Mr.  James  Mill’s  Analysis  of  the 
Phenomena  of  the  Human  Mind. 

f Mr.  Bailey  agrees  with  me  in  thinking  that  whenever  “from  something  actually  present 
to  my  senses,  conjoined  with  past  experience,  I feel  satisfied  that  something  has  happened,  or 
will  happen,  or  is  happening,  beyond  the  sphere  of  my  personal  observation,”  I may  with  strict 
propriety  be  said  to  reason  : and  of  course' to  reason  inductively,  for  demonstrative  reasoning 
is  excluded  by  the  circumstances  of  the  case.  ( The  Theory  of  Reasoning , 2d  ed.,  p.  27.) 

30 


466 


OPERATIONS  SUBSIDIARY  TO  INDUCTION. 


we  may  reason  from  past  experience  to  a fresh  individual  case  without  the 
intermediate  stage  of  a general  proposition,  yet  without  general  propositions 
we  should  seldom  remember  what  past  experience  we  have  had,  and  scarce- 
ly ever  what  conclusions  that  experience  will  warrant.  The  division  of  the 
inductive  process  into  two  parts,  the  first  ascertaining  what  is  a mark  of 
the  given  fact,  the  second  whether  in  the  new  case  that  mark  exists,  is 
natural,  and  scientifically  indispensable.  It  is,  indeed,  in  a majority  of 
cases,  rendered  necessary  by  mere  distance  of  time.  Tbe  experience  by 
which  we  are  to  guide  our  judgments  may  be  other  people’s  experience, 
little  of  which  can  be  communicated  to  us  otherwise  than  by  language; 
when  it  is  our  own,  it  is  generally  experience  long  past;  unless,  therefore, 
it  were  recorded  by  means  of  artificial  signs,  little  of  it  (except  in  cases  in- 
volving our  intenser  sensations  or  emotions,  or  the  subjects  of  our  daily  and 
hourly  contemplation)  would  be  retained  in  the  memory.  It  is  hardly  nec- 
essary to  add,  that  when  the  inductive  inference  is  of  any  but  the  most 
direct  and  obvious  nature — when  it  requires  several  observations  or  exper- 
iments, in  varying  circumstances,  and  the  comparison  of  one  of  these  with 
another — it  is  impossible  to  proceed  a step,  without  the  artificial  memory 
which  words  bestow.  Without  words,  we  should,  if  we  had  often  seen  A 
and  B in  immediate  and  obvious  conjunction,  expect  B whenever  we  saw 
A;  but  to  discover  their  conjunction  when  not  obvious,  or  to  determine 
whether  it  is  really  constant  or  only  casual,  and  whether  there  is  reason  to 
expect  it  under  any  given  change  of  circumstances,  is  a process  far  too  com- 
plex to  be  performed  without  some  contrivance  to  make  our  remembrance 
of  our  own  mental  operations  accurate.  Now,  language  is  such  a contriv- 
ance. When  that  instrument  is  called  to  our  aid,  the  difficulty  is  reduced 
to  that  of  making  our  remembrance  of  the  meaning  of  words  accurate. 
This  being  secured,  whatever  passes  through  our  minds  may  be  remem- 
bered accurately,  by  putting  it  carefully  into  words,  and  committing  the 
words  either  to  writing  or  to  memory. 

The  function  of  Naming,  and  particularly  of  General  Names,  in  Induc- 
tion, may  be  recapitulated  as  follows.  Every  inductive  inference  which  is 
good  at  all,  is  good  for  a whole  class  of  cases;  and,  that  the  inference  may 
have  any  better  warrant  of  its  correctness  than  the  mere  clinging  together 
of  two  ideas,  a process  of  experimentation  and  comparison  is  necessary ; in 
which  the  whole  class  of  cases  must  Ire  brought  to  view,  and  some  uniform- 
ity in  the  course  of  nature  evolved  and  ascertained,  since  the  existence 
of  such  a uniformity  is  required  as  a justification  for  drawing  the  infer- 
ence in  even  a single  case.  This  uniformity,  therefore,  may  be  ascertained 
once  for  all ; and  if,  being  ascertained,  it  can  be  remembered,  it  will  serve 
as  a formula  for  making,  in  particular  cases,  all  such  inferences  as  the  pre- 
vious experience  will  warrant.  But  we  can  only  secure  its  being  remem- 
bered, or  give  ourselves  even  a chance  of  carrying  in  our  memory  any  con- 
siderable number  of  such  uniformities,  by  registering  them  through  the 
medium  of  permanent  signs;  which  (being,  from  the  nature  of  the  case, 
signs  not  of  an  individual  fact,  but  of  a uniformity,  that  is,  of  an  indefinite 
number  of  facts  similar  to  one  another)  are  general  signs;  universals;  gen- 
eral names,  and  general  propositions. 

§ 4.  And  here  I can  not  omit  to  notice  an  oversight  committed  by  some 
eminent  thinkers;  who  have  said  that  the  cause  of  our  using  general  names 
is  the  infinite  multitude  of  individual  objects,  which,  making  it  impossible 
to  have  a name  for  each,  compels  us  to  make  one  name  serve  for  many. 


REQUISITES  OF  LANGUAGE. 


467 


This  is  a very  limited  view  of  the  function  of  general  names.  Even  if 
there  were  a name  for  every  individual  object,  we  should  require  general 
names  as  much  as  we  now  do.  Without  them  we  could  not  express  the 
result  of  a single  comparison,  nor  record  any  one  of  the  uniformities  ex- 
isting in  nature;  and  should  be  hardly  better  off  in  respect  to  Induction 
than  if  we  had  no  names  at  all.  With  none  but  names  of  individuals  (or, 
in  other  words,  proper  names),  we  might,  by  pronouncing  the  name,  sug- 
gest the  idea  of  the  object,  but  we  could  not  assert  any  proposition ; ex- 
cept the  unmeaning  ones  formed  by  predicating  two  proper  names  one  of 
another.  It  is  only  by  means  of  general  names  that  we  can  convey  any 
information,  predicate  any  attribute,  even  of  an  individual,  much  more  of 
a class.  Rigorously  speaking,  we  could  get  on  without  any  other  general 
names  than  the  abstract  names  of  attributes ; all  our  propositions  might 
be  of  the  form  “such  an  individual  object  possesses  such  an  attribute,”  or 
“such  an  attribute  is  always  (or  never)  conjoined  with  such  another  attri- 
bute.” In  fact,  however,  mankind  have  always  given  general  names  to 
objects  as  well  as  attributes,  and  indeed  before  attributes:  but  the  general 
names  given  to  objects  imply  attributes,  derive  their  whole  meaning  from 
attributes ; and  are  chiefly  useful  as  the  language  by  means  of  which  we 
predicate  the  attributes  which  they  connote. 

It  remains  to  be  considered  what  principles  are  to  be  adhered  to  in 
giving  general  names,  so  that  these  names,  and  the  general  propositions  in 
which  they  fill  a place,  may  conduce  most  to  the  purposes  of  Induction. 


CHAPTER  IY. 

OF  THE  REQUISITES  OF  A PHILOSOPHICAL  LANGUAGE,  AND  THE  PRINCI- 
PLES OF  DEFINITION. 

§ 1.  In  order  that  we  may  possess  a language  perfectly  suitable  for  the 
investigation  and  expression  of  general  truths,  there  are  two  principal,  and 
several  minor  requisites.  The  first  is,  that  every  general  name  should 
have  a meaning,  steadily  fixed,  and  precisely  determined.  When,  by  the 
fulfillment  of  this  condition,  such  names  as  we  possess  are  fitted  for  the 
due  performance  of  their  functions,  the  next  requisite,  and  the  second  in 
order  of  importance,  is  that  we  should  possess  a name  wherever  one  is 
needed ; wherever  there  is  any  thing  to  be  designated  by  it,  which  it  is  of 
importance  to  express. 

The  former  of  these  requisites  is  that  to  which  our  attention  will  be  ex- 
clusively directed  in  the  present  chapter. 

§ 2.  Every  general  name,  then,  must  have  a certain  and  knowable  mean- 
ing. Now  the  meaning  (as  has  so  often  been  explained)  of  a general  con- 
notative  name,  resides  in  the  connotation ; in  the  attribute  on  account  of 
which,  and  to  express  which,  the  name  is  given.  Thus,  the  name  animal 
being  given  to  all  things  which  possess  the  attributes  of  sensation  and 
voluntary  motion,  the  word  connotes  those  attributes  exclusively,  and  they 
constitute  the  whole  of  its  meaning.  If  the  name  be  abstract,  its  denota- 
tion is  the  same  with  the  connotation  of  the  corresponding  concrete;  it 
designates  directly  the  attribute,  which  the  concrete  term  implies.  To  give 
a precise  meaning  to  general  names  is,  then,  to  fix  with  steadiness  the 


468 


OPERATIONS  SUBSIDIARY  TO  INDUCTION. 


attribute  or  attributes  connoted  by  each  concrete  general  name,  and  de- 
noted by  the  corresponding  abstract.  Since  abstract  names,  in  the  order 
of  their  creation,  do  not  precede  but  follow  concrete  ones,  as  is  proved  by 
the  etymological  fact  that  they  are  almost  always  derived  from  them;  we 
may  consider  their  meaning  as  determined  by,  and  dependent  on,  the  mean- 
ing of  their  concrete ; and  thus  the  problem  of  giving  a distinct  meaning 
to  general  language,  is  all  included  in  that  of  giving  a precise  connotation 
to  all  concrete  general  names. 

This  is  not  difficult  in  the  case  of  new  names  ; of  the  technical  terms 
created  by  scientific  inquirers  for  the  purposes  of  science  or  art.  But 
when  a name  is  in  common  use,  the  difficulty  is  greater ; the  problem  in 
this  case  not  being  that  of  choosing  a convenient  connotation  for  the  name, 
but  of  ascertaining  and  fixing  the  connotation  with  which  it  is  already 
used.  That  this  can  ever  be  a matter  of  doubt,  is  a sort  of  paradox.  But 
the  vulgar  (including  in  that  term  all  who  have  not  accurate  habits  of 
thought)  seldom  know  exactly  what  assertion  they  intend  to  make,  what 
common  property  they  mean  to  express,  when  they  apply  the  same  name  to 
a number  of  different  things.  All  which  the  name  expresses  with  them, 
when  they  predicate  it  of  an  object,  is  a confused  feeling  of  resemblance 
between  that  object  and  some  of  the  other  things  which  they  have  been 
accustomed  to  denote  by  the  name.  They  have  applied  the  name  Stone 
to  various  objects  previously  seen ; they  see  a new  object,  which  appears 
to  them  somewhat  like  the  former,  and  they  call  it  a stone,  without  asking 
themselves  in  what  respect  it  is  like,  or  what  mode  or  degree  of  resem- 
blance the  best  authorities,  or  even  they  themselves,  require  as  a warrant 
for  using  the  name.  This  rough  general  impression  of  resemblance  is, 
however,  made  up  of  particular  circumstances  of  resemblance  ; and  into 
these  it  is  the  business  of  the  logician  to  analyze  it ; to  ascertain  what 
points  of  resemblance  among  the  different  things  commonly  called  by  the 
name,  have  produced  in  the  common  mind  this  vague  feeling  of  likeness: 
have  given  to  the  things  the  similarity  of  aspect,  which  has  made  them  a 
class,  and  has  caused  the  same  name  to  be  bestowed  upon  them. 

But  though  general  names  are  imposed  by  the  vulgar  without  any  more 
definite  connotation  than  that  of  a vague  resemblance;  general  proposi- 
tions come  in  time  to  be  made,  in  which  predicates  are  applied  to  those 
names,  that  is,  general  assertions  are  made  concerning  the  whole  of  the 
things  which  are  denoted  by  the  name.  And  since  by  each  of  these  prop- 
ositions some  attribute,  more  or  less  precisely  conceived,  is  of  course  pred- 
icated, the  ideas  of  these  various  attributes  thus  become  associated  with 
the  name,  and  in  a sort  of  uncertain  way  it  comes  to  connote  them ; there 
is  a hesitation  to  apply  the  name  in  any  new  case  in  which  any  of  the  at- 
tributes familiarly  predicated  of  the  class  do  not  exist.  And  thus,  to 
common  minds,  the  propositions  which  they  are  in  the  habit  of  hearing  Cl- 
uttering concerning  a class  make  up  in  a loose  way  a sort  of  connotation 
for  the  class  name.  Let  us  take,  for  instance,  the  word  Civilized.  How 
few  could  be  found,  even  among  the  most  educated  persons,  who  would 
undertake  to  say  exactly  what  the  term  Civilized  connotes.  Yet  there  is 
a feeling  in  the  minds  of  all  who  use  it,  that  they  are  using  it  with  a mean- 
ing; and  this  meaning  is  made  up,  in  a confused  manner,  of  every  thing 
which  they  have  heard  or  read  that  civilized  men  or  civilized  communities 
are,  or  may  be  expected  to  be. 

It  is  at  this  stage,  probably,  in  the  progress  of  a concrete  name,  that  the 
corresponding  abstract  name  generally  comes  into  use.  Under  the  notion 


REQUISITES  OE  LANGUAGE. 


469 


that  the  concrete  name  must  of  course  convey  a meaning,  or,  in  other  words, 
that  there  is  some  property  common  to  all  things  which  it  denotes,  people 
give  a name  to  this  common  property ; from  the  concrete  Civilized,  they 
form  the  abstract  Civilization.  But  since  most  people  have  never  com- 
pared the  different  things  which  are  called  by  the  concrete  name,  in  such  a 
manner  as  to  ascertain  what  properties  these  things  have  in  common,  or 
whether  they  have  any;  each  is  thrown  back  upon  the  marks  by  which  he 
himself  has  been  accustomed  to  be  guided  in  his  application  of  the  term ; 
and  these,  being  merely  vague  hearsays  and  current  phrases,  are  not  the 
same  in  any  two  persons,  nor  in  the  same  person  at  different  times.  Hence 
the  word  (as  Civilization,  for  example)  which  professes  to  be  the  designa- 
tion of  the  unknown  common  property,  conveys  scarcely  to  any  two  minds 
the  same  idea.  No  two  persons  agree  in  the  things  they  predicate  of  it; 
and  when  it  is  itself  predicated  of  any  thing,  no  other  person  knows,  nor 
does  the  speaker  himself  know  with  precision,  what  he  means  to  assert. 
Many  other  words  which  could  be  named,  as  the  word  honor , or  the  word 
gentleman , exemplify  this  uncertainty  still  more  strikingly. 

It  needs  scarcely  be  observed,  that  general  propositions  of  which  no 
one  can  tell  exactly  what  they  assert,  can  not  possibly  have  been  brought 
to  the  test  of  a correct  induction.  Whether  a name  is  to  be  used  as 
an  instrument  of  thinking,  or  as  a means  of  communicating  the  result  of 
thought,  it  is  imperative  to  determine  exactly  the  attribute  or  attributes 
which  it  is  to  express ; to  give  it,  in  short,  a fixed  and  ascertained  connota- 
tion. 

§ 3.  It  would,  however,  be  a complete  misunderstanding  of  the  proper  of- 
fice of  a logician  in  dealing  with  terms  already  in  use,  if  we  were  to  think 
that  because  a name  has  not  at  present  an  ascertained  connotation,  it  is 
competent  to  any  one  to  give  it  such  a connotation  at  his  own  choice.  The 
meaning  of  a term  actually  in  use  is  not  an  arbitrary  quantity  to  be  fixed, 
but  an  unknown  quantity  to  be  sought. 

In  the  first  place,  it  is  obviously  desirable  to  avail  ourselves,  as  far  as 
possible,  of  the  associations  already  connected  with  the  name;  not  enjoin- 
ing the  employment  of  it  in  a manner  which  conflicts  with  all  previous 
habits,  and  especially  not  so  as  to  require  the  rupture  of  those  strongest 
of  all  associations  between  names,  which  are  created  by  familiarity  with 
propositions  in  which  they  are  predicated  of  one  another.  A philosopher 
would  have  little  chance  of  having  his  example  followed,  if  he  were  to  give 
such  a meaning  to  his  terms  as  should  require  us  to  call  the  North  Ameri- 
can Indians  a civilized  people,  or  the  higher  classes  in  Europe  savages ; or 
to  say  that  civilized  people  live  by  hunting,  and  savages  by  agriculture. 
Were  there  no  other  reason,  the  extreme  difficulty  of  effecting  so  complete 
a revolution  in  speech  would  be  more  than  a sufficient  one.  The  endeavor 
should  be,  that  all  generally  received  propositions  into  which  the  term  en- 
ters, should  be  at  least  as  true  after  its  meaning  is  fixed,  as  they  were  be- 
fore ; and  that  the  concrete  name,  therefore,  should  not  receive  such  a con- 
notation as  shall  prevent  it  from  denoting  things  which,  in  common  lan- 
guage, it  is  currently  affirmed  of.  The  fixed  and  precise  connotation  which 
it  receives  should  not  be  in  deviation  from,  but  in  agreement  (as  far  as  it 
goes)  with,  the  vague  and  fluctuating  connotation  which  the  term  already 
had. 

To  fix  the  connotation  of  a concrete  name,  or  the  denotation  of  the  cor- 
responding abstract,  is  to  define  the  name.  When  this  can  be  done  with- 


470 


OPERATIONS  SUBSIDIARY  TO  INDUCTION. 


out  rendering  any  received  assertions  inadmissible,  the  name  can  be  de- 
fined in  accordance  with  its  received  use,  which  is  vulgarly  called  defining 
not  the  name  but  the  thing.  What  is  meant  by  the  improper  expression 
of  defining  a thing  (or  rather  a class  of  things — for  nobody  talks  of  defin- 
ing an  individual),  is  to  define  the  name,  subject  to  the  condition  that  it 
shall  denote  those  things.  This,  of  course,  supposes  a comparison  of  the 
things,  feature  by  feature  and  property  by  property,  to  ascertain  what  at- 
tributes they  agree  in ; and  not  unfrequently  an  operation  strictly  induc- 
tive, for  the  purpose  of  ascertaining  some  unobvious  agreement,  which  is 
the  cause  of  the  obvious  agreements. 

For,  in  order  to  give  a connotation  to  a name,  consistently  with  its  de- 
noting certain  objects,  we  have  to  make  our  selection  from  among  the  vari- 
ous attributes  in  which  those  objects  agree.  To  ascertain  in  what  they  do 
agree  is,  therefore,  the  first  logical  operation  requisite.  When  this  has 
been  done  as  far  as  is  necessary  or  practicable,  the  question  arises,  which 
of  these  common  attributes  shall  be  selected  to  be  associated  with  the 
name.  For  if  the  class  which  the  name  denotes  be  a Kind,  the  common 
properties  are  innumerable;  and  even  if  not,  they  are  often  extremely  nu- 
merous. Our  choice  is  first  limited  by  the  preference  to  be  given  to  prop- 
erties which  are  well  known,  and  familiarly  predicated  of  the  class  ; but 
even  these  are  often  too  numerous  to  be  all  included  in  the  definition,  and, 
besides,  the  properties  most  generally  known  may  not  be  those  which  serve 
best  to  mark  out  the  class  from  all  others.  We  should  therefore  select 
from  among  the  common  properties  (if  among  them  any  such  are  to  be 
found)  those  on  which  it  has  been  ascertained  by  expedience,  or  proved  by 
deduction,  that  many  others  depend ; or  at  least  which  are  sure  marks  of 
them,  and  from  whence,  therefore,  many  others  will  follow  by  inference. 
We  thus  see  that  to  frame  a good  definition  of  a name  already  in  use,  is 
not  a matter  of  choice  but  of  discussion,  and  discussion  not  merely  respect- 
ing the  usage  of  language,  but  respecting  the  properties  of  things,  and 
even  the  origin  of  those  properties.  And  hence  every  enlargement  of 
our  knowledge  of  the  objects  to  which  the  name,  is  applied,  is  liable  to 
suggest  an  improvement  in  the  definition.  It  is  impossible  to  frame  a per- 
fect set  of  definitions  on  any  subject,  until  the  theory  of  the  subject  is  per- 
fect ; and  as  science  makes  progress,  its  definitions  are  also  progressive. 

§ 4.  The  discussion  of  Definitions,  in  so  far  as  it  does  not  turn  on  the 
use  of  words  but  on  the  properties  of  things,  Dr.  Whewell  calls  the  Expli- 
cation of  Conceptions.  The  act  of  ascertaining,  better  than  before,  in  what 
particulars  any  phenomena  which  are  classed  together  agree,  he  calls  in  his 
technical  phraseology,  unfolding  the  general  conception  in  virtue  of  which 
they  are  so  classed.  Making  allowance  for  what  appears  to  me  the  dark- 
ening and  misleading  tendency  of  this  mode  of  expression,  several  of  his 
remarks  are  so  much  to  the  purpose,  that  I shall  take  the  liberty  of  tran- 
scribing them. 

He  observes,*  that  many  of  the  controversies  which  have  had  an  impor- 
tant share  in  the  formation  of  the  existing  body  of  science,  have  “ assumed 
the  form  of  a battle  of  Definitions.  For  example,  the  inquiry  concerning 
the  laws  of  falling  bodies  led  to  the  question  whether  the  proper  definition 
of  a uniform  force  is  that  it  generates  a velocity  proportional  to  the  space 
from  rest,  or  to  the  time.  The  controversy  of  the  vis  viva  was  what  was 


Novum  Organum  Renovatum,  pp.  35-37. 


REQUISITES  OF  LANGUAGE. 


471 


the  proper  definition  of  the  measure  of  force.  A principal  question  in  the 
classification  of  minerals  is,  what  is  the  definition  of  a mineral  species. 
Physiologists  have  endeavored  to  throw  light  on  their  subject  by  defining 
organization , or  some  similar  term.”  Questions  of  the  same  nature  were 
long  open  and  are  not  yet  completely  closed,  respecting  the  definitions  of 
Specific  Heat,  Latent  Heat,  Chemical  Combination,  and  Solution. 

“ It  is  very  important  for  us  to  observe,  that  these  controversies  have 
never  been  questions  of  insulated  and  arbitrary  definitions,  as  men  seem 
often  tempted  to  imagine  them  to  have  been.  In  all  cases  there  is  a tacit 
assumption  of  some  proposition  which  is  to  be  expressed  by  means  of  the 
definition,  and  which  gives  it  its  importance.  The  dispute  concerning  the 
definition  thus  acquires  a real  value,  and  becomes  a question  concerning 
true  and  false.  Thus,  in  the  discussion  of  the  question,  What  is  a uniform 
force?’  it  was  taken  for  granted  that  gravity  is  a uniform  force.  In  the 
debate  of  the  vis  viva,  it  was  assumed  that  in  the  mutual  action  of  bodies 
the  whole  effect  of  the  force  is  unchanged.  In  the  zoological  definition  of 
species  (that  it  consists  of  individuals  which  have,  or  may  have,  sprung 
from  the  same  parents),  it  is  presumed  that  individuals  so  related  resemble 
each  other  more  than  those  which  are  excluded  by  such  a definition  ; or, 
perhaps,  that  species  so  defined  have  permanent  and  definite  differences. 
A "definition  of  organization,  or  of  some  other  term  which  was  not  employed 
to  express  some  principle,  would  be  of  no  value. 

“The  establishment,  therefore,  of  a right  definition  of  a term,  may  be  a 
useful  step  in  the  explication  of  our  conceptions;  but  this  will  be  the  case 
then  only  when  we'have  under  our  consideration  some  proposition  in  which 
the  term  is  employed.  For  then  the  question  really  is,  how  the  conception 
shall  be  understood  and  defined  in  order  that  the  proposition  may  be  true. 

“To  unfold  our  conceptions  by  means  of  definitions  has  never  been  serv- 
iceable to  science,  except  when  it  has  been  associated  with  an  immediate 
use  of  the  definitions.  The  endeavor  to  define  a Uniform  Force  was  com- 
bined with  the  assertion  that  gravity  is  a uniform  force;  the  attempt  to 
define  Accelerating  Force  was  immediately  followed  by  the  doctrine  that 
accelerating  forces  may  be  compounded;  the  process  of  defining  Momen- 
tum was  connected  with  the  principle  that  momenta  gained  and  lost  are 
equal ; naturalists  would  have  given  in  vain  the  definition  of  Species  which 
we  have  quoted,  if  they  had  not  also  given  the  characters  of  species  so  sepa- 
rated  Definition  may  be  the  best  mode  of  explaining  our  conception, 

but  that  which  alone  makes  it  worth  while  to  explain  it  in  any  mode,  is  the 
opportunity  of  using  it  in  the  expression  of  truth.  When  a definition  is 
propounded  to  us  as  a useful  step  in  knowledge,  we  are  always  entitled  to 
ask  what  principle  it  serves  to  enunciate.” 

In  giving,  then,  an  exact  connotation  to  the  phrase,  “a  uniform  force,” 
the  cbndition  was  understood,  that  the  phrase  should  continue  to  denote 
gravity.  The  discussion,  therefore,  respecting  the  definition,  resolved  itself 
into  this  question,  What  is  there  of  a uniform  nature  in  the  motions  pro- 
duced by  gravity?  By  observations  and  comparisons,  it  was  found  that 
what  was  uniform  in  those  motions  was  the  ratio  of  the  velocity  acquired 
to  the  time  elapsed;  equal  velocities  being  added  in  equal  times.  A uni- 
form force,  therefore,  was  defined  a force  which  adds  equal  .velocities  in 
equal  times  So,  again,  in  defining  momentum.  It  was  already  a received 
doctrine  that,  when  two  objects  impinge  upon  one  another,  the  momentum 
lost  by  the  one  is  equal  to  that  gained  by  the  other.  This  proposition  it 
was  deemed  necessary  to  preserve,  not  from  the  motive  (which  operates  in 


472 


OPERATIONS  SUBSIDIARY  TO  INDUCTION. 


many  other  cases)  that  it  was  firmly  fixed  in  popular  belief ; for  the  propo- 
sition in  question  had  never  been  heard  of  by  any  but  the  scientifically  in- 
structed. But  it  was  felt  to  contain  a truth  ; even  a superficial  observation 
of  the  phenomena  left  no  doubt  that  in  the  propagation  of  motion  from 
one  body  to  another,  there  was  something  of  which  the  one  body  gained 
precisely  what  the  other  lost;  and  the  word  momentum  had  been  invented 
to  express  this  unknown  something.  The  settlement,  therefore,  of  the  defi- 
nition of  momentum,  involved  the  determination  of  the  question,  What  is 
that  of  which  a body,  when  it  sets  another  body  in  motion,  loses  exactly 
as  much  as  it  communicates?  And  when  experiment  had  shown  that  this 
something  was  the  product  of  the  velocity  of  the  body  by  its  mass,  or  quan- 
tity of  matter,  this  became  the  definition  of  momentum. 

The  following  remarks,*  therefore,  are  perfectly  just:  “The  business  of 

definition  is  part  of  the  business  of  discovery To  define,  so  that  our 

definition  shall  have  any  scientific  value,  requires  no  small  portion  of  that 

sagacity  by  which  truth  is  detected When  it  has  been  clearly  seen 

what  ought  to  be  our  definition,  it  must  be  pretty  well  known  what  truth 
we  have  to  state.  The  definition,  as  well  as  the  discovery,  supposes  a de- 
cided step  in  our  knowledge  to  have  been  made.  The  writers  on  Logic, 
in  the  Middle  Ages,  made  Definition  the  last  stage  in  the  progress  of  knowl- 
edge ; and  in  this  arrangement  at  least,  the  history  of  science,  and  the  phi- 
losophy derived  from  the  history,  confirm  their  speculative  views.”  For 
in  order  to  judge  finally  how  the  name  which  denotes  a class  may  best  bo 
defined,  we  must  know  all  the  properties  common  to  the  class,  and  all  the 
relations  of  causation  or  dependence  among  those  properties. 

If  the  properties  which  are  fittest  to  be  selected  as  marks  of  other  com- 
mon properties  are  also  obvious  and  familiar,  and  especially  if  they  bear  a 
great  part  in  producing  that  general  air  of  resemblance  which  was  the 
original  inducement  to  the  formation  of  the  class,  the  definition  will  then 
be  most  felicitous.  But  it  is  often  necessary  to  define  the  class  by  some 
property  not  familiarly  known,  provided  that  property  be  the  best  mark  of 
those  which  are  known.  M.  De  Blainville,  for  instance,  founded  his  defini- 
tion of  life  on  the  process  of  decomposition  and  recomposition  which  in- 
cessantly takes  place  in  every  living  body,  so  that  the  particles  composing 
it  are  never  for  two  instants  the  same.  This  is  by  no  means  one  of  the 
most  obvious  properties  of  living  bodies ; it  might  escape  altogether  the 
notice  of  an  unscientific  observer.  Yet  great  authorities  (independently  of 
M.  De  Blainville,  who  is  himself  a first-rate  authority)  have  thought  that  no 
other  property  so  well  answers  the  conditions  required  for  the  definition. 

§ 5.  Having  laid  down  the  principles  which  ought  for  the  most  part  to 
be  observed  in  attempting  to  give  a precise  connotation  to  a term  in  use, 
I must  now  add,  that  it  is  not  always  practicable  to  adhere  to  those  princi- 
ples, and  that  even  when  practicable,  it  is  occasionally  not  desirable. 

Cases  in  which  it  is  impossible  to  comply  with  all  the  conditions  of  a 
precise  definition  of  a name  in  agreement  with  usage,  occur  very  frequent- 
ly. There  is  often  no  one  connotation  capable  of  being  given  to  a word, 
so  that  it  shall  still  denote  every  thing  it  is  accustomed  to  denote;  or  that 
all  the  propositions  into  which  it  is  accustomed  to  enter,  and  which  have 
any  foundation  in  truth,  shall  remain  true.  Independently  of  accidental 
ambiguities,  in  which  the  different  meanings  have  no  connection  with  one 


Novum  Organum  Renovatum,  pp.  39,  40. 


REQUISITES  OF  LANGUAGE. 


473 


another ; it  continually  happens  that  a word  is  used  in  two  or  more  senses 
derived  from  each  other,  but  yet  radically  distinct.  So  long  as  a term  is 
vague,  that  is,  so  long  as  its  connotation  is  not  ascertained  and  permanent- 
ly fixed,  it  is  constantly  liable  to  be  applied  by  extension  from  one  thing  tc 
another,  until  it  reaches  things  which  have  little,  or  even  no,  resemblance 
to  those  which  were  first  designated  by  it. 

“Suppose,”  says  Dugald  Stewart,  in  his  Philosophical  Essays * “that 
the  letters  A,  B,  C,  D,  E,  denote  a series  of  objects  ; that  A possesses  some 
one  quality  in  common  with  B ; B a quality  in  common  with  C ; C a qual- 
ity in  common  with  D ; D a quality  in  common  with  E ; while  at  the  same 
time,  no  quality  can  be  found  which  belongs  in  common  to  any  three  ob- 
jects in  the  series.  Is  it  not  conceivable,  that  the  affinity  between  A and  B 
may  produce  a transference  of  the  name  of  the  first  to  the  second;  and 
that,  in  consequence  of  the  other  affinities  which  connect  the  remaining  ob- 
jects together,  the  same  name  may  pass  in  succession  from  B to  C ; from 
C to  D ; and  from  D to  E?  In  this  manner,  a common  appellation  will 
arise  between  A and  E,  although  the  two  objects  may,  in  their  nature  and 
properties,  be  so  widely  distant  from  each  other,  that  no  stretch  of  im- 
agination can  conceive  how  the  thoughts  were  led  from  the  former  to  the 
latter.  The  transitions,  nevertheless,  may  have  been  all  so  easy  and  grad- 
ual, that,  were  they  successfully  detected  by  the  fortunate  ingenuity  of  a 
theorist,  we  should  instantly  recognize,  not  only  the  verisimilitude,  but  the 
truth  of  the  conjecture:  in  the  same  way  as  we  admit,  with  the  confidence 
of  intuitive  conviction,  the  certaiuty  of  the  well-known  etymological  process 
which  connects  the  Latin  preposition  e or  ex  with  the  English  substantive 
stranger , the  moment  that  the  intermediate  links  of  the  chain  are  submitted 
to  our  examination.”f 

The  applications  which  a word  acquires  by  this  gradual  extension  of  it 
from  one  set  of  objects  to  another,  Stewart,  adopting  an  expression  from 
Mr.  Payne  Knight,  calls  its  transitive  applications ; and  after  briefly  illustra- 
ting such  of  them  as  are  the  result  of  local  or  casual  associations,  he  pro- 
ceeds as  follows  :J 

“But  although  by  far  the  greater  part  of  the  transitive  or  derivative  ap- 
plications of  words  depend  on  casual  and  unaccountable  caprices  of  the 
feelings  or  the  fancy,  there  are  certain  cases  in  which  they  open  a very  in- 

* P.  217,  4to  edition. 

t “ E,  ex,  extra,  extranens,  etranger,  stranger.” 

Another  etymological  example  sometimes  cited  is  the  derivation  of  the  English  uncle  from 
the  Latin  avus.  It  is  scarcely  possible  for  two  words  to  bear  fewer  outward  marks,  of  rela- 
tionship, yet  there  is  but  one  step  between  them,  avus,  avunculus,  uncle.  So  pilgrim,  from 
ager : per  agrum , peragrinus,  peregrinus,  pellegrino,  pilgrim. 

Professor  Bain  gives  some  apt  examples  of  these  transitions  of  meaning.  “The  word 
‘damp’  primarily  signified  moist,  humid,  wet.  But  the  property  is  often  accompanied  with 
the  feeling  of  cold  or  chilliness,  and  hence  the  idea  of  cold  is  strongly  suggested  by  the  word. 
This  is  not  all.  Proceeding  upon  the  superadded  meaning,  we  speak  of  damping  a man’s 
ardor,  a metaphor  where  the  cooling  is  the  only  circumstance  concerned ; we  go  on  still  fur- 
ther to  designate  the  iron  slide  that  shuts  off  the  draft  of  a stove,  ‘the  damper,’  the  primary 
meaning  being  now  entirely  dropped.  ‘Dry,’  in  like  manner,  through  signifying  the  absence 
of  moisture,  water,  or  liquidity,  is  applied  to  sulphuric  acid  containing  water,  although  not 
thereby  ceasing  to  be  a moist,  wet,  or  liquid  substance.”  So  in  the  phrases,  dry  sherry,  or 
Champagne. 

“‘Street,’  originally  a paved  way,  with  or  without  houses,  has  been  extended  to  roads 
lined  with  houses,  whether  paved  or  unpaved.  ‘ Impertinent  ’ signified  at  first  irrelevant, 
alien  to  the  purpose  in  hand : through  which  it  has  come  to  mean,  meddling,  intrusive,  un- 
mannerly, insolent.”  {Logic,  ii. , 173,  174.) 

t Pp.  226,  227. 


OPERATIONS  SUBSIDIARY  TO  INDUCTION. 


474 

teresting  field  of  philosophical  speculation.  Such  are  those,  in  which  an 
analogous  transference  of  the  corresponding  term  may  be  remarked  uni- 
versally, or  very  generally,  in  other  languages ; and  in  which,  of  course,  the 
uniformity  of  the  result  must  be  ascribed  to  the  essential  principles  of  the 
human  frame.  Even  in  such  cases,  however,  it  will  by  no  means  be  always 
found,  on  examination,  that  the  various  applications  of  the  same  term  have 
arisen  from  any  common  quality  or  qualities  in  the  objects  to  which  they 
relate.  In  the  greater  number  of  instances,  they  may  be  traced  to  some 
natural  and  universal  associations  of  ideas,  founded  in  the  common  facul- 
ties, common  organs,  and  common  condition  of  the  human  race Ac- 

cording to  the  different  degrees  of  intimacy  and  strength  in  the  associa- 
tions on  which  the  transitions  of  language  arc  founded,  very  different  ef- 
fects may  be  expected  to  arise.  Where  the  association  is  slight  and  casu- 
al, the  several  meanings  will  remain  distinct  from  each  other,  and  will  often, 
in  process  of  time,  assume  the  appearance  of  capricious  varieties  in  the  use 
of  the  same  arbitrary  sign.  Where  the  association  is  so  natural  'and  ha- 
bitual as  to  become  virtually  indissoluble,  the  transitive  meanings  will  coa- 
lesce in  one  complex  conception;  and  every  new  transition  will  become  a 
more  comprehensive  generalization  of  the  term  in  question .” 

I solicit  particular  attention  to  the  law  of  mind  expressed  in  the  last  sen- 
tence, and  which  is  the  source  of  the  perplexity  so  often  experienced  in  de- 
tecting these  transitions  of  meaning.  Ignorance  of  that  law  is  the  shoal  on 
which  some  of  the  most  powerful  intellects  which  have  adorned  the  human 
race  have  been  stranded.  The  inquiries  of  Plato  into  the  definitions  of 
some  of  the  most  general  terms  of  moral  speculation  are  characterized  by 
Bacon  as  a far  nearer  approach  to  a true  inductive  method  than  is  else- 
where to  be  found  among  the  ancients,  and  are,  indeed,  almost  perfect  ex- 
amples of  the  preparatory  process  of  comparison  and  abstraction;  but, 
from  being  unaware  of  the  law  just  mentioned,  he  often  wasted  the  powers 
of  this  great  logical  instrument  on  inquiries  in  which  it  could  realize  no  re- 
sult, since  the  phenomena,  whose  common  properties  he  so  elaborately  en- 
deavored to  detect,  had  not  really  any  common  properties.  Bacon  himself 
fell  into  the  same  error  in  his  speculations  on  the  nature  of  heat,  in  which 
he  evidently  confounded  under  the  name  hot,  classes  of  phenomena  which 
have  no  property  in  common.  Stewart  certainly  overstates  the  matter 
when  he  speaks  of  “a prejudice  which  has  descended  to  modern  times  from 
the  scholastic  ages,  that  when  a word  admits  of  a variety  of  significations, 
these  different  significations  must  all  be  species  of  the  same  genus,  and 
must  consequently  include  some  essential  idea  common  to  every  individual 
to  which  the  generic  term  can  be  applied;”*  for  both  Aristotle  and  his 
followers  were  well  aware  that  there  are  such  things  as  ambiguities  of 
language,  and  delighted  in  distinguishing  them.  But  they  never  suspected 
ambiguity  in  the  cases  where  (as  Stewart  remarks)  the  association  on  which 
the  transition  of  meaning  was  founded  is  so  natural  and  habitual,  that  the 
two  meanings  blend  together  in  the  mind,  and  a real  transition  becomes  an 
apparent  generalization.  Accordingly  they  wasted  infinite  pains  in  endeav- 
oring to  find  a definition  which  would  serve  for  several  distinct  meanings 
at  once;  as  in  an  instance  noticed  by  Stewart  himself,  that  of  “causation; 
the  ambiguity  of  the  word  which,  in  the  Greek  language  corresponds  to 
the  English  word  cause,  having  suggested  to  them  the  vain  attempt  of  tra- 
cing the  common  idea  which,  in  the  case  of  any  effect,  belongs  to  the  effi- 


Essays,  p.  214. 


REQUISITES  OF  LANGUAGE. 


475 


c ient,  to  the  matter , to  the  form , and  to  the  end.  The  idle  generalities  ” 
(he  adds)  “ we  meet  with  in  other  philosophers,  about  the  ideas  of  the  good , 
the  fit,  and  the  becoming,  have  taken  their  rise  from  the  same  undue  influ- 
ence of  popular  epithets  on  the  speculations  of  the  learned.”* 

Among  the  words  which  have  undergone  so  many  successive  transitions 
of  meaning  that  every  trace  of  a property  common  to  all  the  things  they 
are  applied  to,  or  at  least  common  and  also  peculiar  to  those  things,  has 
been  lost,  Stewart  considers  the  word  Beautiful  to  be  one.  And  (without 
attempting  to  decide  a question  which  in  no  respect  belongs  to  logic)  I can 
not  but  feel,  with  him,  considerable  doubt  whether  the  word  beautiful  con- 
notes the  same  property  when  we  speak  of  a beautiful  color,  a beautiful 
face,  a beautiful  scene,  a beautiful  character,  and  a beautiful  poem.  The 
word  was  doubtless  extended  from  one  of  these  objects  to  another  on  ac- 
count of  a resemblance  between  them,  or,  more  probably,  between  the  emo- 
tions they  excited ; and,  by  this  progressive  extension,  it  has  at  last  reach- 
ed things  very  remote  from  those  objects  of  sight  to  which  there  is  no 
doubt  that  it  was  flrst  appropriated;  and  it  is  at  least  questionable  wheth- 
er there  is  now  any  property  common  to  all  the  things  which,  consistently 
with  usage,  may  be  called  beautiful,  except  the  property  of  agreeableness, 
which  the  term  certainly  does  connote,  but  which  can  not  be  all  that  people 
usually  intend  to  express  by  it,  since  there  are  many  agreeable  things  which 
are  never  called  beautiful.  If  such  be  the  case,  it  is  impossible  to  give  to 
the  word  Beautiful  any  fixed  connotation,  such  that  it  shall  denote  all  the 
objects  which  in  common  use  it  now  denotes,  but  no  others.  A fixed  con- 
notation, however,  it  ought  to  have;  for,  so  long  as  it  has  not,  it  is  unfit  to 
be  used  as  a scientific  term,  and  is  a perpetual  source  of  false  analogies  and 
erroneous  generalizations. 

This,  then,  constitutes  a case  in  exemplification  of  our  remark,  that  even 
when  there  is  a property  common  to  all  the  things  denoted  by  a name,  to 
erect  that  property  into  the  definition  and  exclusive  connotation  of  the  name 
is  not  always  desirable.  The  various  things  called  beautiful  unquestionably 
resemble  one  another  in  being  agreeable ; but  to  make  this  the  definition  of 
beauty,  and  so  extend  the  word  Beautiful  to  all  agreeable  things,  would  be 
to  drop  altogether  a portion  of  meaning  which  the  word  really,  though  in- 
distinctly, conveys,  and  to  do  what  depends  on  us  toward  causing  those 
qualities  of  the  objects  which  the  word  previously,  though  vaguely,  pointed 
at,  to  be  overlooked  and  forgotten.  It  is  better,  in  such  a case,  to  give  a 
fixed  connotation  to  the  term  by  restricting,  than  by  extending  its  use ; 
rather  excluding  from  the  epithet  Beautiful  some  things  to  which  it  is  com- 
monly considered  applicable,  than  leaving  out  of  its  connotation  any  of  the 
qualities  by  which,  though  occasionally  lost  sight  of,  the  general  mind  may 
have  been  habitually  guided  in  the  commonest  and  most  interesting  appli- 
cations of  the  term.  For  there  is  no  question  that  when  people  call  any 
thing  beautiful,  they  think  they  are  asserting  more  than  that  it  is  merely 
agreeable.  They  think  they  are  ascribing  a peculiar  sort  of  agreeableness, 
analogous  to  that  which  they  find  in  some  other  of  the  things  to  which  they 
are  accustomed  to  apply  the  same  name.  If,  therefore,  there  be  any  pe- 
culiar sort  of  agreeableness  which  is  common  though  not  to  all,  yet  to  the 
principal  things  which  are  called  beautiful,  it  is  better  to  limit  the  denota- 
tion of  the  term  to  those  things,  than  to  leave  that  kind  of  quality  without 
a term  to  connote  it,  and  thereby  divert  attention  from  its  peculiarities. 


Essays,  p.  215. 


■170 


OPERATIONS  SUBSIDIARY  TO  INDUCTION. 


§ G.  The  last  remark  exemplifies  a rule  of  terminology,  which  is  of  great 
importance,  and  which  has  hardly  yet  been  recognized  as  a rule,  but  by  a 
few  thinkers  of  the  present  century.  In  attempting  to  rectify  the  use  of  a 
vague  term  by  giving  it  a fixed  connotation,  we  must  take  care  not  to  dis- 
card (unless  advisedly,  and  on  the  ground  of  a deeper  knowledge  of  the 
subject)  any  portion  of  the  connotation  which  the  word,  in  however  indis- 
tinct a manner,  previously  carried  with  it.  For  otherwise  language  loses 
one  of  its  inherent  and  most  valuable  properties,  that  of  being  the  conser- 
vator of  ancient  experience ; the  keeper-alive  of  those  thoughts  and  obser- 
vations of  former  ages,  which  may  be  alien  to  the  tendencies  of  the  passing 
time.  This  function  of  language  is  so  often  overlooked  or  undervalued, 
that  a few  observations  on  it  appear  to  be  extremely  required. 

Even  when  the  connotation  of  a term  lias  been  accurately  fixed,  and  still 
more  if  it  lias  been  left  in  the  state  of  a vague  unanalyzed  feeling  of  resem- 
blance; there  is  a constant  tendency  in  the  word,  through  familiar  use,  to 
part  with  a portion  of  its  connotation.  It  is  a well-known  law  of  the  mind, 
that  a word  originally  associated  with  a very  complex  cluster  of  ideas,  is 
far  from  calling  up  all  those  ideas  in  the  mind,  every  time  the  word  is  used ; 
it  calls  up  only  one  or  two,  from  which  the  mind  runs  on  by  fresh  associa- 
tions to  another  set  of  ideas,  without  waiting  for  the  suggestion  of  the  re- 
mainder of  the  complex  cluster.  If  this  were  not  the  case,  processes  of 
thought  could  not  take  place  with  any  thing  like  the  rapidity  which  we 
know  they  possess.  Very  often,  indeed,  when  we  are  employing  a word  in 
our  mental  operations,  we  are  so  far  from  waiting  until  the  complex  idea 
which  corresponds  to  the  meaning  of  the  word  is  consciously  brought  be- 
fore us  in  all  its  parts,  that  we  run  on  to  new  trains  of  ideas  by  the  other 
associations  which  the  mere  word  excites,  without  having  realized  in  our 
imagination  any  part  whatever  of  the  meaning ; thus  using  the  word,  and 
even  using  it  well  and  accurately,  and  carrying  on  important  processes  of 
reasoning  by  means  of  it,  in  an  almost  mechanical  manner ; so  much  so, 
that  some  metaphysicians,  generalizing  from  an  extreme  case,  have  fancied 
that  all  reasoning  is  but  the  mechanical  use  of  a set  of  terms  according  to 
a certain  form.  We  may  discuss  and  settle  the  most  important  interests 
of  towns  or  nations,  by  the  application  of  general  theorems  or  practical 
maxims  previously  laid  down,  without  having  had  consciously  suggested  to 
us,  once  in  the  whole  process,  the  houses  and  green  fields,  the  thronged 
market-places  and  domestic  hearths,  of  which  not  only  those  towns  and  na- 
tions consist,  but  which  the  words  town  and  nation  confessedly  mean. 

Since,  then,  general  names  come  in  this  manner  to  be  used  (and  even  to 
do  a portion  of  their  work  well)  without  suggesting  to  the  mind  the  whole 
of  their  meaning,  and  often  with  the  suggestion  of  a very  small,  or  no  part 
at  all  of  that  meaning;  we  can  not  wonder  that  words  so  used  come  in  time 
to  be  no  longer  capable  of  suggesting  any  other  of  the  ideas  appropriated 
to  them,  than  those  with  which  the  association  is  most  immediate  and 
strongest,  or  most  kept  up  by  the  incidents  of  life ; the  remainder  being 
lost  altogether;  unless  the  mind,  by  often  consciously  dwelling  on  them, 
keeps  up  the  association.  Words  naturally  retain  much  more  of  their 
meaning  to  persons  of  active  imagination,  who  habitually  represent  to  them- 
selves things  in  the  concrete,  with  the  detail  which  belongs  to  them  in  the 
actual  world.  To  minds  of  a different  description,  the  only  antidote  to  this 
corruption  of  language  is  predication.  The  habit  of  predicating  of  the 
name,  all  the  various  properties  which  it  originally  connoted,  keeps  up  the 
association  between  the  name  and  those  properties. 


REQUISITES  OF  LANGUAGE. 


477 


But  in  order  that  it  may  do  so,  it  is  necessary  that  the  predicates  should 
themselves  retain  their  association  with  the  properties  which  they  several- 
ly connote.  For  the  propositions  can  not  keep  the  meaning  of  the  words 
alive,  if  the  meaning  of  the  propositions  themselves  should  die.  And  noth- 
ing is  more  common  than  for  propositions  to  be  mechanically  repeated, 
mechanically  retained  in  the  memory,  and  their  truth  undoubtingly  assented 
to  and  relied  on,  while  yet  they  carry  no  meaning  distinctly  home  to  the 
mind ; and  while  the  matter  of  fact  or  law  of  nature  which  they  originally 
expressed  is  as  much  lost  sight  of,  and  practically  disregarded,  as  if  it  never 
had  been  heard  of  at  all.  In  those  subjects  which  are  at  the  same  time 
familiar  and  complicated,  and  especially  in  those  which  are  so  in  as  great  a 
degree  as  moral  and  social  subjects  are,  it  is  a matter  of  common  remark 
how  many  important  propositions  are  believed  and  repeated  from  habit, 
while  no  account  could  be  given,  and  no  sense  is  practically  manifested,  of 
the  truths  which  they  convey.  Hence  it  is,  that  the  traditional  maxims  of 
old  experience,  though  seldom  questioned,  have  often  so  little  effect  on  the 
conduct  of  life ; because  their  meaning  is  never,  by  most  persons,  really  felt, 
until  personal  experience  has  brought  it  home.  And  thus  also  it  is  that  so 
many  doctrines  of  religion,  ethics,  and  even  politics,  so  full  of  meaning  and 
reality  to  first  converts,  have  manifested  (after  the  association  of  that  mean- 
ing with  the  verbal  formulas  has  ceased  to  be  kept  up  by  the  controversies 
which  accompanied  their  first  introduction)  a tendency  to  degenerate  rap- 
idly into  lifeless  dogmas ; which  tendency,  all  the  efforts  of  an  education 
expressly  and  skillfully  directed  to  keeping  the  meaning  alive,  are  barely 
sufficient  to  counteract. 

Considering,  then,  that  the  human  mind,  in  different  generations,  occu- 
pies itself  with  different  things,  and  in  one  age  is  led  by  the  circumstances 
which  surround  it  to  fix  more  of  its  attention  upon  one  of  the  properties 
of  a thing,  in  another  age  upon  another;  it  is  natural  and  inevitable  that 
in  every  age  a certain  portion  of  our  recorded  and  traditional  knowledge, 
not  being  continually  suggested  by  the  pursuits  and  inquiries  with  which 
mankind  are  at  that  time  engrossed,  should  fall  asleep,  as  it  were,  and  fade 
from  the  memory.  It  would  be  in  danger  of  being  totally  lost,  if  the  prop- 
ositions or  formulas,  the  results  of  the  previous  experience,  did  not  remain, 
as  forms  of  words  it  may  be,  but  of  words  that  once  really  conveyed,  and 
are  still  supposed  to  convey,  a meaning : which  meaning,  though  suspended, 
may  be  historically  traced,  and  when  suggested,  may  be  recognized  by 
minds  of  the  necessary  endowments  as  being  still  matter  of  fact,  or  truth. 
While  the  formulas  remain,  the  meaning  may  at  any  time  revive ; and  as, 
on  the  one  hand,  the  formulas  progressively  lose  the  meaning  they  were  in- 
tended to  convey,  so,  on  the  other,  when  this  forgetfulness  has  reached  its 
height  and  begun  to  produce  obvious  consequences,  minds  arise  which  from 
the  contemplation  of  the  formulas  rediscover  the  truth,  when  truth  it  was, 
which  was  contained  in  them,  and  announce  it  again  to  mankind,  not  as  a 
discovery,  but  as  the  meaning  of  that  which  they  have  been  taught,  and 
still  profess  to  believe. 

Thus  there  is  a perpetual  oscillation  in  spiritual  truths,  and  in  spiritual 
doctrines  of  any  significance,  even  when  not  truths.  Their  meaning  is 
almost  always  in  a process  either  of  being  lost  or  of  being  recovered. 
Whoever  has  attended  to  the  history  of  the  more  serious  convictions  of 
mankind — of  the  opinions  by  which  the  general  conduct  of  their  lives  is, 
or  as  they  conceive  ought  to  be,  more  especially  regulated — is  aware  that 
even  when  recognizing  verbally  the  same  doctrines,  they  attach  to  them  at 


47S 


OPERATIONS  SUBSIDIARY  TO  INDUCTION. 


different  periods  a greater  or  a less  quantity,  and  even  a different  kind  of 
meaning.  The  words  in  their  original  acceptation  connoted,  and  the  prop- 
ositions expressed,  a complication 'of  outward  facts  and  inward  feelings,  to 
different  portions  of  which  the  general  mind  is  more  particularly  alive  in  dif- 
ferent generations  of  mankind.  To  common  minds,  only  that  portion  of  the 
meaning  is  in  each  generation  suggested,  of  which  that  generation  possesses 
the  counterpart  in  its  own  habitual  experience.  But  the  words  and  prop- 
ositions lie  ready  to  suggest  to  any  mind  duly  prepared  the  remainder  of 
the  meaning.  Such  individual  minds  are  almost  always  to  be  found  ; and 
the  lost  meaning,  revived  by  them,  again  by  degrees  works  its  way  into  the 
general  mind. 

The  arrival  of  this  salutary  reaction  may,  however,  be  materially  retarded 
by  the  shallow  conceptions  and  incautious  proceedings  of  mere  logicians. 
It  sometimes  happens  that  toward  the  close  of  the  downward  period,  when 
the  words  have  lost  part  of  their  significance,  and  have  not  yet  begun  to 
recover  it,  persons  arise  whose  leading  and  favorite  idea  is  the  importance 
of  clear  conceptions  and  precise  thought,  and  the  necessity,  therefore,  of 
definite  language.  These  persons,  in  examining  the  old  formulas,  easily 
perceive  that  words  are  used  in  them  without  a meaning ; and  if  they  are 
not  the  sort  of  persons  who  are  capable  of  rediscovering  the  lost  significa- 
tion, they  naturally  enough  dismiss  the  formula,  and  define  the  name  with- 
out reference  to  it.  In  so  doing  they  fasten  down  the  name  to  what  it 
connotes  in  common  use  at  the  time  when  it  conveys  the  smallest  quantity 
of  meaning;  and  introduce  the  practice  of  employing  it,  consistently  and 
uniformly,  according  to  that  connotation.  The  word  in  this  way  acquires 
an  extent  of  denotation  far  beyond  what  it  had  before;  it  becomes  extend- 
ed to  many  things  to  which  it  was  previously,  in  appearance  capriciously, 
refused.  Of  the  propositions  in  which  it  was  formerly  used,  those  which 
were  true  in  virtue  of  the  forgotten  part  of  its  meaning  are  now,  by  the 
clearer  light  which  the  definition  diffuses,  seen  not  to  be  true  according  to 
the  definition ; which,  however,  is  the  recognized  and  sufficiently  correct 
expression  of  all  that  is  perceived  to  be  in  the  mind  of  any  one  by  whom 
the  term  is  used  at  the  present  day.  The  ancient  formulas  are  consequent- 
ly treated  as  prejudices ; and  people  are  no  longer  taught  as  before,  though 
not  to  understand  them,  yet  to  believe  that  there  is  truth  in  them.  They 
no  longer  remain  in  the  general  mind  surrounded  by  respect,  and  ready  at 
any  time  to  suggest  their  original  meaning.  Whatever  truths  they  contain 
are  not  only,  in  these  circumstances,  rediscovered  far  more  slowly,  but, 
when  rediscovered,  the  prejudice  with  which  novelties  are  regarded  is  now, 
in  some  degree  at  least,  against  them,  instead  of  being  on  their  side. 

An  example  may  make  these  remarks  more  intelligible.  In  all  ages,  ex- 
cept where  moral  speculation  has  been  silenced  by  outward  compulsion,  or 
where  the  feelings  which  prompt  to  it  still  continue  to  be  satisfied  by  the 
traditional  doctrines  of  an  established  faith,  one  of  the  subjects  which  have 
most  occupied  the  minds  of  thinking  persons  is  the  inquiry,  What  is  vir- 
tue? or,  What  is  a virtuous  character?  Among  the  different  theories  on 
the  subject  which  have,  at  different  times,  grown  up  aud  obtained  partial 
currency,  every  one  of  which  reflected  as  in  the  clearest  mirror  the  express 
image  of  the  age  which  gave  it  birth;  there  was  one,  according  to  which 
virtue  consists  in  a correct  calculation  of  our  own  personal  interests,  either 
in  this  world  only,  or  also  in  another.  To  make  this  theory  plausible,  it 
was  of  course  necessary  that  the  only  beneficial  actions  which  people  in 
general  were  accustomed  to  see,  or  were  therefore  accustomed  to  praise, 


REQUISITES  OF  LANGUAGE. 


479 


should  be  such  as  were,  or  at  least  might  without  contradicting  obvious 
facts  be  supposed  to  be,  the  result  of  a prudential  regard  to  self-interest; 
so  that  the  words  really  connoted  no  more,  in  common  acceptation,  than 
was  set  down  in  the  definition. 

Suppose,  now,  that  the  partisans  of  this  theory  had  contrived  to  introduce 
a consistent  and  undeviating  use  of  the  term  according  to  this  definition. 
Suppose  that  they  had  seriously  endeavored,  and  had  succeeded  in  the  en- 
deavor, to  banish  the  word  disinterestedness  from  the  language ; had  ob- 
tained the  disuse  of  all  expressions  attaching  odium  to  selfishness  or  com- 
mendation to  self-sacrifice,  or  which  implied  generosity  or  kindness  to  be 
any  thing  but  doing  a benefit  in  order  to  receive  a greater  personal  advan- 
tage in  return.  Need  we  say  that  this  abrogation  of  the  old  formulas  for 
the  sake  of  preserving  clear  ideas  and  consistency  of  thought,  would  have 
been  a great  evil?  while  the  very  inconsistency  incurred  by  the  co-exist- 
ence of  the  formulas  with  philosophical  opinions  which  seemed  to  condemn 
them  as  absurdities,  operated  as  a stimulus  to  the  re-examination  of  the 
subject  and  thus  the  very  doctrines  originating  in  the  oblivion  into  which 
a part  of  the  truth  had  fallen,  were  rendered  indirectly,  but  powerfully, 
instrumental  to  its  revival. 

The  doctrine  of  the  Coleridge  school,  that  the  language  of  any  people 
among  whom  culture  is  of  old  date,  is  a sacred  deposit,  the  property  of  all 
ages,  and  which  no  one  age  should  consider  itself  empowered  to  alter — 
borders  indeed,  as  thus  expressed,  on  an  extravagance  ; but  it  is  grounded 
on  a truth,  frequently  overlooked  by  that  class  of  logicians  who  think  more 
of  having  a clear  than  of  having  a comprehensive  meaning;  and  who  per- 
ceive that  every  age  is  adding  to  the  truths  which  it  has  received  from  its 
predecessors,  but  fail  to  see  that  a counter  process  of  losing  truths  al- 
ready possessed,  is  also  constantly  going  on,  and  requiring  the  most  sedu- 
lous attention  to  counteract  it.  Language  is  the  depository  of  the  accumu- 
lated body  of  experience  to  which  all  former  ages  have  contributed  their 
part,  and  which  is  the  inheritance  of  all  yet  to  come.  We  have  no  right  to 
prevent  ourselves  from  transmitting  to  posterity  a larger  portion  of  this 
inheritance  than  we  may  ourselves  have  profited  by.  However  much  we 
may  be  able  to  improve  on  the  conclusions  of  our  forefathers,  we  ought  to 
be  careful  not  inadvertently  to  let  any  of  their  premises  slip  through  our 
fingers.  It  may  be  good  to  alter  the  meaning  of  a Avord,  but  it  is  bad  to  let 
any  part  of  the  meaning  drop.  Whoever  seeks  to  introduce  a more  correct 
use  of  a term  with  Avhich  important  associations  are  connected,  should  be  re- 
quired to  possess  an  accurate  acquaintance  vvith  the  history  of  the  particular 
word,  and  of  the  opinions  which  in  different  stages  of  its  progress  it  seiwed 
to  express.  To  be  qualified  to  define  the  name,  Ave  must  knoAV  all  that  has 
ever  been  known  of  the  properties  of  the  class  of  objects  which  are,  or 
originally  were,  denoted  by  it.  For  if  Ave  give  it  a meaning  according  to 
Avhich  any  proposition  will  be  false  Avhich  has  ever  been  generally  held  to 
be  true,  it  is  incumbent  on  us  to  be  sure  that  Ave  knoAV  and  have  considered 
all  which  those  Avho  believed  the  proposition  understood  by  it. 


4S0 


OPERATIONS  SUBSIDIARY  TO  INDUCTION. 


CHAPTER  Y. 

ON  THE  NATURAL  HISTORY  OF  THE  VARIATIONS  IN  THE  MEANING  OF 

TERMS. 

§ 1.  It  is  not  only  in  the  mode  which  has  now  been  pointed  out,  namely 
by  gradual  inattention  to  a portion  of  the  ideas  conveyed,  that  words  in 
common  use  are  liable  to  shift  their  connotation.  The  truth  is,  that  the 
connotation  of  such  words  is  perpetually  varying ; as  might  be  expected 
from  the  manner  in  which  words  in  common  use  acquire  their  connotation. 
A technical  term,  invented  for  purposes  of  art  or  science,  has,  from  the  first, 
the  connotation  given  to  it  by  its  inventor;  but  a name  which  is  in  every 
one’s  mouth  before  any  one  thinks  of  defining  it,  derives  its  connotation 
only  from  the  circumstances  which  are  habitually  brought  to  mind  when  it 
is  pronounced.  Among  these  circumstances,  the  properties  common  to  the 
things  denoted  by  the  name,  have  naturally  a principal  place ; and  would 
have  the  sole  place,  if  language  were  regulated  by  convention  rather  than 
bv  custom  and  accident.  But  besides  these  common  properties,  which  if 
they  exist  are  certainly  present  whenever  the  name  is  employed,  any  other 
circumstance  may  casually  be  found  along  with  it,  so  frequently  as  to  be- 
come associated  with  it  in  the  same  manner,  and  as  strongly,  as  the  common 
properties  themselves.  In  proportion  as  this  association  forms  itself,  peo- 
ple give  up  using  the  name  in  cases  in  which  those  casual  circumstances  do 
not  exist.  They  prefer  using  some  other  name,  or  the  same  name  with 
some  adjunct,  rather  than  employ  an  expression  which  will  call  up  an  idea 
they  do  not  want  to  excite.  The  circumstance  originally  casual,  thus  be- 
comes regularly  a part  of  the  connotation  of  the  word. 

It  is  this  continual  incorporation  of  circumstances  originally  accident- 
al, into  the  permanent  signification  of  words,  which  is  the  cause  that  there 
are  so  few  exact  synonyms.  It  is  this  also  which  renders  the  dictionary 
meaning  of  a word,  by  universal  remark  so  imperfect  an  exponent  of  its 
real  meaning.  The  dictionary  meaning  is  marked  out  in  a broad,  blunt 
way,  and  probaby  includes  all  that  was  originally  necessary  for  the  correct 
employment  of  the  term  ; but  in  process  of  time  so  many  collateral  asso- 
ciations adhere  to  words,  that  whoever  should  attempt  to  use  them  with 
no  other  guide  than  the  dictionary,  would  confound  a thousand  nice  dis- 
tinctions and  subtle  shades  of  meaning  which  dictionaries  take  no  account 
of;  as  we  notice  in  the  use  of  a language  in  conversation  or  writing  by  a 
foreigner  not  thoroughly  master  of  it.  The  history  of  a word,  by  showing 
the  causes  which  determine  its  use,  is  in  these  cases  a better  guide  to  its 
employment  than  any  definition  ; for  definitions  can  only  show  its  meaning 
at  the  particular  time,  or  at  most  the  series  of  its  successive  meanings,  but 
its  history  may  show  the  law  by  which  the  succession  was  produced.  The 
word  gentleman , for  instance,  to  the  correct  employment  of  which  a dic- 
tionary would  be  no  guide,  originally  meant  simply  a man  born  in  a certain 
rank.  From  this  it  came  by  degrees  to  connote  all  such  qualities  or  ad- 
ventitious circumstances  as  were  usually  found  to  belong  to  persons  of  that 
rank.  This  consideration  at  once  explains  why  in  one  of  its  vulgar  accep- 
tations it  means  any  one  who  lives  without  labor,  in  another  without  man- 


VARIATIONS  IN  MEANING  OF  TERMS. 


481 


ual  labor,  and  in  its  more  elevated  signification  it  has  in  every  age  signified 
the  conduct,  character,  habits,  and  outward  appearance,  in  whomsoever 
found,  which,  according  to  the  ideas  of  that  age,  belonged  or  were  expect- 
ed to  belong  to  persons  born  and  educated  in  a high  social  position. 

It  continually  happens  that  of  two  words,  whose  dictionary  meanings 
are  either  the  same  or  very  slightly  different,  one  will  be  the  proper  word 
to  use  in  one  set  of  circumstances,  another  in  another,  without  its  being 
possible  to  show  how  the  custom  of  so  employing  them  originally  grew  up. 
The  accident  that  one  of  the  words  was  used  and  not  the  other  on  a par- 
ticular occasion  or  in  a particular  social  circle,  will  be  sufficient  to  produce 
so  strong  an  association  between  the  word  and  some  specialty  of  circum- 
stances, that  mankind  abandon  the  use  of  it  in  any  other  case,  and  the 
specialty  becomes  part  of  its  signification.  The  tide  of  custom  first  drifts 
the  word  on  the  shore  of  a particular  meaning,  then  retires  and  leaves  it 
there. 

An  instance  in  point  is  the  remarkable  change  which,  in  the  English  lan- 
guage at  least,  has  taken  place  in  the  signification  of  the  word  loyalty. 
That  word  originally  meant  in  English,  as  it  still  means  in  the  language 
from  whence  it  came,  fair,  open  dealing,  and  fidelity  to  engagements ; in 
that  sense  the  quality  it  expressed  was  part  of  the  ideal  chivalrous  or 
knightly  character.  By  what  process,  in  England,  the  term  became  re- 
stricted to  the  single  case  of  fidelity  to  the  throne,  I am  not  sufficiently 
versed  in  the  history  of  courtly  language  to  be  able  to  pronounce.  The 
interval  between  a loyal  chevalier  and  a loyal  subject  is  certainly  great. 
I can  only  suppose  that  the  word  was,  at  some  period,  the  favorite  term  at 
court  to  express  fidelity  to  the  oath  of  allegiance ; until  at  length  those  who 
wished  to  speak  of  any  other,  and  as  it  was  probably  deemed,  inferior  sort 
of  fidelity,  either  did  not  venture  to  use  so  dignified  a term,  or  found  it 
convenient  to  employ  some  other  in  order  to  avoid  being  misunderstood. 

§ 2.  Cases  are  not  unfrequent  in  which  a circumstance,  at  first  casually 
incorporated  into  the  connotation  of  a word  which  originally  had  no  refer- 
ence to  it,  in  time  wTholly  supersedes  the  original  meaning,  and  becomes 
not  merely  a part  of  the  connotation,  but  the  whole  of  it.  This  is  exem- 
plified in  the  word  pagan, paganus;  which  originally,  as  its  etymology  im- 
ports, was  equivalent  to  villager ; the  inhabitant  of  a pagus , or  village. 
At  a particular  era  in  the  extension  of  Christianity  over  the  Roman  em- 
pire, the  adherents  of  the  old  religion,  and  the  villagers  or  country  people, 
were  nearly  the  same  body  of  individuals,  the  inhabitants  of  the  towns  hav- 
ing been  earliest  converted ; as  in  our  own  day,  and  at  all  times,  the  great- 
er activity  of  social  intercourse  renders  them  the  earliest  recipients  of  new 
opinions  and  modes,  while  old  habits  and  prejudices  linger  longest  among 
the  country  people ; not  to  mention  that  the  towns  were  more  immediate- 
ly under  the  direct  influence  of  the  Government,  which  at  that  time  had 
embraced  Christianity.  From  this  casual  coincidence,  the  word  2:)aQanus 
carried  with  it,  and  began  more  and  more  steadily  to  suggest,  the  idea  of 
a worshiper  of  the  ancient  divinities ; until  at  length  it  suggested  that 
idea  so  forcibly  that  people  who  did  not  desire  to  suggest  the  idea  avoided 
using  the  word.  But  when  joagamts  had  come  to  connote  heathenism,  the 
very  unimportant  circumstance,  with  reference  to  that  fact,  of  the  place  of 
residence,  was  soon  disregarded  in  the  employment  of  the  word.  As  there 
■ was  seldom  any  occasion  for  making  separate  assertions  respecting  hea- 
thens who  lived  in  the  country,  there  was  no  need  for  a separate  word  to 

31 


4S2 


OPERATIONS  SUBSIDIARY  TO  INDUCTION. 


denote  them;  and  pagan  came  not  only  to  mean  heathen, but  to  mean  that 
exclusively. 

A case  still  more  familiar  to  most  readers  is  that  of  the  word  villain  or 
villein.  This  term,  as  every  body  knows,  had  in  the  Middle  Ages  a conno- 
tation as  strictly  defined,  as  a word  could  have,  being  the  proper  legal  des- 
ignation for  those  persons  who  were  the  subjects  of  the  less  onerous  forms 
of  feudal  bondage.  The  scorn  of  the  semi-barbarous  military  aristocracy 
for  these  their  abject  dependants,  rendered  the  act  of  likening  any  person 
to  this  class  of  people  a mark  of  the  greatest  contumely;  the  same  scorn 
led  them  to  ascribe  to  the  same  people  all  manner  of  hateful  qualities,  which 
doubtless  also,  in  the  degrading  situation  in  which  they  were  held,  were 
often  not  unjustly  imputed  to  them.  These  circumstances  combined  to  at- 
tach to  the  term  villain  ideas  of  crime  and  guilt,  in  so  forcible  a manner 
that  the  application  of  the  epithet  even  to  those  to  whom  it  legally  belong- 
ed became  an  affront,  and  was  abstained  from  whenever  no  affront  was  in- 
tended. From  that  time  guilt  was  part  of  the  connotation;  and  soon  be- 
came the  whole  of  it,  since  mankind  were  not  prompted  by  any  urgent  mo- 
tive to  continue  making  a distinction  in  their  language  between  bad  men 
of  servile  station  and  bad  men  of  any  other  rank  in  life. 

These  and  similar  instances  in  which  the  original  signification  of  a term 
is  totally  lost — another  and  an  entirely  distinct  meaning  being  first  ingraft- 
ed upon  the  former,  and  finally  substituted  for  it — afford  examples  of  the 
double  movement  which  is  always  taking  place  in  language:  two  counter- 
movements,  one  of  Generalization,  by  which  words  are  perpetually  losing 
portions  of  their  connotation,  and  becoming  of  less  meaning  and  more  gen- 
eral acceptation ; the  other  of  Specialization,  by  which  other,  or  even  these 
same  words,  are  continually  taking  on  fresh  connotation ; acquiring  addi- 
tional meaning  by  being  restricted  in  their  employment  to  a part  only  of 
the  occasions  on  which  they  might  properly  be  used  before.  This  double 
movement  is  of  sufficient  importance  in  the  natural  history  of  language 
(to  which  natural  history  the  artificial  modifications  ought  always  to  have 
some  degree  of  reference),  to  justify  our  dwelling  a little  longer  on  the 
nature  of  the  twofold  phenomenon,  and  the  causes  to  which  it  owes  its 
existence. 

§ 3.  To  begin  with  the  movement  of  generalization.  It  might  seem  un- 
necessary to  dwell  on  the  changes  in  the  meaning  of  names  which  take 
place  merely  from  their  being  used  ignorantly,  by  persons  who,  not  having 
properly  mastered  the  received  connotation  of  a word,  apply  it  in  a looser 
and  wider  sense  than  belongs  to  it.  This,  however,  is  a real  source  of  al- 
terations in  the  language ; for  when  a word,  from  being  often  employed  in 
cases  where  one  of  the  qualities  which  it  connotes  does  not  exist,  ceases  to 
suggest  that  quality  with  certainty,  then  even  those  who  are  under  no  mis- 
take as  to  the  proper  meaning  of  the  word,  prefer  expressing  that  meaning 
in  some  other  way,  and  leave  the  original  word  to  its  fate.  The  word 
’Squire,  as  standing  for  an  owner  of  a landed  estate;  Parson,  as  denoting 
not  the  rector  of  the  parish,  but  clergymen  in  general ; Artist,  to  denote 
only  a painter  or  sculptor;  are  cases  in  point.  Such  cases  give  a clear  in- 
sight into  the  process  of  the  degeneration  of  languages  in  periods  of  his- 
tory when  literary  culture  was  suspended;  and  we  are  now  in  danger  of 
experiencing  a similar  evil  through  the  superficial  extension  of  the  same 
culture.  So  many  persons  without  any  thing  deserving  the  name  of  edu- 
cation have  become  writers  by  profession,  that  written  language  may  al- 


VARIATIONS  IN  MEANING  OF  TERMS. 


483 


most  be  said  to  be  principally  wielded  by  persons  ignorant  of  the  proper 
use  of  the  instrument,  and  who  are  spoiling  it  more  and  more  for  those 
who  understand  it.  Vulgarisms,  which  creep  in  nobody  knows  how,  are 
daily  depriving  the  English  language  of  valuable  modes  of  expressing 
thought.  To  take  a present  instance:  the  verb  transpire  formerly  con- 
veyed very  expressively  its  correct  meaning,  viz.,  to  become  known  through 
unnoticed  channels — to  exhale,  as  it  were,  into  publicity  through  invisible 
pores,  like  a vapor  or  gas  disengaging  itself.  But  of  late  a practice  has 
commenced  of  employing  this  word,  for  the  sake  of  finery,  as  a mere  syno- 
nym of  to  happen : “the  events  which  have  transpired  in  the  Crimea,” 
meaning  the  incidents  of  the  war.  This  vile  specimen  of  bad  English  is 
already  seen  in  the  dispatches  of  noblemen  and  viceroys ; and  the  time  is 
apparently  not  far  distant  when  nobody  will  understand  the  word  if  used 
in  its  proper  sense.  In  other  cases  it  is  not  the  love  of  finery,  but  simple 
want  of  education,  which  makes  writers  employ  words  in  senses  unknown 
to  genuine  English.  The  use  of  “ aggravating”  for  “provoking,”  in  my 
boyhood  a vulgarism  of  the  nursery,  has  crept  into  almost  all  newspapers, 
and  into  many  books ; and  when  the  word  is  used  in  its  proper  sense,  as 
when  writers  on  criminal  law  speak  of  aggravating  and  extenuating  cir- 
cumstances, their  meaning,  it  is  probable,  is  already  misunderstood.  It  is 
a great  error  to  think  that  these  corruptions  of  language  do  no  harm. 
Those  who  are  struggling  with  the  difficulty  (and  who  know  by  experience 
how  great  it  already  is)  of  expressing  one’s  self  clearly  with  precision,  find 
their  resources  continually  narrowed  by  illiterate  writers,  who  seize  and 
twist  from  its  purpose  some  form  of  speech  which  once  served  to  convey 
briefly  and  compactly  an  unambiguous  meaning.  It  would  hardly  be  be- 
lieved how  often  a writer  is  compelled  to  a circumlocution  by  the  single 
vulgarism,  introduced  during  the  last  few  years,  of  using  the  word  alone 
as  an  abverb,  only  not  being  fine  enough  for  the  rhetoric  of  ambitious  ig- 
norance. A man  will  say  “ to  which  I am  not  alone  bound  by  honor  but 
also  by  law,”  unaware  that  what  he  has  unintentionally  said  is,  that  he  is 
not  alone  bound,  some  other  person  being  bound  with  him.  Formerly,  if 
any  one  said,  “ I am  not  alone  responsible  for  this,”  he  was  understood  to 
mean  (what  alone  his  words  mean  in  correct  English),  that  he  is  not  the 
sole  person  responsible;  but  if  he  now  used  such  an  expression,  the  reader 
would  be  confused  between  that  and  two  other  meanings : that  he  is  not 
only  responsible  but  something  more ; or  that  he  is  responsible  not  only 
for  this  but  for  something  besides.  The  time  is  coming  when  Tennyson’s 
CEnone  could  not  say,  “ I will  not  die  alone,”  lest  she  should  be  supposed 
to  mean  that  she  would  not  only  die  but  do  something  else. 

The  blunder  of  writing  predicate  for  predict  has  become  so  widely  dif- 
fused that  it  bids  fair  to  render  one  of  the  most  useful  terms  in  the  sci- 
entific vocabulary  of  Logic  unintelligible.  The  mathematical  and  logical 
term  “ to  eliminate  ” is  undergoing  a similar  destruction.  All  who  are  ac- 
quainted either  with  the  proper  use  of  the  word  or  with  its  etymology 
know  that  to  eliminate  a thing  is  to  thrust  it  out:  but  those  who  know 
nothing  about  it,  except  that  it  is  a fine-looking  phrase,  use  it  in  a sense 
precisely  the  reverse,  to  denote,  not  turning  any  thing  out,  but  bringing  it 
in.  They  talk  of  eliminating  some  truth,  or  other  useful  result,  from  a 
mass  of  details.*  A similar  permanent  deterioration  in  the  language  is 

* Though  no  such  evil  consequences  ns  take  place  in  these  instances  are  likely  to  arise  from 
the  modern  freak  of  writing  sanatory  instead  of  sanitary,  it  deserves  notice  as  a charming 
specimen  of  pedantry  ingrafted  upon  ignorance.  Those  who  thus  undertake  to  correct  the 


484 


OPERATIONS  SUBSIDIARY  TO  INDUCTION. 


in  danger  of  being  produced  by  the  blunders  of  translators.  The  writers 
of  telegrams,  and  the  foreign  correspondents  of  newspapers,  have  gone  on 
so  long  translating  demander  by  “ to  demand,”  without  a suspicion  that  it 
means  only  to  ask,  that  (the  context  generally  showing  that  nothing  else 
is  meant)  English  readers  are  gradually  associating  the  English  word  de- 
mand with  simple  asking,  thus  leaving  the  language  without  a term  to 
express  a demand  in  its  proper  sense.  In  like  manner,  “ transaction,”  the 
French  word  for  a compromise,  is  translated  into  the  English  word  trans- 
action ; while,  curiously  enough,  the  inverse  change  is  taking  place  in 
France,  where  the  word  “ compromis  ” has  lately  begun  to  be  used  for  ex- 
pressing the  same  idea.  If  this  continues,  the  two  countries  will  have  ex- 
changed phrases. 

Independently,  however,  of  the  generalization  of  names  through  then- 
ignorant  misuse,  there  is  a tendency  in  the  same  direction  consistently 
with  a perfect  knowledge  of  their  meaning;  arising  from  the  fact,  that  the 
number  of  things  known  to  us,  and  of  which  we  feel  a desire  to  speak, 
multiply  faster  than  the  names  for  them.  Except  on  subjects  for  which 
there  has  been  constructed  a scientific  terminology,  with  which  unscientific 
persons  do  not  meddle,  great  difficulty  is  generally  found  in  bringing  a 
new  name  into  use  ; and  independently  of  that  difficulty,  it  is  natural  to 
prefer  giving  to  a new  object  a name  which  at  least  expresses  its  resem- 
blance to  something  already  known,  since  by  predicating  of  it  a name  en- 
tirely new  we  at  first  convey  no  information.  In  this  manner  the  name  of 
a species  often  becomes  the  name  of  a genus ; as  salt,  for  example,  or  oil; 
the  former  of  which  words  originally  denoted  only  the  muriate  of  soda, 
the  latter,  as  its  etymology  indicates,  only  olive-oil;  but  which  now  de- 
note large  and  diversified  classes  of  substances  resembling  these  in  some 
of  their  qualities,  and  connote  only  those  common  qualities,  instead  of 
the  whole  of  the  distinctive  properties  of  olive-oil  and  sea-salt.  The  words 
glass  and  soap  are  used  by  modern  chemists  in  a similar  manner,  to  denote 
genera  of  which  the  substances  vulgarly  so  called  are  single  species.  And 
it  often  happens,  as  in  those  instances,  that  the  term  keeps  its  special  sig- 
nification in  addition  to  its  more  general  one,  and  becomes  ambiguous,  that 
is,  two  names  instead  of  one. 

These  changes,  by  which  words  in  ordinary  use  become  more  and  more 
generalized,  and  less  and  less  expressive,  take  place  in  a still  greater  degree 
with  the  words  which  express  the  complicated  phenomena  of  mind  and  so- 
ciety. Historians,  travelers,  and  in  general  those  who  speak  or  write  con- 
cerning moral  and  social  phenomena  with  which  they  are  not  familiarly  ac- 
quainted, are  the  great  agents  in  this  modification  of  language.  The  vo- 
cabulary of  all  except  unusually  instructed  as  well  as  thinking  persons,  is, 
on  such  subjects,  eminently  scanty.  They  have  a certain  small  set  of  words 
to  which  they  are  accustomed,  and  which  they  employ  to  express  phenom- 
ena the  most  heterogeneous,  because  they  have  never  sufficiently  analyzed 
the  facts  to  which  those  words  correspond  in  their  own  country,  to  have 
attached  perfectly  definite  ideas  to  the  words.  The  first  English  conquer- 
ors of  Bengal,  for  example,  carried  with  them  the  phrase  landed  proprietor 
into  a country  where  the  rights  of  individuals  over  the  soil  were  extremely 
different  in  degree,  and  even  in  nature,  from  those  recognized  in  England. 
Applying  the  term  with  all  its  English  associations  in  such  a state  ot 

spelling  of  the  classical  English  writers,  are  not  aware  that  the  meaning  of  sanatory,  if  there 
were  such  a word  in  the  language,  would  have  reference  not  to  the  preservation  of  health,  but 
to  the  cure  of  disease. 


VARIATIONS  IN  MEANING  OF  TERMS. 


485 


things;  to  one  who  had  only  a limited  right  they  gave  an  absolute  right, 
from  another  because  he  had  not  an  absolute  right  they  took  away  all 
right,  drove  whole  classes  of  people  to  ruin  and  despair,  filled  the  country 
with  banditti,  created  a feeling  that  nothing  was  secure,  and  produced,  with 
the  best  intentions,  a disorganization  of  society  which  had  not  been  pro- 
duced in  that  country  by  the  most  ruthless  of  its  barbarian  invaders.  Yet 
the  usage  of  persons  capable  of  so  gross  a misapprehension  determines  the 
meaning  of  language ; and  the  words  they  thus  misuse  grow  in  generality, 
until  the  instructed  are  obliged  to  acquiesce;  and  to  employ  those  words 
(first  freeing  them  from  vagueness  by  giving  them  a definite  connotation) 
as  generic  terms,  subdividing  the  genera  into  species. 

§ 4.  While  the  more  rapid  growth  of  ideas  than  of  names  thus  creates  a 
perpetual  necessity  for  making  the  same  names  serve,  even  if  imperfect- 
ly, on  a greater  number  of  occasions ; a counter-operation  is  going  on,  by 
which  names  become  on  the  contrary  restricted  to  fewer  occasions,  by  tak- 
ing on,  as  it  were,  additional  connotation,  from  circumstances  not  originally 
included  in  the  meaning,  but  which  have  become  connected  with  it  in  the 
mind  by  some  accidental  cause.  We  have  seen  above,  in  the  words  pagan 
and  villain , remarkable  examples  of  the  specialization  of  the  meaning  of 
words  from  casual  associations,  as  well  as  of  the  generalization  of  it  in  a 
new  direction,  which  often  follows. 

Similar  specializations  are  of  frequent  occurrence  in  the  history  even  of 
scientific  nomenclature.  “It  is  by  no  means  uncommon,”  says  Dr.  Paris, 
in  his  Pharmacoloc/ia  * “to  find  a word  which  is  used  to  express  general 
characters  subsequently  become  the  name  of  a specific  substance  in  which 
such  characters  are  predominant ; and  we  shall  find  that  some  important 
anomalies  in  nomenclature  may  be  thus  explained.  The  term  A paeviKov, 
from  which  the  word  Arsenic  is  derived,  was  an  ancient  epithet  applied  to 
those  natural  substances  which  possessed  strong  and  acrimonious  proper- 
ties ; and  as  the  poisonous  quality  of  arsenic  was  found  to  be  remarkably 
powerful,  the  term  was  especially  applied  to  Orpiment,  the  form  in  which 
this  metal  most  usually  occurred.  So  the  term  Verbena  (quasi  Herbena ) 
originally  denoted  all  those  herbs  that  were  held  sacred  on  account  of  their 
being  employed  in  the  rites  of  sacrifice,  as  we  learn  from  the  poets ; but  as 
one  herb  was  usually  adopted  upon  these  occasions,  the  word  Verbena  came 
to  denote  that  particular  herb  only , and  it  is  transmitted  to  us  to  this  day 
under  the  same  title,  viz., Verbena  or  Vervain,  and  indeed  until  lately  it  en- 
joyed the  medical  reputation  which  its  sacred  origin  conferred  upon  it,  for 
it  was  worn  suspended  around  the  neck  as  an  amulet.  Vitriol,  in  the  orig- 
inal application  of  the  word,  denoted  any  crystalline  body  with  a certain 
degree  of  transparency  ( vitrimi ) ; it  is  hardly  necessary  to  observe  that  the 
term  is  now  appropriated  to  a particular  species : in  the  same  manner, 
Bark,  which  is  a general  term,  is  applied  to  express  one  genus,  and  by  way 
of  eminence  it  has  the  article  The  prefixed,  as  The  bark ; the  same  obser- 
vation will  apply  to  the  word  Opium,  which,  in  its  primitive  sense,  signifies 
any  juice  (throe,  Succas),  while  it  now  only  denotes  one  species,  viz.,  that  of 
the  poppy.  So,  again,  Elaterium  w'as  used  by  Hippocrates  to  signify  vari- 
ous internal  applications,  especially  purgatives,  of  a violent  and  drastic  na- 
ture (from  the  word  i\avv u,  agito,  moveo,  stimulo),  but  by  succeeding  au- 
thors it  was  exclusively  applied  to  denote  the  active  matter  which  subsides 


* Historical  Introduction,  vol.  i.,  pp.  66-68. 


4S6 


OPERATIONS  SUBSIDIARY  TO  INDUCTION. 


from  the  juice  of  the  wild  cucumber.  The  word  Fecula,  again,  originally 
meant  to  imply  any  substance  which  was  derived  by  spontaneous  subsid- 
ence from  a liquid  (from  fee x,  the  grounds  or  settlement  of  any  liquor) ; 
afterward  it  was  applied  to  Starch,  which  is  deposited  in  this  manner  by 
agitating  the  flour  of  wheat  in  water;  and,  lastly,  it  has  been  applied  to  a 
peculiar  vegetable  principle,  which,  like  starch,  is  insoluble  in  cold,  but  com- 
pletely soluble  in  boiling  water,  with  which  it  forms  a gelatinous  solution. 
This  indefinite  meaning  of  the  word  fecula  has  created  numerous  mistakes 
in  pharmaceutic  chemistry;  Elaterium,  for  instance,  is  said  to  be  fecula, 
and,  in  the  original  sense  of  the  word,  it  is  properly  so  called,  inasmuch  as 
it  is  procured  from  a vegetable  juice  by  spontaneous  subsidence,  but  in  the 
limited  and  modern  acceptation  of  the  term  it  conveys  an  erroneous  idea; 
for  instead  of  the  active  principle  of  the  juice  residing  in  fecula , it  is  a pe- 
culiar proximate  principle,  sui  generis,  to  which  I have  ventured  to  bestow 
the  name  of  Elatin.  For  the  same  reason,  much  doubt  and  obscurity  in- 
volve the  meaning  of  the  word  Extract,  because  it  is  applied  generally  to 
any  substance  obtained  by  the  evaporation  of  a vegetable  solution,  and 
specifically  to  a peculiar  proximate  principle,  possessed  of  certain  charac- 
ters, by  which  it  is  distinguished  from  every  other  elementary  body.” 

A generic  term  is  always  liable  to  become  thus  limited  to  a single  spe- 
cies, or  even  individual,  if  people  have  occasion  to  think  and  speak  of  that 
individual  or  species  much  oftener  than  of  any  thing  else  which  is  contain- 
ed in  the  genus.  Thus  by  cattle,  a stage-coachman  will  understand  horses; 
beasts,  in  the  language  of  agriculturists,  stands  for  oxen ; and  birds,  with 
some  sportsmen,  for  partridges  only.  The  law  of  language  which  operates 
in  these  trivial  instances  is  the  very  same  in  conformity  to  which  the  terms 
Qeog,  Deus,  and  God,  were  adopted  from  Polytheism  by  Christianity,  to  ex- 
press the  single  object  of  its  own  adoration.  Almost  all  the  terminology 
of  the  Christian  Church  is  made  up  of  words  originally  used  in  a much 
more  general  acceptation : Ecclesia,  Assembly;  Bishop,  Episcopus, Overseer ; 
Priest,  Presbyter,  Elder;  Deacon,  Diaconus,  Administrator  ; Sacrament,  a 
vow  of  allegiance ; Evangelium,  good  tidings  ; and  some  words,  as  Minister, 
are  still  used  both  in  the  general  and  in  the  limited  sense.  It  would  be  in- 
teresting to  trace  the  progress  by  which  author  came,  in  its  most  familiar 
sense,  to  signify  a writer,  and  noirjT^g,  or  maker,  a poet. 

Of  the  incorporation  into  the  meaning  of  a term,  of  circumstances  acci- 
dentally connected  with  it  at  some  particular  period,  as  in  the  case  of  Pa- 
gan, instances  might  easily  be  multiplied.  Physician  or  natural- 

ist) became,  in  England,  synonymous  with  a healer  of  diseases,  because 
until  a comparatively  late  period  medical  practitioners  were  the  only  natu- 
ralists. Clerc,  or  clericus,  a scholar,  came  to  signify  an  ecclesiastic,  because 
the  clergy  were  for  many  centuries  the  only  scholars. 

Of  all  ideas,  however,  the  most  liable  to  cling  by  association  to  any  thing 
with  which  they  have  ever  been  connected  by  proximity,  are  those  of  our 
pleasures  and  pains,  or  of  the  things  which  we  habitually  contemplate  as 
sources  of  our  pleasures  or  pains.  The  additional  connotation,  therefore, 
which  a word  soonest  and  most  readily  takes  on,  is  that  of  agreeableness 
or  painfulness,  in  their  various  kinds  and  degrees ; of  being  a good  or  bad 
tiling ; desirable  or  to  be  avoided  ; an  object  of  hatred,  of  dread,  contempt, 
admiration,  hope,  or  love.  Accordingly  there  is  hardly  a single  name,  ex- 
pressive of  any  moral  or  social  fact  calculated  to  call  forth  strong  affections 
either  of  a favorable  or  of  a hostile  nature,  which  does  not  carry  with  it  de- 
cidedly and  irresistibly  a connotation  of  those  strong  affections,  or,  at  the 


TERMINOLOGY  AND  NOMENCLATURE. 


487 


least, 'of  approbation  or  censure ; insomuch  that  to  employ  those  names  in 
conjunction  with  others  by  which  the  contrary  sentiments  were  expressed, 
would  produce  the  effect  of  a paradox,  or  even  a contradiction  in  terms. 
The  baneful  influence  of  a connotation  thus  acquired,  on  the  prevailing  hab- 
its of  thought,  especially  in  morals  and  politics,  has  been  well  pointed  out 
on  many  occasions  by  Bentham.  It  gives  rise  to  the  fallacy  of  “ question-beg- 
ging names.”  The  very  property  which  we  are  inquiring  whether  a thing 
possesses  or  not,  has  become  so  associated  with  the  name  of  the  thing  as  to 
be  pait  of  its  meaning,  insomuch  that  by  merely  uttering  the  name  we  as- 
sume the  point  which  was  to  be  made  out ; o»'e  of  the  most  frequent  sources 
of  apparently  self-evident  propositions. 

Without  any  further  multiplication  of  examples  to  illustrate  the  changes 
which  usage  is  continually  making  in  the  signification  of  terms,  I shall  add, 
as  a practical  rule,  that  the  logician,  not  being  able  to  prevent  such  transfor- 
mations, should  submit  to  them  with  a good  grace  when  they  are  irrevocably 
effected,  and  if  a definition  is  necessary,  define  the  word  according  to  its  new 
meaning;  retaining  the  former  as  a second  signification,  if  it  is  needed,  and 
if  there  is  any  chance  of  being  able  to  preserve  it  either  in  the  language  of 
philosophy  or  in  common  use.  Logicians  can  not  malce  the  meaning  of  any 
but  scientific  terms ; that  of  all  other  words  is  made  by  the  collective  hu- 
man race.  But  logicians  can  ascertain  clearly  what  it  is  which,  working 
obscurely,  has  guided  the  general  mind  to  a particular  employment  of  a 
name;  and  when  they  have  found  this,  they  can  clothe  it  in  such  distinct 
and  permanent  terms,  that  mankind  shall  see  the  meaning  which  before 
they  only  felt,  and  shall  not  suffer  it  to  be  afterward  forgotten  or  misappre- 
hended. 


CHAPTER  YI. 

THE  PRINCIPLES  OF  A PHILOSOPHICAL  LANGUAGE  FURTHER  CONSIDERED. 

§ 1.  We  have,  thus  far,  considered  only  one  of  the  requisites  of  a lan- 
guage adapted  for  the  investigation  of  truth ; that  its  terms  shall  each  of 
them  convey  a determinate  and  unmistakable  meaning.  There  are,  howev- 
er, as  we  have  already  remarked,  other  requisites;  some  of  them  important 
only  in  the  second  degree,  but  one  which  is  fundamental,  and  barely  yields 
in  point  of  importance,  if  it  yields  at  all,  to  the  quality  which  we  have  al- 
ready discussed  at  so  much  length.  That  the  language  may  be  fitted  for 
its  purposes,  not  only  should  every  word  perfectly  express  its  meaning,  but 
there  should  be  no  important  meaning  without  its  word.  Whatever  we 
have  occasion  to  think  of  often,  and  for  scientific  purposes,  ought  to  have 
a name  appropriated  to  it. 

This  requisite  of  philosophical  language  may  be  considered  under  three 
different  heads;  that  number  of  separate  conditions  being  involved  in  it. 

§ 2.  First,  there  ought  to  be  all  such  names,  as  are  needful  for  making 
such  a record  of  individual  observations  that  the  words  of  the  record  shall 
exactly  show  what  fact  it  is  which  has  been  observed.  In  other  words, 
there  should  be  an  accurate  Descriptive  Terminology. 

The  only  things  which  we  can  observe  directly  being  our  own  sensations, 
or  other  feelings,  a complete  descriptive  language  would  be  one  in  which 
there  should  be  a name  for  every  variety  of  elementary  sensation  or  feel- 


4S8 


OPERATIONS  SUBSIDIARY  TO  INDUCTION. 


iug.  Combinations  of  sensations  or  feelings  may  always  be  described,  if 
we  have  a name  for  each  of  the  elementary  feelings  which  compose  them-, 
bnt  brevity  of  description,  and  clearness  (which  often  depends  very  much 
on  brevity),  are  greatly  promoted  by  giving  distinctive  names  not  to  the 
elements  alone,  but  also  to  all  combinations  which  are  of  frequent  recur- 
rence. On  this  occasion  I can  not  do  better  than  quote  from  Dr.  Whe- 
well*  some  of  the  excellent  remarks  which  he  has  made  on  this  important 
branch  of  our  subject. 

“The  meaning  of  [descriptive]  technical  terms  can  be  fixed  in  the  first 
instance  only  by  convention,  and  can  be  made  intelligible  only  by  present- 
ing to  the  senses  that  which  the  terms  are  to  signify.  The  knowledge  of 
a color  by  its  name  can  only  be  taught  through  the  eye.  No  description 
can  convey  to  a hearer  what  we  mean  by  apple-green  or  French  gray. 
It  might,  perhaps,  be  supposed  that,  in  the  first  example,  the  term  apple , 
referring  to  so  familiar  an  object,  sufficiently  suggests  the  color  intended. 
But  it  may  easily  be  seen  that  this  is  not  true;  for  apples  are  of  many  dif- 
ferent hues  of  green,  and  it  is  only  by  a conventional  selection  that  we  can 
appropriate  the  term  to  one  special  shade.  When  this  appropriation  is 
once  made,  the  term  refers  to  the  sensation,  and  not  to  the  parts  of  the 
term ; for  these  enter  into  the  compound  merely  as  a help  to  the  memory, 
whether  the  suggestion  be  a natural  connection  as  in  ‘ apple-green,’  or  a 
casual  one  as  in  ‘French  gray.’  In  order  to  derive  due  advantage  from 
technical  terms  of  the  kind,  they  must  be  associated  immediately  with  the 
perception  to  which  they  belong  ; and  not  connected  with  it  through  the 
vague  usages  of  common  language.  The  memory  must  retain  the  sensa- 
tion ; and  the  technical  word  must  be  understood  as  directly  as  the  most 
familiar  word,  and  more  distinctly.  When  we  find  such  terms  as  tin-white 
or  pinchbeck-brown,  the  metallic  color  so  denoted  ought  to  start  up  in  our 
memory  without  delay  or  search. 

“This,  which  it  is  most  important  to  recollect  with  respect  to  the  sim- 
pler properties  of  bodies,  as  color  and  form,  is  no  less  true  with  respect  to 
more  compound  notions.  In  all  cases  the  term  is  fixed  to  a peculiar  mean- 
ing by  convention  ; and  the  student,  in  order  to  use  the  word,  must  be  com- 
pletely familiar  with  the  convention,  so  that  he  has  no  need  to  frame  con- 
jectures from  the  word  itself.  Such  conjectures  would  always  be  insecure, 
and  often  erroneous.  Thus  the  term  papilionaceous  applied  to  a flower  is 
employed  to  indicate,  not  only  a resemblance  to  a butterfly,  but  a resem- 
blance arising  from  five  petals  of  a certain  peculiar  shape  and  arrangement; 
and  even  if  the  resemblance  were  much  stronger  than  it  is  in  such  cases, 
yet,  if  it  were  produced  in  a different  way,  as,  for  example,  by  one  petal,  or 
two  only,  instead  of  a ‘ standard,’ two  ‘ wings,’ and  a ‘keel’  consisting  of 
two  parts  more  or  less  united  into  one,  we  should  be  no  longer  justified  in 
speaking  of  it  as  a ‘ papilionaceous  ’ flower.” 

When,  however,  the  thing  named  is,  as  in  this  last  case,  a combination 
of  simple  sensations,  it  is  not  necessary,  in  order  to  learn  the  meaning  of 
the  word,  that  the  student  should  refer  back  to  the  sensations  themselves; 
it  may  be  communicated  to  him  through  the  medium  of  other  words ; the 
terms,  in  short,  may  be  defined.  But  the  names  of  elementary  sensations, 
or  elementary  feelings  of  any  sort,  can  not  be  defined;  nor  is  there  any 
mode  of  making  their  signification  known  but  by  making  the  learner  ex- 
perience the  sensation,  or  referring  him,  through  some  known  mark,  to  his 


History  of  Scientific  Ideas , ii.,  110,  111. 


TERMINOLOGY  AND  NOMENCLATURE. 


489 


remembrance  of  having  experienced  it  before.  Hence  it  is  only  the  im- 
pressions on  the  outward  senses,  or  those  inward  feelings  which  are  con- 
nected in  a very  obvious  and  uniform  manner  with  outward  objects,  that 
are  really  susceptible  of  an  exact  descriptive  language.  The  countless  va- 
riety of  sensations  which  arise,  for  instance,  from  disease,  or  from  peculiar 
physiological  states,  it  would  be  in  vain  to  attempt  to  name ; for  as  no  one 
can  judge  whether  the  sensation  I have  is  the  same  with  his,  the  name  can 
not  have,  to  us  two,  real  community  of  meaning.  The  same  may  be  said, 
to  a considerable  extent,  of  purely  mental  feelings.  But  in  some  of  the 
sciences  which  are  conversant  with  external  objects,  it  is  scarcely  possible 
to  surpass  the  perfection  to  which  this  quality  of  a philosophical  language 
has  been  carried. 

“The  formation*  of  an  exact  and  extensive  descriptive  language  for 
botany  has  been  executed  with  a degree  of  skill  and  felicity,  which,  before 
it  was  attained,  could  hardly  have  been  dreamed  of  as  attainable.  Every 
part  of  a plant  has  been  named  ; and  the  form  of  every  part,  even  the  most 
minute,  has  had  a large  assemblage  of  descriptive  terms  appropriated  to 
it,  by  means  of  which  the  botanist  can  convey  and  receive  knowledge  of 
form  and  structure,  as  exactly  as  if  each  minute  part  were  presented  to 
him  vastly  magnified.  This  acquisition  was  part  of  the  Linn  man  re- 
form  £ Tournefort,’ says  Decandolle, ‘appears  to  have  been  the  first 

who  really  perceived  the  utility  of  fixing  the  sense  of  terms  in  such  a way 
as  always  to  employ  the  same  word  in  the  same  sense,  and  always  to  ex- 
press the  same  idea  by  the  same  words;  but  it  was  Linnaeus  who  really 
created  and  fixed  this  botanical  language,  and  this  is  his  fairest  claim  to 
glory,  for  by  this  fixation  of  language  he  has  shed  clearness  and  precision 
over  all  parts  of  the  science.’ 

“It  is  not  necessary  here  to  give  any  detailed  account  of  the  terms  of 
botany.  The  fundamental  ones  have  been  gradually  introduced,  as  the 
parts  of  plants  were  more  carefully  and  minutely  examined.  Thus  the 
flower  was  necessarily  distinguished  into  the  calyx , the  corolla , the  sta- 
mens, and  the  pistils;  the  sections  of  the  corolla  were  termed  petals  by 
Columna;  those  of  the  calyx  were  called  sepals  by  ISTecker.  Sometimes 
terms  of  greater  generality  were  devised  ; as  perianth,  to  include  the  calyx 
and  corolla,  whether  one  or  both  of  these  were  present;  pericarp , for  the 
part  inclosing  the  grain,  of  whatever  kind  it  be,  fruit,  nut,  pod,  etc.  And 
it  may  easily  be  imagined,  that  descriptive  terms  may,  by  definition  and 
combination,  become  very  numerous  and  distinct.  Thus  leaves  may  be 
called  pinnatifid , pinnatipartite,  pinnatisect , pinnatilobate, palmatifid,  pal- 
matipartite,  etc.,  and  each  of  these  words  designates  different  combinations 
of  the  modes  and  extent  of  the  divisions  of  the  leaf  with  the  divisions  of 
its  outline.  In  some  cases,  arbitrary  numerical  relations  are  introduced 
into  the  definition : thus,  a leaf  is  called  bilobate,  when  it  is  divided  into 
two  parts  bv  a notch ; but  if  the  notch  go  to  the  middle  of  its  length,  it 
is  bifid ; if  it  go  near  the  base  of  the  leaf,  it  is  bipartite;  if  to  the  base,  it 
is  bisect.  Thus,  too,  a pod  of  a cruciferous  plant  is  a siliqua,  if  it  is  four 
times  as  long  as  it  is  broad,  but  if  it  be  shorter  than  this  it  is  a silicula. 
Such  terms  being  established,  the  form  of  the  very  complex  leaf  or  frond 
of  a fern  (Hymenophyllum  Wilsoni)  is  exactly  conveyed  by  the  following 
phrase : £ fronds  rigid  pinnate,  pinnae  recurved  subunilateral,  pinnatifid,  the 
segments  linear  undivided  or  bifid,  spinuloso-serrate.’ 


History  of  Scientific  Ideas,  ii. , 111-113. 


490 


OPERATIONS  SUBSIDIARY  TO  INDUCTION. 


“Other  characters,  as  well  as  form,  are  conveyed  with  the  like  precision: 

Color  by  means  of  a classified  scale  of  colors This  was  done  with 

most  precision  by  Werner,  and  his  scale  of  colors  is  still  the  most  usual 
standard  of  naturalists.  Werner  also  introduced  a more  exact  terminology 
with  regard  to  other  characters  which  are  important  in  mineralogy,  as  lustre, 
hardness.  But  Mohs  improved  upon  this  step  by  giving  a numerical  scale 

of  hardness,  in  which  talc  is  I,  gypsum  2,  calc  spar  3,  and  so  on Some 

properties,  as  specific  gravity,  by  their  definition  give  at  once  a numerical 
measure;  and  others,  as  crystalline  form,  require  a very  considerable  array 
of  mathematical  calculation  and  reasoning,  to  point  out  their  relations  and 
gradations.” 


§ 3.  Thus  far  of  Descriptive  Terminology,  or  of  the  language  requisite 
for  placing  on  record  our  observation  of  individual  instances.  But  when 
we  proceed  from  this  to  Induction,  or  rather  to  that  comparison  of  ob- 
served instances  which  is  the  preparatory  step  toward  it,  we  stand  in  need 
of  an  additional  and  a different  sort  of  general  names. 

Whenever,  for  purposes  of  Induction,  we  find  it  necessary  to  introduce 
(in  Dr.  Whewell’s  phraseology)  some  new  general  conception;  that  is, 
whenever  the  comparison  of  a set  of  phenomena  leads  to  the  recognition 
in  them  of  some  common  circumstance,  which,  our  attention  not  having 
been  directed  to  it  on  any  former  occasion,  is  to  us  a new  phenomenon  ; it 
is  of  importance  that  this  new  conception,  or  this  new  result  of  abstraction, 
should  have  a name  appropriated  to  it ; especially  if  the  circumstance  it 
involves  be  one  which  leads  to  many  consequences,  or  which  is  likely  to 
be  found  also  in  other  classes  of  phenomena.  No  doubt,  in  most  cases  of 
the  kind,  the  meaning  might  be  conveyed  by  joining  together  several 
words  already  in  use.  But  when  a thing  has  to  be  often  spoken  of,  there 
are  more  reasons  than  the  saving  of  time  and  space,  for  speaking  of  it  in 
the  most  concise  manner  possible.  What  darkness  would  be  spread  over 
geometrical  demonstrations,  if  wherever  the  word  circle  is  used,  the  defini- 
tion of  a circle  were  inserted  instead  of  it.  In  mathematics  and  its  appli- 
cations, where  the  nature  of  the  processes  demands  that  the  attention 
should  be  strongly  concentrated,  but  does  not  require  that  it  should  be 
widely  diffused,  the  importance  of  concentration  also  in  the  expressions 
has  always  been  duly  felt;  and  a mathematician  no  sooner  finds  that  he 
shall  often  have  occasion  to  speak  of  the  same  two  things  together,  than  he 
at  once  creates  a term  to  express  them  whenever  combined:  just  as,  in  his 


algebraical  operations,  he  substitutes  for  (am-\-bn)  or  for  etc-> 


the  single  letter  P,  Q,  or  S ; not  solely  to  shorten  his  symbolical  ex- 
pressions, but  to  simplify  the  purely  intellectual  part  of  his  operations,  by 
enabling  the  mind  to  give  its  exclusive  attention  to  the  relation  between 
the  quantity  S and  the  other  quantities  which  enter  into  the  equation, 
without  being  distracted  by  thinking  unnecessarily  of  the  parts  of  which 
S is  itself  composed. 

But  there  is  another  reason,  in  addition  to  that  of  promoting  perspicui- 
ty, for  giving  a brief  and  compact  name  to  each  of  the  more  considerable 
results  of  abstraction  which  are  obtained  in  the  course  of  our  intellectual 
phenomena.  By  naming  them,  we  fix  our  attention  upon  them;  we  keep 
them  more  constantly  before  the  mind.  The  names  are  remembered,  and 
being  remembered,  suggest  their  definition ; while  if  instead  of  specific 


TERMINOLOGY  AND  NOMENCLATURE. 


491 


and  characteristic  names,  the  meaning  had  been  expressed  by  putting  to- 
gether a number  of  other  names,  that  particular  combination  of  words  al- 
ready in  common  use  for  other  purposes  would  have  had  nothing  to  make 
itself  remembered  by.  If  we  want  to  render  a particular  combination  of 
ideas  permanent  in  the  mind,  there  is  nothing  which  clinches  it  like  r, 
name  specially  devoted  to  express  it.  If  mathematicians  had  been  obliged 
to  speak  of  “that  to  which  a quantity,  in  increasing  or  diminishing,  is  al- 
ways approaching  nearer,  so  that  the  difference  becomes  less  than  any  as- 
signable quantity,  but  to  which  it  never  becomes  exactly  equal,”  instead 
of  expressing  all  this  by  the  simple  phrase,  “ the  limit  of  a quantity,”  we 
should  probably  have  long  remained  without  most  of  the  important  truths 
which  have  been  discovered  by  means  of  the  relation  between  quantities  of 
various  kinds  and  their  limits.  If  instead  of  speaking  of  momentum , it 
had  been  necessary  to  say,  “ the  product  of  the  number  of  units  of  velocity 
in  the  velocity  by  the  number  of  units  of  mass  in  the  mass,”  many  of  the 
dynamical  truths  now  apprehended  by  means  of  this  complex  idea  would 
probably  have  escaped  notice,  for  want  of  recalling  the  idea  itself  with 
sufficient  readiness  and  familiarity.  And  on  subjects  less  remote  from  the 
topics  of  popular  discussion,  whoever  wishes  to  draw  attention  to  some 
new  or  unfamiliar  distinction  among  things,  will  find  no  way  so  sure  as  to 
invent  or  select  suitable  names  for  the  express  purpose  of  marking  it. 

A volume  devoted  to  explaining  what  the  writer  means  by  civilization, 
does  not  raise  so  vivid  a conception  of  it  as  the  single  expression,  that  Civ- 
ilization is  a different  thing  from  Cultivation;  the  compactness  of  that 
brief  designation  for  the  contrasted  quality  being  an  equivalent  for  a long 
discussion.  So,  if  we  would  impress  forcibly  upon  the  understanding  and 
memory  the  distinction  between  the  two  different  conceptions  of  a repre- 
sentative government,  we  can  not  more  effectually  do  so  than  by  saying 
that  Delegation  is  not  Representation.  Hardly  any  original  thoughts  on 
mental  or  social  subjects  ever  make  their  way  among  mankind,  or  assume 
their  proper  importance  in  the  minds  even  of  their  inventors,  until  aptly- 
selected  words  or  phrases  have,  as  it  were,  nailed  them  down  and  held 
them  fast. 

§ 4.  Of  the  three  essential  parts  of  a philosophical  language,  we  have 
now  mentioned  two : a terminology  suited  for  describing  with  precision 
the  individual  facts  observed ; and  a name  for  every  common  property  of 
any  importance  or  interest,  which  we  detect  by  comparing  those  facts;  in- 
cluding (as  the  concretes  corresponding  to  those  abstract  terms)  names  for 
the  classes  which  we  artificially  construct  in  virtue  of  those  properties,  or 
as  many  of  them,  at  least,  as  we  have  frequent  occasion  to  predicate  any 
thing  of. 

But  there  is  a sort  of  classes,  for  the  recognition  of  which  no  such  elab- 
orate process  is  necessary ; because  each  of  them  is  marked  out  from  all 
others  not  by  some  one  property,  the  detection  of  which  may  depend  on  a 
difficult  act  of  abstraction,  but  by  its  properties  generally.  I mean,  the 
Kinds  of  things,  in  the  sense  which,  in  this  treatise,  has  been  specially  at- 
tached to  that  term.  By  a Kind,  it  will  be  remembered,  we  mean  one  of 
those  classes  which  are  distinguished  from  all  others  not  by  one  or  a few 
definite  properties,  but  by  an  unknown  multitude  of  them ; the  combina- 
tion of  properties  on  which  the  class  is  grounded,  being  a mere  index  to 
an  indefinite  number  of  other  distinctive  attributes.  The  class  horse  is  a 
Kind,  because  the  things  which  agree  in  possessing  the  characters  by  which 


492 


OPERATIONS  SUBSIDIARY  TO  INDUCTION. 


we  recognize  a horse,  agree  in  a great  number  of  other  properties,  as  we 
know,  and,  it  can  not  be  doubted,  in  many  more  than  we  know.  Animal, 
again,  is  a Kind,  because  no  definition  that  could  be  given  of  the  name 
animal  could  either  exhaust  the  properties  common  to  all  animals,  or  sup- 
ply premises  from  which  the  remainder  of  those  properties  could  be  in- 
ferred. But  a combination  of  properties  which  does  not  give  evidence  of 
the  existence  of  any  other  independent  peculiarities,  does  not  constitute  a 
Kind.  White  horse,  therefore,  is  not  a Kind;  because  horses  which  agree 
in  whiteness,  do  not  agree  in  any  thing  else,  except  the  qualities  common 
to  all  horses,  and  whatever  may  be  the  causes  or  effects  of  that  particular 
color. 

On  the  principle  that  there  should  be  a name  for  every  thing  which  we 
have  frequent  occasion  to  make  assertions  about,  there  ought  evidently  to 
be  a name  for  every  Kind ; for  as  it  is  the  very  meaning  of  a Kind  that 
the  individuals  composing  it  have  an  indefinite  multitude  of  properties  in 
common,  it  follows  that,  if  not  with  our  present  knowledge,  yet  with  that 
which  we  may  hereafter  acquire,  the  Kind  is  a subject  to  which  there  will 
have  to  be  applied  many  predicates.  The  third  component  element  of  a 
philosophical  language,  therefore,  is  that  there  shall  be  a name  for  every 
Kind.  In  other  words,  there  must  not  only  be  a terminology,  but  also  a 
nomenclature. 

The  words  Nomenclature  and  Terminology  are  employed  by  most  au- 
thors almost  indiscriminately;  Dr.  Whewell  being,  as  far  as  I am  aware, 
the  first  writer  who  has  regularly  assigned  to  the  two  words  different 
meanings.  The  distinction,  however,  which  he  has  drawn  between  them 
being  real  and  important,  his  example  is  likely  to  be  followed  ; and  (as  is 
apt  to  be  the  case  when  such  innovations  in  language  are  felicitously  made) 
a vague  sense  of  the  distinction  is  found  to  have  influenced  the  employ- 
ment of  the  terms  in  common  practice,  before  the  expediency  had  been 
pointed  out  of  discriminating  them  philosophically.  Every  one  would  say 
that  the  reform  effected  by  Lavoisier  and  Guvton-Morveau  in  the  language 
of  chemistry  consisted  in  the  introduction  of  a new  nomenclature,  not  of  a 
new  terminology.  Linear,  lanceolate,  oval,  or  oblong,  serrated,  dentate,  or 
crenate  leaves,  are  expressions  forming  part  of  the  terminology  of  botany, 
while  the  names  “Viola  odorata,”  and  “IJlex  Europseus,”  belong  to  its 
nomenclature. 

A nomenclature  may  be  defined,  the  collection  of  the  names  of  all  the 
Kinds  with  which  any  branch  of  knowledge  is  conversant;  or  more  prop- 
erly, of  all  the  lowest  Kinds,  or  infimioe  species — those  which  may  be  sub- 
divided indeed,  but  not  into  Kinds,  and  which  generally  accord  with  what 
in  natural  history  are  termed  simply  species.  Science  possesses  two  splen- 
did examples  of  a systematic  nomenclature ; that  of  plants  and  animals, 
constructed  by  Linnaeus  and  his  successors,  and  that  of  chemistry,  which 
we  owe  to  the  illustrious  group  of  chemists  who  flourished  in  France  to- 
ward the  close  of  the  eighteenth  century.  In  these  two  departments,  not 
only  has  every  known  species,  or  lowest  Kind,  a name  assigned  to  it,  but 
when  new  lowest  Kinds  are  discovered,  names  are  at  once  given  to  them 
on  a uniform  principle.  In  other  sciences  the  nomenclature  is  not  at  pres- 
ent constructed  on  any  system,  either  because  the  species  to  be  named  are 
not  numerous  enough  to  require  one  (as  in  geometry,  for  example),  or  be- 
cause no  one  has  yet  suggested  a suitable  principle  for  such  a system,  as 
in  mineralogy ; in  which  the  want  of  a scientifically  constructed  nomencla- 
ture is  now  the  principle  cause  which  retards  the  progress  of  the  science. 


TERMINOLOGY  AND  NOMENCLATURE. 


493 


§ 5.  A word  which  carries  on  its  face  that  it  belongs  to  a nomenclature, 
seems  at  first  sight  to  differ  from  other  concrete  general  names  in  this — 
that  its  meaning  does  not  reside  in  its  connotation,  in  the  attributes  im- 
plied in  it,  but  in  its  denotation,  that  is,  in  the  particular  group  of  things 
which  it  is  appointed  to  designate;  and  can  not,  therefore,  be  unfolded  by 
means  of  a definition,  but  must  be  made  known  in  another  way.  This 
opinion,  however,  appears  to  me  erroneous.  Words  belonging  to  a no- 
menclature differ,  I conceive,  from  other  words  mainly  in  this,  that  besides 
the  ordinary  connotation,  they  have  a peculiar  one  of  their  own : besides 
connoting  certain  attributes,  they  also  connote  that  those  attributes  are 
distinctive  of  a Kind.  The  term  “ peroxide  of  iron,”  for  example,  belong- 
ing by  its  form  to  the  systematic  nomenclature  of  chemistry,  bears  on  its 
face  that  it  is  the  name  of  a peculiar  Kind  of  substance.  It  moreover  con- 
notes, like  the  name  of  any  other  class,  some  portion  of  the  properties 
common  to  the  class ; in  this  instance  the  property  of  being  a compound 
of  iron  and  the  largest  dose  of  oxygen  with  which  iron  will  combine. 
These  two  things,  the  fact  of  being  such  a compound,  and  the  fact  of  being 
a Kind,  constitute  the  connotation  of  the  name  peroxide  of  iron.  When 
we  say  of  the  substance  before  us,  that  it  is  the  peroxide  of  iron,  we  there- 
by assert,  first,  that  it  is  a compound  of  iron  and  a maximum  of  oxygen, 
and  next,  that  the  substance  so  composed  is  a peculiar  Kind  of  substance. 

Now,  this  second  part  of  the  connotation  of  any  word  belonging  to  a 
nomenclature  is  as  essential  a portion  of  its  meaning  as  the  first  part,  while 
the  definition  only  declares  the  first ; and  hence  the  appearance  that  the 
signification  of  such  terms  can  not  be  conveyed  by  a definition  : which  ap- 
pearance, however,  is  fallacious.  The  name  Yiola  odorata  denotes  a Kind, 
of  which  a certain  number  of  characters,  sufficient  to  distinguish  it,  are 
enunciated  in  botanical  works.  This  enumeration  of  characters  is  surely, 
as  in  other  cases,  a definition  of  the  name.  No,  say  some,  it  is  not  a defi- 
nition, for  the  name  Yiola  odorata  does  not  mean  those  characters;  it  means 
that  particular  group  of  plants,  and  the  characters  are  selected  from  among 
a much  greater  number,  merely  as  marks  by  which  to  recognize  the  group. 
But  to  this  I reply,  that  the  name  does  not  mean  that  group,  for  it  would 
be  applied  to  that  group  no  longer  than  while  the  group  is  believed  to  be 
an  infima  species  / if  it  were  to  be  discovered  that  several  distinct  Kinds 
have  been  confounded  under  this  one  name,  no  one  would  any  longer  ap- 
ply the  name  Viola  odorata  to  the  whole  of  the  group,  but  would  apply  it, 
if  retained  at  all,  to  one  only  of  the  Kinds  retained  therein.  What  is  im- 
perative, therefore,  is  not  that  the  name  shall  denote  one  particular  collec- 
tion of  objects,  but  that  it  shall  denote  a Kind,  and  a lowest  Kind.  The 
form  of  the  name  declares  that,  happen  what  will,  it  is  to  denote  an  infima 
species ; and  that,  therefore,  the  properties  which  it  connotes,  and  which 
are  expressed  in  the  definition,  are  to  be  connoted  by  it  no  longer  than 
while  we  continue  to  believe  that  those  properties,  when  found  together, 
indicate  a Kind,  and  that  the  whole  of  them  are  found  in  no  more  than  one 
Kind. 

With  the  addition  of  this  peculiar  connotation,  implied  in  the  form  of 
every  word  which  belongs  to  a systematic  nomenclature ; the  set  of  char- 
acters which  is  employed  to  discriminate  each  Kind  from  all  other  Kinds 
(and  which  is  a real  definition)  constitutes  as  completely  as  in  any  oth- 
er case  the  whole  meaning  of  the  term.  It  is  no  objection  to  say  that 
(as  is  often  the  case  in  natural  history)  the  set  of  characters  may  be 
changed,  and  another  substituted  as  being  better  suited  for  the  purpose 


494 


OPERATIONS  SUBSIDIARY  TO  INDUCTION. 


of  distinction,  while  the  word,  still  continuing  to  denote  the  same  group  or 
things,  is  not  considered  to  have  changed  its  meaning.  For  this  is  no  more 
than  may  happen  in  the  case  of  any  other  general  name  : we  may,  in  re- 
forming its  connotation,  leave  its  denotation  untouched ; and  it  is  general- 
ly desirable  to  do  so.  The  connotation,  however,  is  not  the  less  for  this 
the  real  meaning,  for  we  at  once  apply  the  name  wherever  the  characters 
set  down  in  the  definition  are  found ; and  that  which  exclusively  guides 
us  in  applying  the  term,  must  constitute  its  signification.  If  we  find,  con- 
trary to  our  previous  belief,  that  the  characters  are  not  peculiar  to  one  spe- 
cies, we  cease  to  use  the  term  co-extensively  with  the  characters ; but  then 
it  is  because  the  other  portion  of  the  connotation  fails;  the  condition  that 
the  class  must  be  a Kind.  The  connotation,  therefore,  is  still  the  meaning  ; 
the  set  of  descriptive  characters  is  a true  definition  ; and  the  meaning  is 
unfolded,  not  indeed  (as  in  other  cases)  by  the  definition  alone,  but  by  the 
definition  and  the  form  of  the  word  taken  together. 

§ 6.  We  have  now  analyzed  what  is  implied  in  the  two  principal  requisites 
of  a philosophical  language  ; first,  precision,  or  definiteness;  and,  secondly, 
completeness.  Any  further  remarks  on  the  mode  of  constructing  a nomen- 
clature must  be  deferred  until  we  treat  of  Classification  ; the  mode  of  naming 
the  Kinds  of  things  being  necessarily  subordinate  to  the  mode  of  arranging 
those  Kinds  into  larger  classes.  With  respect  to  the  minor  requisites  of 
terminology,  some  of  them  are  well  stated  and  illustrated  in  the  “Aphorisms 
concerning  the  Language  of  Science,”  included  in  Dr.  Whewell’s  Philosophy 
of  the  Inductive  Sciences.  These,  as  being  of  secondary  importance  in  the 
peculiar  point  of  view  of  Logic,  I shall  not  further  refer  to,  but  shall  confine 
my  observations  to  one  more  quality,  which,  next  to  the  two  already  treat- 
ed of,  appears  to  be  the  most  valuable  which  the  language  of  science  can 
possess.  Of  this  quality  a general  notion  may  be  conveyed  by  the  follow- 
ing aphorism : 

Whenever  the  nature  of  the  subject  permits  our  reasoning  processes  to 
be,  without  danger,  carried  on  mechanically,  the  language  should  be  con- 
structed on  as  mechanical  principles  ns  possible;  while,  in  the  contrary 
case,  it  should  be  so  constructed  that  there  shall  be  the  greatest  possible  ob- 
stacles to  a merely  mechanical  use  of  it. 

I am  aware  that  this  maxim  requires  much  explanation,  which  I shall  at 
once  proceed  to  give.  At  first,  as  to  what  is  meant  by  using  a language 
mechanically".  The  complete  or  extreme  case  of  the  mechanical  use  of  lan- 
guage, is  when  it  is  used  without  any  consciousness  of  a meaning,  and  with 
only  the  consciousness  of  using  certain  visible  or  audible  marks  in  con- 
formity to  technical  rules  previously  laid  down.  This  extreme  case  is  no- 
where realized  except  in  the  figures  of  arithmetic,  and  still  more  the  sym- 
bols of  algebra,  a language  unique  in  its  kind,  and  approaching  as  nearly  to 
perfection,  for  the  purposes  to  which  it  is  destined,  as  can,  perhaps,  be 
said  of  any  creation  of  the  human  mind.  Its  perfection  consists  in  the 
completeness  of  its  adaptation  to  a purely  mechanical  use.  The  symbols  are 
mere  counters,  without  even  the  semblance  of  a meaning  apart  from  the 
convention  which  is  renewed  each  time  they  are  employed,  and  which  is  al- 
tered at  each  renewal,  the  same  symbol  a or  x being  used  on  different  oc- 
casions to  represent  things  which  (except  that,  like  all  things,  they  are  sus- 
ceptible of  being  numbered)  have  no  property  in  common.  There  is  noth- 
ing, therefore,  to  distract  the  mind  from  the  set  of  mechanical  operations 
■which  are  to  be  performed  upon  the  symbols,  such  as  squaring  both  sides 


TERMINOLOGY  AND  NOMENCLATURE. 


495 


of  the  equation,  multiplying  or  dividing  them  by  the  same  or  by  equivalent 
symbols,  and  so  forth.  Each  of  these  operations,  it  is  true,  corresponds  to 
a syllogism ; represents  one  step  of  a ratiocination  relating  not  to  the  sym- 
bols, but  to  the  things  signified  by  them.  But  as  it  has  been  found  practi- 
cable to  frame  a technical  form,  by  conforming  to  which  we  can  make  sure 
of  finding  the  conclusion  of  the  ratiocination,  our  end  can  be  completely  at- 
tained without  our  ever  thinking  of  any  thing  but  the  symbols.  Being 
thus  intended  to  work  merely  as  mechanism,  they  have  the  qualities  which 
mechanism  ought  to  have.  They  are  of  the  least  possible  bulk,  so  that  they 
take  up  scarcely  any  room,  and  waste  no  time  in  their  manipulation ; they 
are  compact,  and  fit  so  closely  together  that  the  eye  can  take  in  the  whole 
at  once  of  almost  every  operation  which  they  are  employed  to  perform. 

These  admirable  properties  of  the  symbolical  language  of  mathematics 
have  made  so  strong  an  impression  on  the  minds  of  many  thinkers,  as  to 
have  led  them  to  consider  the  symbolical  language  in  question  as  the  ideal 
type  of  philosophical  language  generally  ; to  think  that  names  in  general,  or 
(as  they  are  fond  of  calling  them)  signs,  are  fitted  for  the  purposes  of 
thought  in  proportion  as  they  can  be  made  to  approximate  to  the  compact- 
ness, the  entire  unmeaningness,  and  the  capability  of  being  used  as  counters 
without  a thought  of  what  they  represent,  which  are  characteristic  of  the  a 
and  b,  the  x and  y,  of  algebra.  This  notion  has  led  to  sanguine  views  of 
the  acceleration  of  the  progress  of  science  by  means  which,  I conceive,  can 
not  possibly  conduce  to  that  end,  and  forms  part  of  that  exaggerated  esti- 
mate of  the  influence  of  signs,  which  has  contributed  in  no  small  degree  to 
prevent  the  real  laws  of  our  intellectual  operations  from  being  rightly  un- 
derstood. 

In  the  first  place,  a set  of  signs  by  which  we  reason  without  consciousness 
of  their  meaning,  can  be  serviceable,  at  most,  only  in  our  deductive  opera- 
tions. In  our  direct  inductions  we  can  not  for  a moment  dispense  with  a 
distinct  mental  image  of  the  phenomena,  since  the  whole  operation  turns 
on  a perception  of  the  particulars  in  which  those  phenomena  agree  and  dif- 
fer. But,  further,  this  reasoning  by  counters  is  only  suitable  to  a very  lim- 
ited portion  even  of  our  deductive  processes.  In  our  reasonings  respecting 
numbers,  the  only  general  principles  which  we  ever  have  occasion  to  intro- 
duce are  these,  Things  which  are  equal  to  the  same  thing  are  equal  to  one 
another,  and  The  sums  or  differences  of  equal  things  are  equal;  with  their 
various  corollaries.  Not  only  can  no  hesitation  ever  arise  respecting  the  ap- 
plicability of  these  principles,  since  they  are  true  of  all  magnitudes  what- 
ever; but  every  possible  application  of  which  they  are  susceptible,  may  be 
reduced  to  a technical  rule;  and  such,  in  fact,  the  rules  of  the  calculus  are. 
But  if  the  symbols  represent  any  other  things  than  mere  numbers,  let  us 
say  even  straight  or  curve  lines,  we  have  then  to  apply  theorems  of  geom- 
etry not  true  of  all  lines  without  exception,  and  to  select  those  which  are 
true  of  the  lines  we  are  reasoning  about.  And  how  can  we  do  this  unless 
we  keep  completely  in  mind  what  particular  lines  these  are?  Since  ad- 
ditional geometrical  truths  may  be  introduced  into  the  ratiocination  in  any 
stage  of  its  progress,  we  can  not  suffer  ourselves,  during  even  the  smallest 
part  of  it,  to  use  the  names  mechanically  (as  we  use  algebraical  symbols) 
without  an  image  annexed  to  them.  It  is  only  after  ascertaining  that  the 
solution  of  a question  concerning  lines  can  be  made  to  depend  on  a previous 
question  concerning  numbers,  or,  in  other  words,  after  the  question  has  been 
(to  speak  technically)  reduced  to  an  equation,  that  the  unmeaning  signs  be- 
come available,  and  that  the  nature  of  the  facts  themselves  to  which  the  in- 


496 


OPERATIONS  SUBSIDIARY  TO  INDUCTION. 


vestigation  relates  can  be  dismissed  from  the  mind.  Up  to  the  establish- 
ment of  the  equation,  the  language  in  which  mathematicians  carry  on  their 
reasoning  does  not  differ  in  character  from  that  employed  by  close  reason- 
ers  on  any  other  kind  of  subject. 

I do  not  deny  that  every  correct  ratiocination,  when  thrown  into  the  syl- 
logistic shape,  is  conclusive  from  the  mere  form  of  the  expression,  provided 
none  of  the  terms  used  be  ambiguous ; and  this  is  one  of  the  circumstances 
which  have  led  some  writers  to  think  that  if  all  names  were  so  judicious- 
ly constructed  and  so  carefully  defined  as  not  to  admit  of  any  ambiguity, 
the  improvement  thus  made  in  language  would  not  only  give  to  the  con- 
clusions of  every  deductive  science  the  same  certainty  with  those  of  mathe- 
matics, but  would  reduce  all  reasonings  to  the  application  of  a technical 
form,  and  enable  their  conclusiveness  to  be  rationally  assented  to  after  a 
merely  mechanical  process,  as  is  undoubtedly  the  case  in  algebra.  But,  if 
we  except  geometry,  the  conclusions  of  which  are  already  as  certain  and 
exact  as  they  can  be  made,  there  is  no  science  but  that  of  number,  in  which 
t he  practical  validity  of  a reasoning  can  be  apparent  to  any  person  who  has 
looked  only  at  the  reasoning  itself.  Whoever  has  assented  to  what  was 
said  in  the  last  Book  concerning  the  case  of  the  Composition  of  Causes, 
and  the  still  stronger  case  of  the  entire  supersession  of  one  set  of  laws  by 
another,  is  aware  that  geometry  and  algebra  are  the  only  sciences  of  which 
the  propositions  are  categorically  true ; the  general  propositions  of  all  oth- 
er sciences  are  true  only  hypothetically,  supposing  that  no  counteracting 
cause  happens  to  interfere.  A conclusion,  therefore,  however  correctly  de- 
duced, in  point  of  form,  from  admitted  laws  of  nature,  will  have  no  other 
than  an  hypothetical  certainty.  At  every  step  we  must  assure  ourselves 
that  no  other  law  of  nature  has  sujaerseded,  or  intermingled  its  operation 
with,  those  which  are  the  premises  of  the  reasoning;  and  how  can  this  be 
done  by  merely  looking  at  the  words?  We  must  not  only  be  constantly 
thinking  of  the  phenomena  themselves,  but  we  must  be  constantly  studying 
them  ; making  ourselves  acquainted  with  the  peculiarities  of  every  case  to 
which  we  attempt  to  apply  our  general  principles. 

The  algebraic  notation,  considered  as  a philosophical  language,  is  per- 
fect in  its  adaptation  to  the  subjects  for  which  it  is  commonly  employ- 
ed, namely  those  of  which  the  investigations  have  already  been  reduced 
to  the  ascertainment  of  a relation  between  numbers.  But,  admirable  as 
it  is  for  its  own  purpose,  the  properties  by  which  it  is  rendered  such 
are  so  far  from  constituting  it  the  ideal  model  of  philosophical  language 
in  general,  that  the  more  nearly  the  language  of  any  other  branch  of 
science  approaches  to  it,  the  less  fit  that  language  is  for  its  own  proper 
functions.  On  all  other  subjects,  instead  of  contrivances  to  prevent  our  at- 
tention from  being  distracted  by  thinking  of  the  meaning  of  our  signs,  we 
ought  to  wish  for  contrivances  to  make  it  impossible  that  we  should  ever 
lose  sight  of  that  meaning  even  for  an  instant. 

With  this  view,  as  much  meaning  as  possible  should  be  thrown  into  the 
formation  of  the  word  itself;  the  aids  of  derivation  and  analogy  being 
made  available  to  keep  alive  a consciousness  of  all  that  is  signified  by  it. 
In  this  respect  those  languages  have  an  immense  advantage  which  form  their 
compounds  and  derivatives  from  native  roots,  like  the  German,  and  not  from 
those  of  a foreign  or  dead  language,  as  is  so  much  the  case  with  English, 
French,  and  Italian ; and  the  best  are  those  which  form  them  according  to 
fixed  analogies,  corresponding  to  the  relations  between  the  ideas  to  be  ex- 
pressed. All  languages  do  this  more  or  less,  but  especially,  among  modern 


CLASSIFICATION. 


497 


European  languages,  the  German ; while  even  that  is  inferior  to  the  Greek, 
in  which  the  relation  between  the  meaning  of  a derivative  word  and  that 
of  its  primitive  is  in  general  clearly  marked  by  its  mode  of  formation,  ex- 
cept in  the  case  of  words  compounded  with  prepositions,  which  are  often, 
in  both  those  languages,  extremely  anomalous. 

But  all  that  can  be  done,  by  the  mode  of  constructing  words,  to  prevent 
them  from  degenerating  into  sounds  passing  through  the  mind  without  any 
distinct  apprehension  of  what  they  signify,  is  far  too  little  for  the  necessity 
of  the  case.  Words,  however  well  constructed  originally,  are  always  tend- 
ing, like  coins,  to  have  their  inscription  worn  off  by  passing  from  hand  to 
hand;  and  the  only  possible  mode  of  reviving  it  is  to  be  ever  stamping 
it  afresh,  by  living  in  the  habitual  contemplation  of  the  phenomena  them- 
selves, and  not  resting  in  our  familiarity  with  the  words  that  express  them. 
If  any  one,  having  possessed  himself  of  the  laws  of  phenomena  as  recorded 
in  words,  whether  delivered  to  him  originally  by  others,  or  even  found  out 
by  himself,  is  content  from  thenceforth  to  live  among  those  formulas,  to 
think  exclusively  of  them,  and  of  applying  them  to  cases  as  they  arise,  with- 
out keeping  up  his  acquaintance  with  the  realities  from  which  these  laws 
were  collected — not  only  will  he  continually  fail  in  his  practical  efforts,  be- 
cause he  will  apply  his  formulae  without  duly  considering  whether,  in  this 
case  and  in  that,  other  laws  of  nature  do  not  modify  or  supersede  them ; 
but  the  formulae  themselves  will  progressively  lose  their  meaning  to  him, 
and  he  will  ceaSe  at  last  even  to  be  capable  of  recognizing  with  certainty 
whether  a case  falls  within  the  contemplation  of  his  formula  or  not.  It  is, 
in  short,  as  necessary,  on  all  subjects  not  mathematical,  that  the  things  on 
which  we  reason  should  be  conceived  by  us  in  the  concrete,  and  “ clothed 
in  circumstances,”  as  it  is  in  algebra  that  we  should  keep  all  individualiz- 
ing peculiarities  sedulously  out  of  view. 

With  this  remark  we  close  our  observations  on  the  Philosophy  of  Lan- 
guage. 


CHAPTER  VII. 

OF  CLASSIFICATION,  AS  SUBSIDIARY  TO  INDUCTION. 

§ 1.  There  is,  as  has  been  frequently  remarked  in  this  work,  a classifi- 
cation of  things,  ivhich  is  inseparable  from  the  fact  of  giving  them  general 
names.  Every  name  which  connotes  an  attribute,  divides,  by  that  very 
fact,  all  things  whatever  into  two  classes,  those  which  have  the  attribute 
and  those  which  have  it  not;  those  of  which  the  name  can  be  predicated, 
and  those  of  which  it  can  not.  And  the  division  thus  made  is  not  merely 
a division  of  such  things  as  actually  exist,  or  are  known  to  exist,  but  of  all 
such  as  may  hereafter  be  discovered,  and  even  of  all  which  can  be  imagined. 

On  this  kind  of  Classification  we  have  nothing  to  add  to  what  has  previ- 
ously been  said.  The  Classification  which  requires  to  be  discussed  as  a sep- 
arate act  of  the  mind,  is  altogether  different.  In  the  one,  the  arrangement 
of  objects  in  groups,  and  distribution  of  them  into  compartments,  is  a mere 
incidental  effect  consequent  on  the  use  of  names  given  for  another  purpose, 
namely  that  of  simply  expressing  some  of  their  qualities.  In  the  other,  the 
arrangement  and  distribution  are  the  main  object,  and  the  naming  is  sec- 
ondary to,  and  purposely  conforms  itself  to,  instead  of  governing,  that 
‘more  important  operation. 


32 


498 


OPERATIONS  SUBSIDIARY  TO  INDUCTION. 


Classification,  thus  regarded,  is  a contrivance  for  the  best  possible  order- 
ing of  the  ideas  of  objects  in  our  minds;  for  causing  the  ideas  to  accom- 
pany or  succeed  one  another  in  such  a way  as  shall  give  us  the  greatest 
command  over  our  knowledge  already  acquired,  and  lead  most  directly  to 
the  acquisition  of  more.  The  general  problem  of  Classification,  in  refer- 
ence to  these  purposes,  may  be  stated  as  follows : To  provide  that  things 
shall  be  thought  of  in  such  groups,  and  those  groups  in  sucli  an  order,  as 
will  best  conduce  to  the  remembrance  and  to  the  ascertainment  of  their 
laws. 

Classification  thus  considered,  differs  from  classification  in  the  wider 
sense,  in  having  reference  to  real  objects  exclusively,  and  not  to  all  that  are 
imaginable:  its  object  being  the  due  co-ordination  in  our  minds  of  those 
things  only,  with  the  properties  of  which  we  have  actually  occasion  to  make 
ourselves  acquainted.  But,  on  the  other  hand,  it  embraces  all  really  ex- 
isting objects.  We  can  not  constitute  any  one  class  properly,  except  in 
reference  to  a general  division  of  the  whole  of  nature;  we  can  not  deter- 
mine the  group  in  which  any  one  object  can  most  conveniently  be  placed, 
without  taking  into  consideration  all  the  varieties  of  existing  objects,  all  at 
least  which  have  any  degree  of  affinity  with  it.  No  one  family  of  plants 
or  animals  could  have  been  rationally  constituted,  except  as  pai't  of  a sys- 
tematic arrangement  of  all  plants  or  animals;  nor  could  such  a general  ar- 
rangement have  been  properly  made,  without  first  determining  the  exact 
place  of  plants  and  animals  in  a general  division  of  nature.' 

§ 2.  There  is  no  property  of  objects  which  may  not  be  taken,  if  we 
please,  as  the  foundation  for  a classification  or  mental  grouping  of  those 
objects;  and  in  our  first  attempts  we  are  likely  to  select  for  that  purpose 
properties  which  are  simple,  easily  conceived,  and  perceptible  on  a first 
view,  without  any  previous  process  of  thought.  Thus  Tournefort’s  ar- 
rangement of  plants  was  founded  on  the  shape  and  divisions  of  the  corolla; 
and  that  which  is  commonly  called  the  Linnasan  (though  Linnaeus  also  sug- 
gested another  and  more  scientific  arrangement)  was  grounded  chiefly  on 
the  number  of  the  stamens  and  pistils. 

But  these  classifications,  which  are  at  first  recommended  by  the  facility 
they  afford  of  ascertaining  to  what  class  any  individual  belongs,  are  seldom 
much  adapted  to  the  ends  of  that  Classification  which  is  the  subject  of  our 
present  remarks.  The  Linnaean  arrangement  answers  the  purpose  of  mak- 
ing us  think  together  of  all  those  kinds  of  plants  which  possess  the  same 
number  of  stamens  and  pistils ; but  to  think  of  them  in  that  manner  is  of 
little  use,  since  we  seldom  have  any  thing  to  affirm  in  common  of  the  plants 
which  have  a given  number  of  stamens  and  pistils.  If  plants  of  the  class 
Pentandria,  order  Monogynia,  agreed  in  any  other  properties,  the  habit  of 
thinking  and  speaking  of  the  plants  under  a common  designation  would 
conduce  to  our  remembering  those  common  properties  so  far  as  they  were 
ascertained,  and  would  dispose  us  to  be  on  the  lookout  for  such  of  them 
as  were  not  yet  known.  But  since  this  is  not  the  case,  the  only  purpose  of 
thought  which  the  Linnsean  classification  serves  is  that  of  causing  us  to  re- 
member, better  than  we  should  otherwise  have  done,  the  exact  number  of 
stamens  and  pistils  of  every  species  of  plants.  Now,  as  this  property  is  of 
little  importance  or  interest,  the  remembering  it  with  any  particular  accu- 
racy is  of  no  moment.  And,  inasmuch  as,  by  habitually  thinking  of  plants 
in  those  groups,  we  are  prevented  from  habitually  thinking  of  them  in 
groups  which  have  a greater  number  of  properties  in  common,  the  effect  of 


CLASSIFICATION. 


499 


such  a classification,  when  systematically  adhered  to,  upon  our  habits  of 
thought,  must  be  regarded  as  mischievous. 

The  ends  of  scientific  classification  are  best  answered,  when  the  objects 
are  formed  into  groups  respecting  which  a greater  number  of  general  prop- 
ositions can  be  made,  and  those  propositions  more  important,  than  could 
be  made  respecting  any  other  groups  into  which  the  same  things  could  be 
distributed.  The  properties,  therefore,  according  to  which  objects  are 
classified,  should,  if  possible,  be  those  which  are  causes  of  many  other  prop- 
erties; or,  at  any  rate,  which  are  sure  marks  of  them.  Causes  are  prefera- 
ble, both  as  being  the  surest  and  most  direct  of  marks,  and  as  being  them- 
selves the  properties  on  which  it  is  of  most  use  that  our  attention  should 
be  strongly  fixed.  But  the  property  which  is  the  cause  of  the  chief  pecul- 
iarities of  a class,  is  unfortunately  seldom  fitted  to  serve  also  as  the  diag- 
nostic of  the  class.  Instead  of  the  cause,  we  must  generally  select  some  of 
its  more  prominent  effects,  which  may  serve  as  marks  of  the  other  effects 
and  of  the  cause. 

A classification  thus  formed  is  properly  scientific  or  philosophical,  and 
is  commonly  called  a Natural,  in  contradistinction  to  a Technical  or  Arti- 
ficial, classification  or  arrangement.  The  phrase  Natural  Classification 
seems  most  peculiarly  appropriate  to  such  arrangements  as  correspond,  in 
the  groups  which  they  form,  to  the  spontaneous  tendencies  of  the  mind, 
by  placing  together  the  objects  most  similar  in  their  general  aspect;  in  op- 
position to  those  technical  systems  which,  arranging  things  according  to 
their  agreement  in  some  circumstance  arbitrarily  selected,  often  throw  into 
the  same  group  objects  which  in  the  general  aggregate  of  their  properties 
present  no  resemblance,  and  into  different  and  remote  groups,  others  which 
have  the  closest  similarity.  It  is  one  of  the  most  valid  recommendations 
of  any  classification  to  the  character  of  a scientific  one,  that  it  shall  be  a 
natural  classification  in  this  sense  also ; for  the  test  of  its  scientific  charac- 
ter is  the  number  and  importance  of  the  properties  which  can  be  asserted 
in  common  of  all  objects  included  in  a group;  and  properties  on  which  the 
general  aspect  of  the  things  depends  are,  if  only  on  that  ground,  impor- 
tant, as  well  as,  in  most  cases,  numerous.  But,  though  a strong  recommen- 
dation, this  circumstance  is  not  a sine  qua  non;  since  the  most  obvious 
properties  of  things  may  be  of  trifling  importance  compared  with  others 
that  are  not  obvious.  I have  seen  it  mentioned  as  a great  absurdity  in 
the  Linnsean  classification,  that  it  places  (which  by-the-way  it  does  not) 
the  violet  by  the  side  of  the  oak  ; it  certainly  dissevers  natural  affinities, 
and  brings  together  things  quite  as  unlike  as  the  oak  and  the  violet  are. 
But  the  difference,  apparently  so  wide,  which  renders  the  juxtaposition  of 
those  two  vegetables  so  suitable  an  illustration  of  a bad  arrangement,  de- 
pends, to  the  common  eye,  mainly  on  mere  size  and  texture  ; now  if  we 
made  it  our  study  to  adopt  the  classification  which  would  involve  the  least 
peril  of  similar  rapprochements , we  should  return  to  the  obsolete  division 
into  trees,  shrubs,  and  herbs,  which  though  of  primary  importance  with  re- 
gard to  mere  general  aspect,  yet  (compared  even  with  so  petty  and  unob- 
vious  a distinction  as  that  into  dicotyledons  and  monocotyledons)  answers 
to  so  few  differences  in  the  other  properties  of  plants,  that  a classification 
founded  on  it  (independently  of  the  indistinctness  of  the  lines  of  demarka- 
tion)  would  be  as  completely  artificial  and  technical  as  the  Linnrean. 

Our  natural  groups,  therefore,  must  often  be  founded  not  on  the  obvi- 
ous but  on  the  unobvious  properties  of  things,  when  these  are  of  greater 
importance.  But  in  such  cases  it  is  essential  that  there  should  be  some 


500 


OPERATIONS  SUBSIDIARY  TO  INDUCTION. 


other  property  or  set  of  properties,  more  readily  recognizable  by  the  ob« 
server,  which  co-exist  with,  and  may  be  received  as  marks  of,  the  proper- 
ties which  are  the  real  groundwork  of  the  classification.  A natural  ar- 
rangement, for  example,  of  animals,  must  be  founded  in  the  main  on  their 
internal  structure,  but  (as  M.  Comte  remarks)  it  would  be  absurd  that  we 
should  not  be  able  to  determine  the  genus  and  species  of  an  animal  with- 
out first  killing  it.  On  this  ground,  the  preference,  among  zoological  clas- 
sifications, is  probably  due  to  that  of  M.  De  Blainville,  founded  on  the  dif- 
ferences in  the  external  integuments;  differences  which  correspond,  much 
more  accurately  than  might  be  supposed,  to  the  really  important  varieties, 
both  in  the  other  parts  of  the  structure,  and  in  the  habits  and  history  of 
the  animals. 

This  shows,  more  strongly  than  ever,  how  extensive  a knowledge  of  the 
properties  of  objects  is  necessary  for  making  a good  classification  of  them. 
And  as  it  is  one  of  the  uses  of  such  a classification  that  by  drawing  atten- 
tion to  the  properties  on  which  it  is  founded,  and  which,  if  the  classifica- 
tion be  good,  are  marks  of  many  others,  it  facilitates  the  discovery  of  those 
others;  we  see  in  what  manner  our  knowledge  of  things,  and  our  classifi- 
cation of  them,  tend  mutually  and  indefinitely  to  the  improvement  of  each 
other. 

We  said  just  now  that  the  classification  of  objects  should  follow  those 
of  their  properties  which  indicate  not  only  the  most  numerous,  but  also 
the  most  important  peculiarities.  What  is  here  meant  by  importance? 
It  has  reference  to  the  particular  end  in  view  ; and  the  same  objects,  there- 
fore, may  admit  with  propriety  of  several  different  classifications.  Each 
science  or  art  forms  its  classification  of  things  according  to  the  properties 
which  fall  within  its  special  cognizance,  or  of  which  it  must  take  account 
in  order  to  accomplish  its  peculiar  practical  end.  A farmer  does  not  di- 
vide plants,  like  a botanist,  into  dicotyledonous  and  monocotyledonous,  but 
into  useful  plants  and  weeds.  A geologist  divides  fossils,  not  like  a zoolo- 
gist, into  families  corresponding  to  those  of  living  species,  but  into  fossils 
of  the  paleozoic,  mesozoic,  and  tertiary  periods,  above  the  coal  and  below 
the  coal,  etc.  Whales  are  or  are  not  fish  according  to  the  purpose  for 
which -we  are  considering  them.  “If  we  are  speaking  of  the  internal  struc- 
ture and  physiology  of  the  animal,  we  must  not  call  them  fish ; for  in  these 
respects  they  deviate  widely  from  fishes ; they  have  warm  blood,  and  pro- 
duce and  suckle  their  young  as  land  quadrupeds  do.  But  this  would  not 
prevent  our  speaking  of  the  whale-fishery , and  calling  such  animals  fish  on 
all  occasions  connected  with  this  employment;  for  the  relations  thus  arising 
depend  upon  the  animal’s  living  in  the  water,  and  being  caught  in  a man- 
ner similar  to  other  fishes.  A plea  that  human  laws  which  mention  fish  do 
not  apply  to  whales,  would  be  rejected  at  once  by  an  intelligent  judge.”* 

These  different  classifications  are  all  good,  for  the  purposes  of  their  own 
particular  departments  of  knowledge  or  practice.  But  when  we  are  study- 
ing objects  not  for  any  special  practical  end,  but  for  the  sake  of  extending 
our  knowledge  of  the  whole  of  their  properties  and  relations,  we  must  con- 
sider as  the  most  important  attributes  those  which  contribute  most,  either 
by  themselves  or  by  their  effects,  to  render  the  things  like  one  another,  and 
unlike  other  things;  which  give  to  the  class  composed  of  them  the  most 
marked  individuality ; which  fill,  as  it  were,  the  largest  space  in  their  ex- 
istence, and  would  most  impress  the  attention  of  a spectator  who  knew  all 


Nov.  Org.  Renov.,  pp.  286,  287. 


CLASSIFICATION. 


501 


their  properties  but  was  not  specially  interested  in  any.  Classes  formed 
on  this  principle  may  be  called,  in  a more  emphatic  manner  than  any  oth- 
ers, natural  groups. 

§ 3.  On  the  subject  of  these  groups  Dr.  Whewell  lays  down  a theory, 
grounded  on  an  important  truth,  which  he  has,  in  some  respects,  expressed 
and  illustrated  very  felicitously,  but  also,  as  it  appears  to  me,  with  some 
admixture  of  error.  It  will  be  advantageous,  for  both  these  reasons,  to 
extract  the  statement  of  his  doctrine  in  the  very  words  he  has  used. 

“ Natural  groups,”  according  to  this  theory,*  are  “ given  by  Type,  not 
by  Definition.”  And  this  consideration  accounts  for  that  “ indefiniteness 
and  indecision  which  we  frequently  find  in  the  descriptions  of  such  groups, 
and  which  must  appear  so  strange  and  inconsistent  to  any  one  who  does 
not  suppose  these  descriptions  to  assume  any  deeper  ground  of  connection 
than  an  arbitrary  choice  of  the  botanist.  Thus  in  the  family  of  the  rose- 
tree,  we  are  told  that  the  ovules  are  very  rarely  erect,  the  stigmata  usually 
simple.  Of  what  use,  it  might  be  asked,  can  such  loose  accounts  be?  To 
which  the  answer  is,  that  they  are  not  inserted  in  order  to  distinguish  the 
species,  but  in  order  to  describe  the  family,  and  the  total  relations  of  the 
ovules  and  the  stigmata  of  the  family  are  better  known  by  this  general 
statement.  A similar  observation  may  be  made  with  regard  to  the  Anoma- 
lies of  each  group,  which  occur  so  commonly,  that  Dr.  Lindley,  in  his  In- 
troduction to  the  Hatural  System  of  Botany,  makes  the  ‘Anomalies’  an 
article  in  each  family.  Thus,  part  of  the  character  of  the  Rosaceae  is,  that 
they  have  alternate  stipulate  leaves,  and  that  the  albumen  is  obliterated ; 
but  yet  in  Lowea,  one  of  the  genera  of  this  family,  the  stipulie  are  absent; 
and  the  albumen  is  present  in  another,  Neillia.  This  implies,  as  we  have 
already  seen,  that  the  artificial  character  (or  diagnosis,  as  Mr.  Lindley  calls 
it)  is  imperfect.  It  is,  though  very  nearly,  yet  not  exactly,  commensurate 
with  the  natural  group;  and  hence  in  certain  cases  this  character  is  made 
to  yield  to  the  general  weight  of  natural  affinities. 

“ These  views — of  classes  determined  by  characters  which  can  not  be 
expressed  in  words — of  propositions  which  state,  not  what  happens  in  all 
cases,  but  only  usually — of  particulars  which  are  included  in  a class,  though 
they  transgress  the  definition  of  it,  may  probably  surprise  the  reader. 
They  are  so  contrary  to  many  of  the  received  opinions  respecting  the  use 
of  definitions,  and  the  nature  of  scientific  propositions,  that  they  will  prob- 
ably appear  to  many  persons  highly  illogical  and  unphilosophical.  But  a 
disjjosition  to  such  a judgment  arises  in  a great  measure  from  this,  that 
the  mathematical  and  mathematico  - physical  sciences  have,  in  a great  de- 
gree, determined  men’s  views  of  the  general  nature  and  form  of  scientific 
truth ; while  Natural  History  has  not  yet  had  time  or  opportunity  to  exert 
its  due  influence  upon  the  current  habits  of  philosophizing.  The  appar- 
ent indefiniteness  and  inconsistency  of  the  classifications  and  definitions  of 
Natural  History  belongs,  in  a far  higher  degree,  to  all  other  except  mathe- 
matical speculations;  and  the  modes  in  which  approximations  to  exact  dis- 
tinctions and  general  truths  have  been  made  in  Natural  History,  may  be 
worthy  our  attention,  even  for  the  light  they  throw  upon  the  best  modes 
of  pursuing  truth  of  all  kinds. 

“Though  in  a Natural  group  of  objects  a definition  can  no  longer  be  of 
any  use  as  a regulative  principle,  classes  are  not  therefore  left  quite  loose, 


History  of  Scientific  Ideas,  ii. , 120-122. 


502 


OPERATIONS  SUBSIDIARY  TO  INDUCTION. 


without  any  certain  standard  or  guide.  The  class  is  steadily  fixed,  though 
not  precisely  limited;  it  is  given,  though  not  circumscribed;  it  is  deter- 
mined, not  by  a boundary-line  without,  but  by  a central  point  within;  not 
by  what  it  strictly  excludes,  but  by  what  it  eminently  includes;  by  an  ex- 
ample, not  by  a precept ; in  short,  instead  of  a Definition  we  have  a Type 
for  our  director. 

“ A Type  is  an  example  of  any  class,  for  instance  a species  of  a genus, 
which  is  considered  as  eminently  possessing  the  character  of  the  class.  All 
the  species  which  have  a greater  affinity  with  this  type-species  than  with 
any  others,  form  the  genus,  and  are  arranged  about  it,  deviating  from  it 
in  various  directions  and  different  degrees.  Thus  a genus  may  consist  of 
several  species  which  approach  very  near  the  type,  and  of  which  the  claim 
to  a place  with  it  is  obvious;  while  there  may  be  other  species  which 
straggle  farther  from  this  central  knot,  and  which  yet  are  clearly  more 
connected  with  it  than  with  any  other.  And  even  if  there  should  be  some 
species  of  which  the  place  is  dubious,  and  which  appear  to  be  equally 
bound  to  two  generic  types,  it  is  easily  seen  that  this  would  not  destroy 
the  reality  of  the  generic  groups,  any  more  than  the  scattered  trees  of  the 
intervening  plain  prevent  our  speaking  intelligibly  of  the  distinct  forests 
of  two  separate  hills. 

“ The  type-species  of  every  genus,  the  type-genus  of  every  family,  is  then, 
one  which  possesses  all  the  characters  and  properties  of  the  genus  in  a 
marked  and  prominent  manner.  The  type  of  the  Rose  family  has  alter- 
nate stipulate  leaves,  wants  the  albumen,  has  the  ovules  not  erect,  has  the 
stigmata  simple,  and  besides  these  features,  which  distinguish  it  from  the 
exceptions  or  varieties  of  its  class,  it  has  the  features  which  make  it  promi- 
nent in  its  class.  It  is  one  of  those  which  possess  clearly  several  leading 
attributes ; and  thus,  though  we  can  not  say  of  any  one  genus  that  it  must 
be  the  type  of  the  family,  or  of  any  one  species  that  it  must  be  the  type  of 
the  genus,  we  are  still  not  wholly  to  seek;  the  type  must  be  connected  by 
many  affinities  with  most  of  the  others  of  its  group;  it  must  be  near  the 
centre  of  the  crowd,  and  not  one  of  the  stragglers.” 

In  this  passage  (the  latter  part  of  which  especially  I can  not  help  no- 
ticing as  an  admirable  example  of  philosophic  style)  Dr.  Wbewell  has 
stated  very  clearly  and  forcibly,  but  (I  think)  without  making  all  necessary 
distinctions,  one  of  the  principles  of  a Natural  Classification.  What  this 
principle  is,  what  are  its  limits,  and  in  what  manner  he  seems  to  me  to 
have  overstepped  them,  will  appear  when  we  have  laid  down  another  rule 
of  Natural  Arrangement,  which  appears  to  me  still  more  fundamental. 

§ 4.  The  reader  is  by  this  time  familiar  with  the  general  truth  (which  I 
restate  so  often  on  account  of  the  great  confusion  in  which  it  is  common- 
ly involved),  that  there  are  in  nature  distinctions  of  Kind ; distinctions 
not  consisting  in  a given  number  of  definite  properties  the  effects 
which  follow  from  those  properties,  but  running  through  the  whole  nature, 
through  the  attributes  generally,  of  the  things  so  distinguished.  Our 
knowledge  of  the  properties  of  a Kind  is  never  complete.  We  are  always 
discovering,  and  expecting  to  discover,  new  ones.  Where  the  distinction 
between  two  classes  of  things  is  not  one  of  Kind,  we  expect  to  find  their 
properties  alike,  except  where  there  is  some  reason  for  their  being  differ- 
ent. On  the  contrary,  when  the  distinction  is  in  Kind,  we  expect  to  find 
the  properties  different  unless  there  be  some  cause  for  their  being  the 
same.  All  knowledge  of  a Kind  must  be  obtained  by  observation  and 


CLASSIFICATION. 


503 


experiment  upon  the  Kind  itself;  no  inference  respecting  its  properties 
from  the  properties  of  things  not  connected  with  it  by  Kind,  goes  for 
more  than  the  sort  of  presumption  usually  characterized  as  an  analogy, 
and  generally  in  one  of  its  fainter  degrees. 

Since  the  common  properties  of  a true  Kind,  and  consequently  the  gen- 
eral assertions  which  can  be  made  respecting  it,  or  which  are  certain  to 
be  made  hereafter  as  our  knowledge  extends,  are  indefinite  and  inexhausti- 
ble ; and  since  the  very  first  principle  of  natural  classification  is  that  of 
forming  the  classes  so  that  the  objects  composing  each  may  have  the  great- 
est number  of  properties  in  common;  this  principle  prescribes  that  every 
such  classification  shall  recognize  and  adopt  into  itself  all  distinctions  of 
Kind,  which  exist  among  the  objects  it  professes  to  classify.  To  pass  over 
any  distinctions  of  Kind,  and  substitute  definite  distinctions,  which,  how- 
ever considerable  they  may  be,  do  not  point  to  ulterior  unknown  differ- 
ences, wTould  be  to  replace  classes  with  more  by  classes  with  fewer  attri- 
butes in  common;  and  would  be  subversive  of  the  Natural  Method  of 
Classification. 

Accordingly  all  natural  arrangements,  whether  the  reality  of  the  distinc- 
tion of  Kinds  was  felt  or  not  by  their  framers,  have  been  led,  by  the  mere 
pursuit  of  their  own  proper  end,  to  conform  themselves  to  the  distinctions 
of  Kind,  so  far  as  these  have  been  ascertained  at  the  time.  The  species 
of  Plants  are  not  only  real  Kinds,  but  are  probably,  all  of  them,  real  lowest 
Kinds,  Infimm  Species;  which,  if  we  were  to  subdivide,  as  of  course  it  is 
open  to  us  to  do,  into  sub-classes,  the  subdivision  would  necessarily  be 
founded  on  definite  distinctions,  not  pointing  (apart  from  what  may  be 
known  of  their  causes  or  effects)  to  any  difference  beyond  themselves. 

In  so  far  as  a natural  classification  is  grounded  on  real  Kinds,  its  groups 
are  certainly  not  conventional : it  is  perfectly  true  that  they  do  not  depend 
upon  an  arbitrary  choice  of  the  naturalist.  But  it  does  not  follow,  nor,  I 
conceive,  is  it  true,  that  these  classes  are  determined  by  a type,  and  not  by 
characters.  To  determine  them  by  a type  would  be  as  sure  a way  of  miss- 
ing the  Kind,  as  if  we  were  to  select  a set  of  characters  arbitrarily.  They 
are  determined  by  characters,  but  these  are  not  arbitrary.  The  problem 
is,  to  find  a few  definite  characters  which  point  to  the  multitude  of  indefi- 
nite ones.  Kinds  are  Classes  between  which  there  is  an  impassable  bar- 
rier; and  what  we  have  to  seek  is,  marks  whereby  we  may  determine  on 
which  side  of  the  barrier  an  object  takes  its  place.  The  characters  which 
will  best  do  this  should  be  chosen : if  they  are  also  important  in  them- 
selves, so  much  the  better.  When  we  have  selected  the  characters,  we 
parcel  out  the  objects  according  to  those  characters,  and  not,  I conceive, 
according  to  resemblance  to  a type.  We  do  not  compose  the  species  Ra- 
nunculus acris,  of  all  plants  which  bear  a satisfactory  degree  of  resemblance 
to  a model  buttercup,  but  of  those  which  possess  certain  characters  select- 
ed as  marks  by  which  we  might  recognize  the  possibility  of  a common 
parentage ; and  the  enumeration  of  those  characters  is  the  definition  of  the 
species. 

The  question  next  arises,  whether,  as  all  Kinds  must  have  a place  among 
the  classes,  so  all  the  classes  in  a natural  arrangement  must  be  Kinds? 
And  to  this  I answer,  certainly  not.  The  distinctions  of  Kinds  are  not 
numerous  enough  to  make  up  the  whole  of  a classification.  Very  few  of 
the  genera  of  plants,  or  even  of  the  families,  can  be  pronounced  with  cer- 
tainty to  be  Kinds.  The  great  distinctions  of  Vascular  and  Cellular,  Di- 
cotyledonous or  Exogenous  and  Monocotyledonous  or  Endogenous  plants, 


504 


OPERATIONS  SUBSIDIARY  TO  INDUCTION. 


are  perhaps  differences  of  kind;  the  lines  of  demarkation  which  divide 
those  classes  seem  (though  even  on  this  I would  not  pronounce  positively) 
to  go  through  the  whole  nature  of  the  plants.  But  the  different  species 
of  a genus,  or  genera  of  a family,  usually  have  in  common  only  a limited 
number  of  characters.  A Rose  does  not  seem  to  differ  from  a Rubus,  or 
the  Umbellifene  from  the  Ranunculaceas,  in  much  else  than  the  characters 
botanically  assigned  to  those  genera  or  those  families.  Unenumcrated  dif- 
ferences certainly  do  exist  in  some  cases;  there  are  families  of  plants 
which  have  peculiarities  of  chemical  composition,  or  yield  products  having 
peculiar  effects  on  the  animal  economy.  The  Cruciferas  and  Fungi  contain 
an  unusual  proportion  of  nitrogen ; the  Labiatae  are  the  chief  sources  of 
essential  oils,  the  Solaneae  are  very  commonly  narcotic,  etc.  In  these  and 
similar  cases  there  are  possibly  distinctions  of  Kind  ; but  it  is  by  no  means 
indispensable  that  there  should  be.  Genera  and  Families  may  be  eminent- 
ly natural,  though  marked  out  from  one  another  by  properties  limited  in 
number;  provided  those  properties  are  important,  and  the  objects  con- 
tained in  each  genus  or  family  resemble  each  other  more  than  they  resem- 
ble any  thing  which  is  excluded  from  the  genus  or  family. 

After  the  recognition  and  definition,  then,  of  the  infimce  species,  the  next 
step  is  to  arrange  those  infimce  species  into  larger  groups : making  these 
groups  correspond  to  Kinds  wherever  it  is  possible,  but  in  most  cases  with- 
out any  such  guidance.  And  in  doing  this  it  is  true  that  we  are  naturally 
and  properly  guided,  in  most  cases  at  least,  by  resemblance  to  a type.  We 
form  our  groups  round  certain  selected  Kinds,  each  of  which  serves  as  a 
sort  of  exemplar  of  its  group.  But  though  the  groups  are  suggested  by 
types,  I can  not  think  that  a group  when  formed  is  determined  by  the  type  ; 
that  in  deciding  whether  a species  belongs  to  the  group,  a reference  is  made 
to  the  type,  and  not  to  the  characters ; that  the  characters  “ can  not  be  ex- 
pressed in  words.”  This  assertion  is  inconsistent  with  Dr.  Whe well’s  own 
statement  of  the  fundamental  principle  of  classification,  namely,  that  “gen- 
eral assertions  shall  be  possible.”  If  the  class  did  not  possess  any  charac- 
ters in  common,  what  general  assertions  would  be  possible  respecting  it? 
Except  that  they  all  resemble  each  other  more  than  they  resemble  any  thing 
else,  nothing  whatever  could  be  predicated  of  the  class. 

The  truth  is,  on  the  contrary,  that  every  genus  or  family  is  framed  with 
distinct  reference  to  certain  characters,  and  is  composed,  first  and  princi- 
pally, of  species  which  agree  in  possessing  all  those  characters.  To  these 
are  added,  as  a sort  of  appendix,  such  other  species,  generally  in  small  num- 
ber, as  possess  nearly  all  the  properties  selected ; wanting  some  of  them 
one  propei  ty,  some  another,  and  which,  while  they  agree  with  the  rest  al- 
most as  much  as  these  agree  with  one  another,  do  not  resemble  in  an  equal 
degree  any  other  group.  Our  conception  of  the  class  continues  to  be 
grounded  on  the  characters;  and  the  class  might  be  defined,  those  things 
which  either  possess  that  set  of  characters,  or  resemble  the  things  that  do 
so,  more  than  they  resemble  any  thing  else. 

And  this  resemblance  itself  is  not,  like  resemblance  between  simple  sen- 
sations, an  ultimate  fact,  unsusceptible  of  analysis.  Even  the  inferior  de- 
gree of  resemblance  is  created  by  the  possession  of  common  characters. 
Whatever  resembles  the  genus  Rose  more  than  it  resembles  any  other  ge- 
nus, does  so  because  it  possesses  a greater  number  of  the  characters  of  that 
genus  than  of  the  characters  of  any  other  genus.  Nor  can  there  be  any 
real  difficulty  in  representing,  by  an  enumeration  of  characters,  the  nature 
and  degree  of  the  resemblance  which  is  strictly  sufficient  to  include  any  ob- 


CLASSIFICATION. 


505 


ject  in  the  class.  There  are  always  some  properties  common  to  all  things 
which  are  included.  Others  there  often  are,  to  which  some  things,  which 
are  nevertheless  included,  are  exceptions.  But  the  objects  which  are  ex- 
ceptions to  one  character  are  not  exceptions  to  another;  the  resemblance 
which  fails  in  some  particulars  must  be  made  up  for  in  others.  The  class, 
therefore,  is  constituted  by  the  possession  of  all  the  characters  which  are 
universal,  and  most  of  those  which  admit  of  exceptions.  If  a plant  had  the 
ovules  erect,  the  stigmata  divided,  possessed  the  albumen,  and  was  without 
stipules,  it  possibly  would  not  be  classed  among  the  Rosacem.  But  it  may 
want  any  or.e,  or  more  than  one  of  these  characters,  and  not  be  excluded. 
The  ends  of  a scientific  classification  are  better  answered  by  including  it. 
Since  it  agrees  so  nearly,  in  its  known  properties,  with  the  sum  of  the  char- 
acters of  the  class,  it  is  likely  to  resemble  that  class  more  than  any  other  in 
those  of  its  properties  which  are  still  undiscovered. 

Not  only,  therefore,  are  natural  groups,  no  less  than  any  artificial  classes, 
determined  by  characters ; they  are  constituted  in  contemplation  of,  and  by 
reason  of,  characters.  But  it  is  in  contemplation  not  of  those  characters 
only  which  are  rigorously  common  to  all  the  objects  included  in  the  group, 
but  of  the  entire  body  of  characters,  all  of  which  are  found  in  most  of  those 
objects,  and  most  of  them  in  all.  And  hence  our  conception  of  the  class, 
the  image  in  our  minds  which  is  representative  of  it,  is  that  of  a specimen 
complete  in  all  the  characters;  most  naturally  a specimen  which,  by  pos- 
sessing them  all  in  the  greatest  degree  in  which  they  are  ever  found,  is  the 
best  fitted  to  exhibit  clearly,  and  in  a marked  manner,  what  they  are.  It  is 
by  a mental  reference  to  this  standard,  not  instead  of,  but  in  illustration  of, 
the  definition  of  the  class,  that  we  usually  and  advantageously  determine 
whether  any  individual  or  species  belongs  to  the  class  or  not.  And  this,  as 
it  seems  to  me,  is  the  amount  of  truth  contained  in  the  doctrine  of  Types. 

We  shall  see  presently  that  where  the  classification  is  made  for  the  ex- 
press purpose  of  a special  inductive  inquiry,  it  is  not  optional,  but  necessary 
for  fulfilling  the  conditions  of  a correct  Inductive  Method,  that  we  should 
establish  a tvpe-species  or  genus,  namely,  the  one  which  exhibits  in  the  most 
eminent  degree  the  particular  phenomenon  under  investigation.  But  of  this 
hereafter.  It  remains,  for  completing  the  theory  of  natural  groups,  that  a 
few  words  should  be  said  on  the  principles  of  the  nomenclature  adapted  to 
them. 

§ 5.  A Nomenclature  in  science  is,  as  we  have  said,  a system  of  the 
names  of  Kinds.  These  names,  like  other  class-names,  are  defined  by  the 
enumeration  of  the  characters  distinctive  of  the  class.  The  only  merit 
which  a set  of  names  can  have  beyond  this,  is  to  convey,  by  the  mode  of 
their  construction,  as  much  information  as  possible : so  that  a person  who 
knows  the  thing,  may  receive  all  the  assistance  which  the  name  can  give  in 
remembering  what  he  knows;  while  he  who  knows  it  not,  may  receive  as 
much  knowledge  respecting  it  as  the  case  admits  of,  by  merely  being  told 
its  name. 

There  are  two  modes  of  giving  to  the  name  of  a Kind  this  sort  of  signifi- 
cance. The  best,  but  which  unfortunately  is  seldom  practicable,  is  when  the 
word  can  be  made  to  indicate,  by  its  formation,  the  very  properties  which 
it  is  designed  to  connote.  The  name  of  a Kind  does  not,  of  course,  connote 
all  the  properties  of  the  Kind,  since  these  are  inexhaustible,  but  such  of 
them  as  are  sufficient  to  distinguish  it ; such  as  are  sure  marks  of  all  the 
rest.  Now,  it  is  very  rarely  that  one  property,  or  even  any  two  or  three 


50G 


OPERATIONS  SUBSIDIARY  TO  INDUCTION. 


properties,  can  answer  this  purpose.  To  distinguish  the  common  daisy 
from  all  other  species  of  plants  would  require  the  specification  of  many 
characters.  And  a name  can  not,  without  being  too  cumbrous  for  use,  give 
indication,  by  its  etymology  or  mode  of  construction,  of  more  than  a very 
small  number  of  these.  The  possibility,  therefore,  of  an  ideally  perfect 
Nomenclature,  is  probably  confined  to  the  one  case  in  which  we  are  hap- 
pily in  possession  of  something  approaching  to  it — the  Nomenclature  of 
elementary  Chemistry.  The  substances,  whether  simple  or  compound,  with 
which  chemistry  is  conversant,  are  Kinds,  and,  as  such,  the  properties  which 
distinguish  each  of  them  from  the  rest  are  innumerable ; but  in  the  case  of 
compound  substances  (the  simple  ones  are  not  numerous  enough  to  require 
a systematic  nomenclature),  there  is  one  property,  the  chemical  composi- 
tion, which  is  of  itself  sufficient  to  distinguish  the  Kind;  and  is  (with  cer- 
tain reservations  not  yet  thoroughly  understood)  a sure  mark  of  all  the 
other  properties  of  the  compound.  All  that  was  needful,  therefore,  was  to 
make  the  name  of  every  compound  express,  on  the  first  hearing,  its  chem- 
ical composition;  that  is, to  form  the  name  of  the  compound,  in  some  uni- 
form manner,  from  the  names  of  the  simple  substances  which  enter  into  it 
as  elements.  This  was  done,  most  skillfully  and  successfully,  by  the  French 
chemists,  though  their  nomenclature  has  become  inadequate  to  the  conven- 
ient expression  of  the  very  complicated  compounds  now  known  to  chemists. 
The  only  thing  left  unexpressed  by  them  was  the  exact  proportion  in  which 
the  elements  were  combined  ; and  even  this,  since  the  establishment  of  the 
atomic  theory,  it  has  been  found  possible  to  express  by  a simple  adaptation 
of  their  phraseology. 

But  where  the  characters  which  must  be  taken  into  consideration,  in 
order  sufficiently  to  designate  the  Kind,  are  too  numerous  to  be  all  signified 
in  the  derivation  of  the  name,  and  where  no  one  of  them  is  of  such  prepon- 
derant importance  as  to  justify  its  being  singled  out  to  be  so  indicated,  we 
may  avail  ourselves  of  a subsidiary  resource.  Though  we  can  not  indicate 
the  distinctive  properties  of  the  Kind,  we  may  indicate  its  nearest  natural 
affinities,  by  incorporating  into  its  name  the  name  of  the  proximate  natural 
group  of  which  it  is  one  of  the  species.  On  this  principle  is  founded  the 
admirable  binary  nomenclature  of  botany  and  zoology.  In  this  nomen- 
clature the  name  of  every  species  consists  of  the  name  of  the  genus,  or 
natural  group  next  above  it,  with  a word  added  to  distinguish  the  particu- 
lar species.  The  last  portion  of  the  compound  name  is  sometimes  taken 
from  some  one  of  the  peculiarities  in  which  that  species  differs  from  others 
of  the  genus  ; as  Clematis  integrifolia,  Potentilla  alba,  Viola  palustris , 
Artemisia  vulgaris  • sometimes  from  a circumstance  of  an  historical  na- 
ture, as  Narcissus  poeticus,  Potentilla  tormentilla  (indicating  that  the  plant 
is  that  which  was  formerly  known  by  the  latter  name),  Exacum  Candollii 
(from  the  fact  that  De  Candolle  was  its  first  discoverer) ; and  sometimes 
the  word  is  purely  conventional,  as  Thlaspi  bursapastoris,  Ranunculus 
thora;  it  is  of  little  consequence  which  ; since  the  second,  or,  as  it  is  usually 
called,  the  specific  name,  could  at  most  express,  independently  of  conven- 
tion, no  more  than  a very  small  portion  of  the  connotation  of  the  term. 
But  by  adding  to  this  the  name  of  the  superior  genus,  we  may  make  the 
best  amends  we  can  for  the  impossibility  of  so  contriving  the  name  as  to 
express  all  the  distinctive  characters  of  the  Kind.  We  make  it,  at  all 
events,  express  as  many  of  those  characters  as  are  common  to  the  proxi- 
inate  natural  group  in  which  the  Kind  is  included.  If  even  those  common 
characters  are  so  numerous  or  so  little  familiar  as  to  require  a further  ex- 


CLASSIFICATION  BY  SERIES. 


507 


tension  of  the  same  resource,  we  might,  instead  of  a binary,  adopt  a ternary 
nomenclature,  employing  not  only  the  name  of  the  genus,  but  that  of  the 
next  natural  group  in  order  of  generality  above  the  genus,  commonly  call- 
ed the  Family.  This  was  done  in  the  mineralogical  nomenclature  proposed 
by  Professor  Mohs.  “ The  names  framed  by  him  were  not  composed  of 
two,  but  of  three  elements,  designating  respectively  the  Species,  the  Genus, 
and  the  Order;  thus  he  has  such  species  as  Rhombohedral  Lime  Haloide, 
Octohedrcd  Fluor  JTcdoide,  Prismatic  Hal  Baryte The  binary  con- 
struction, however,  has  been  found  sufficient  in  botany  and  zoology,  the 
only  sciences  in  which  this  general  principle  has  hitherto  been  successfully 
adopted  in  the  construction  of  a nomenclature. 

Besides  the  advantage  which  this  principle  of  nomenclature  possesses,  in 
giving  to  the  names  of  species  the  greatest  quantity  of  independent  signifi- 
cance which  the  circumstances  of  the  case  admit  of,  it  answers  the  further 
end  of  immensely  economizing  the  use  of  names,  and  preventing  an  other- 
wise intolerable  burden  on  the  memory.  When  the  names  of  species  be- 
come extremely  numerous,  some  artifice  (as  Dr.  Whewellf  observes)  be- 
comes absolutely  necessary  to  make  it  possible  to  recollect  or  apply  them. 
“The  known  species  of  plants,  for  example,  were  ten  thousand  in  the  time 
of  Linnaeus,  and  are  now  probably  sixty  thousand.  It  would  be  useless  to 
endeavor  to  frame  and  employ  separate  names  for  each  of  these  species. 
The  division  of  the  objects  into  a subordinated  system  of  classification  en- 
ables us  to  introduce  a Nomenclature  which  does  not  require  this  enor- 
mous number  of  names.  Each  of  the  genera  has  its  name,  and  the  species 
are  marked  by  the  addition  of  some  ejdthet  to  the  name  of  the  genus.  In  this 
manner  about  seventeen  hundred  generic  names,  with  a moderate  number 
of  specific  names,  were  found  by  Linnaeus  sufficient  to  designate  with  pre- 
cision all  the  species  of  vegetables  known  at  his  time.”  And  though  the 
number  of  generic  names  has  since  greatly  increased,  it  has  not  increased 
in  any  thing  like  the  proportion  of  the  multiplication  of  known  species. 


CHAPTER  VIII. 

OP  CLASSIFICATION  BY  SERIES. 

§ 1.  Thus  far,  we  have  considered  the  principles  of  scientific  classification 
so  far  only  as  relates  to  the  formation  of  natural  groups ; and  at  this  point 
most  of  those  who  have  attempted  a theory  of  natural  arrangement,  in- 
cluding, among  the  rest,  Dr.  Whewell,  have  stopped.  There  remains,  how- 
ever, another,  and  a not  less  important  portion  of  the  theory,  which  has 
not  yet,  as  far  as  I am  aware,  been  systematically  treated  of  by  any  writer 
except  M.  Comte.  This  is,  the  arrangement  of  the  natural  groups  into  a 
natural  series.J 

* Nov.  Org.  Renov.,  p.  274.  t Hist.  Sc.  Id.,  i.  133. 

t Dr.  Whewell,  in  his  reply  ( Philosophy  of  Discovery,  p.  270)  says  that  he  “stopped  short 
of,  or  rather  passed  by,  the  doctrine  of  a series  of  organized  beings,”  because  he  “thought  it 
bad  and  narrow  philosophy.”  If  he  did,  it  was  evidently  without  understanding  this  form  of 
the  doctrine;  for  he  proceeds  to  quote  a passage  from  his  “History,”  in  which  the  doctrine 
he  condemns  is  designated  as  that  of  “ a mere  linear  progression  in  nature,  which  would  place 
each  genus  in  contact  only  with  the  preceding  and  succeeding  ones.”  Now  the  series  treat- 
ed of  in  the  text  agrees  with  this  linear  progression  in  nothing  whatever  but  in  being  a pro- 
gression. 


508 


OPERATIONS  SUBSIDIARY  TO  INDUCTION. 


The  end  of  Classification,  as  an  instrument  for  the  investigation  of  nature, 
is  (as  before  stated)  to  make  us  think  of  those  objects  together  which  have 
the  greatest  number  of  important  common  properties ; and  which,  there- 
fore, we  have  oftenest  occasion,  in  the  course  of  our  inductions,  for  taking 
into  joint  consideration.  Our  ideas  of  objects  are  thus  brought  into  the 
order  most  conducive  to  the  successful  prosecution  of  inductive  inquiries 
generally.  But  when  the  purpose  is  to  facilitate  some  particular  inductive 
inquiry,  more  is  required.  To  be  instrumental  to  that  purpose,  the  classifi- 
cation must  bring  those  objects  together,  the  simultaneous  contemplation 
of  which  is  likely  to  throw  most  light  upon  the  particular  subject.  That 
subject  being  the  laws  of  some  phenomenon  or  some  set  of  connected  phe- 
nomena ; the  very  phenomenon  or  set  of  phenomena  in  question  must  be 
chosen  as  the  groundwork  of  the  classification. 

The  requisites  of  a classification  intended  to  facilitate  the  study  of  a par- 
ticular phenomenon,  are,  first  to  bring  into  one  class  all  Kinds  of  things 
which  exhibit  that  phenomenon,  in  whatever  variety  of  forms  or  degrees  ; 
and,  secondly,  to  arrange  those  Kinds  in  a series  according  to  the  degree  in 
which  they  exhibit  it,  beginning  with  those  which  exhibit  most  of  it,  and 
terminating  with  those  which  exhibit  least.  The  principal  example,  as  yet, 
of  such  a classification,  is  afforded  by  comparative  anatomy  and  physiology, 
from  which,  therefore,  our  illustrations  shall  be  taken. 

§ 2.  The  object  being  supposed  to  be,  the  investigation  of  the  laws  of 
animal  life ; the  first  step,  after  forming  the  most  distinct  conception  of 
the  phenomenon  itself,  possible  in  the  existing  state  of  our  knowledge,  is  to 
erect,  into  one  great  class  (that  of  animals)  all  the  known  Kinds  of  beings 
where  that  phenomenon  presents  itself;  in  however  various  combinations 
with  other  properties,  and  in  however  different  degrees.  As  some  of  these 
Kinds  manifest  the  general  phenomenon  of  animal  life  in  a very  high  de- 
gree, and  others  in  an  insignificant  degree,  barely  sufficient  for  recognition  ; 
we  must,  in  the  next  place,  arrange  the  various  Kinds  in  a series,  following 
one  another  according  to  the  degrees  in  which  they  severally  exhibit  the 
phenomenon  ; beginning  therefore  with  man,  and  ending  with  the  most  im- 
perfect kinds  of  zoophytes. 

This  is  merely  saying  that  we  should  put  the  instances,  from  which  the 
law  is  to  be  inductively  collected,  into  the  order  which  is  implied  in  one  of 
the  four  Methods  of  Experimental  Inquiry  discussed  in  the  preceding  Book  ; 
the  fourth  Method,  that  of  Concomitant  Variations.  As  formerly  remarked, 
this  is  often  the  only  method  to  which  recourse  can  be  had,  with  assurance 
of  a true  conclusion,  in  cases  in  which  we  have  but  limited  means  of  effecting, 
by  artificial  experiments,  a separation  of  circumstances  usually  conjoined. 
The  principle  of  the  method  is,  that  facts  which  increase  or  diminish  to- 
gether, and  disappear  together,  are  either  cause  and  effect,  or  effects  of  a 
common  cause.  When  it  has  been  ascertained  that  this  relation  really  sub- 
sists between  the  variations,  a connection  between  the  facts  themselves  may 
be  confidently  laid  down,  either  as  a law  of  nature  or  only  as  an  empirical 
law,  according  to  circumstances. 

That  the  application  of  this  Method  must  be  preceded  by  the  formation 
of  such  a series  as  we  have  described,  is  too  obvious  to  need  being  pointed 
out;  and  the  mere  arrangement  of  a set  of  objects  in  a series, according  to 

It  would  surely  be  possible  to  arrange  all  places  (for  example)  in  the  order  of  their  distance 
from  the  North  Pole,  though  there  would  be  not  merely  a plurality,  but  a whole  circle  of  places 
at  every  single  gradation  in  the  scale. 


CLASSIFICATION  BY  SERIES. 


509 


the  degrees  in  which  they  exhibit  some  fact  of  which  we  are  seeking  the 
law,  is  too  naturally  suggested  by  the  necessities  of  our  inductive  opera- 
tions, to  require  any  lengthened  illustration  here.  But  there  are  cases  in 
which  the  arrangement  required  for  the  special  purpose  becomes  the  de- 
termining principle  of  the  classification  of  the  same  objects  for  general 
purposes.  This  will  naturally  and  properly  happen,  when  those  laws  of  the 
objects  which  are  sought  in  the  special  inquiry  enact  so  principal  a part  in 
the  general  character  and  history  of  those  objects— exercise  so  much  influ- 
ence in  determining  all  the  phenomena  of  which  they  are  either  the  agents 
or  the  theatre— that  all  other  differences  existing  among  the  objects  are  fit- 
tingly regarded  as  mere  modifications  of  the  one  phenomenon  sought;  ef- 
fects determined  by  the  co-operation  of  some  incidental  circumstance  with 
the  laws  of  that  phenomenon.  Thus  in  the  case  of  animated  beings,  the 
differences  between  one  class  of  animals  and  another  may  reasonably  be 
considered  as  mere  modifications  of  the  general  phenomenon,  animal  life ; 
modifications  arising  either  from  the  different  degrees  in  which  that  phe- 
nomenon is  manifested  in  different  animals,  or  from  the  intermixture  of  the 
effects  of  incidental  causes  peculiar  to  the  nature  of  each,  with  the  effects 
produced  by  the  general  laws  of  life ; those  laws  still  exercising  a predom- 
inant influence  over  the  result.  Such  being  the  case,  no  other  inductive 
inquiry  respecting  animals  can  be  successfully  carried  on,  except  in  sub- 
ordination to  the  great  inquiry  into  the  universal  laws  of  animal  life ; and 
the  classification  of  animals  best  suited  to  that  one  purpose,  is  the  most  suit- 
able to  all  the  other  purposes  of  zoological  science. 

§ 3.  To  establish  a classification  of  this  sort,  or  even  to  apprehend  it 
when  established,  requires  the  power  of  recognizing  the  essential  similarity 
of  a phenomenon,  in  its  minuter  degrees  and  obscurer  forms,  wfith  what  is 
called  the  same  phenomenon  in  the  greatest  perfection  of  its  development ; 
that  is,  of  identifying  with  each  other  all  phenomena  which  differ  only  in 
degree,  and  in  properties  which  we  suppose  to  be  caused  by  difference  of 
degree.  In  order  to  recognize  this  identity,  or,  in  other  words,  this  exact 
similarity  of  quality,  the  assumption  of  a type-species  is  indispensable.  We 
must  consider  as  the  type  of  the  class,  that  among  the  Kinds  included  in 
it,  which  exhibits  the  properties  constitutive  of  the  class,  in  the  highest 
degree ; conceiving  the  other  varieties  as  instances  of  degeneracy,  as  it 
were,  from  that  type ; deviations  from  it  by  inferior  intensity  of  the  char- 
acteristic property  or  properties.  For  every  phenomenon  is  best  studied 
(cceteris  parihits)  where  it  exists  in  the  greatest  intensity.  It  is  there  that 
the  effects  which  either  depend  on  it,  or  depend  on  the  same  causes  with 
it,  will  also  exist  in  the  greatest  degree.  It  is  there,  consequently,  and  only 
there,  that  those  effects  of  it,  or  joint  effects  with  it,  can  become  fully 
known  to  us,  so  that  we  may  learn  to  recognize  their  smaller  degrees,  or 
even  their  mere  rudiments,  in  cases  in  which  the  direct  study  would  have 
been  difficult  or  even  impossible.  Not  to  mention  that  the  phenomenon  in 
its  higher  degrees  may  be  attended  by  effects  or  collateral  circumstances 
which  in  its  smaller  degrees  do  not  occur  at  all,  requiring  for  their  produc- 
tion in  any  sensible  amount  a greater  degree  of  intensity  of  the  cause  than 
is  there  met  with.  In  man,  for  example  (the  species  in  which  both  the 
phenomenon  of  animal  and  that  of  organic  life  exist  in  the  highest  degree), 
many  subordinate  phenomena  develop  themselves  in  the  course  of  his  ani- 
mated existence,  which  the  inferior  varieties  of  animals  do  not  show.  The 
knowledge  of  these  properties  may  nevertheless  be  of  great  avail  toward 


510 


OPERATIONS  SUBSIDIARY  TO  INDUCTION. 


the  discovery  of  the  conditions  and  laws  of  the  general  phenomenon  of  life, 
which  is  common  to  man  with  those  inferior  animals.  And  they  are,  even, 
rightly  considered  as  properties  of  animated  nature  itself;  because  they 
may  evidently  be  affiliated  to  the  general  laws  of  animated  nature ; be- 
cause we  may  fairly  presume  that  some  rudiments  or  feeble  degrees  of 
those  properties  would  be  recognized  in  all  animals  by  more  perfect  or- 
gans, or  even  by  more  perfect  instruments,  than  ours ; and  because  those 
may  be  correctly  termed  properties  of  a class,  which  a thing  exhibits 
exactly  in  proportion  as  it  belongs  to  the  class,  that  is,  in  proportion  as  it 
possesses  the  main  attributes  constitutive  of  the  class. 

§ 4.  It  remains  to  consider  how  the  internal  distribution  of  the  series 
may  most  properly  take  place ; in  what  manner  it  should  be  divided  into 
Orders,  Families,  and  Genera. 

The  main  principle  of  division  must  of  course  be  natural  affinity ; the 
classes  formed  must  be  natural  groups ; and  the  formation  of  these  has  al- 
ready been  sufficiently  treated  of.  But  the  principles  of  natural  grouping 
must  be  applied  in  subordination  to  the  principle  of  a natural  series.  The 
groups  must  not  be  so  constituted  as  to  place  in  the  same  group  things 
which  ought  to  occupy  different  points  of  the  general  scale.  The  precau- 
tion necessary  to  be  observed  for  this  purpose  is,  that  the  primary  divis- 
ions must  be  grounded  not  on  all  distinctions  indiscriminately,  but  on 
those  which  correspond  to  variations  in  the  degree  of  the  main  phenome- 
non. The  series  of  Animated  Nature  should  be  broken  into  parts  at  the 
points  where  the  variation  in  the  degree  of  intensity  of  the  main  phenome- 
non (as  marked  by  its  principal  characters,  Sensation,  Thought,  Voluntary 
Motion,  etc.)  begins  to  be  attended  by  conspicuous  changes  in  the  miscel- 
laneous properties  of  the  animal.  Such  well-marked  changes  take  place, 
for  example,  where  the  class  Mammalia  ends;  at  the  points  where  Fishes 
are  separated  from  Insects,  Insects  from  Mollusca,  etc.  When  so  formed, 
the  primary  natural  groups  will  compose  the  series  by  mere  juxtaposition, 
without  redistribution;  each  of  them  corresponding  to  a definite  portion 
of  the  scale.  In  like  manner  each  family  should,  if  possible,  be  so  subdi- 
vided, that  one  portion  of  it  shall  stand  higher  and  the  other  lower,  though 
of  course  contiguous,  in  the  general  scale;  and  only  when  this  is  impossi- 
ble is  it  allowable  to  ground  the  remaining  subdivisions  on  characters  hav- 
ing no  determinable  connection  with  the  main  phenomenon. 

Where  the  principal  phenomenon  so  far  transcends  in  importance  all 
other  properties  on  which  a classification  could  be  grounded,  as  it  does  in 
the  case  of  animated  existence,  any  considerable  deviation  from  the  rule 
last  laid  down  is  in  general  sufficiently  guarded  against  by  the  first  princi- 
ple of  a natural  arrangement,  that  of  forming  the  groups  according  to  the 
most  important  characters.  All  attempts  at  a scientific  classification  of 
animals,  since  first  their  anatomy  and  physiology  were  successfully  studied, 
have  been  framed  with  a certain  degree  of  instinctive  reference  to  a natu- 
ral series,  and  have  accorded  in  many  more  points  than  they  have  differed, 
with  the  classification  which  would  most  naturally  have  been  grounded  on 
such  a series.  But  the  accordance  has  not  always  been  complete;  and  it 
still  is  often  a matter  of  discussion,  which  of  several  classifications  best  ac- 
cords with  the  true  scale  of  intensity  of  the  main  phenomenon.  Cuvier, 
for  example,  has  been  justly  criticised  for  having  formed  his  natural 
groups,  with  an  undue  degree  of  reference  to  the  mode  of  alimentation,  a 
circumstance  directly  connected  only  with  organic  life,  and  not  leading  to 


CLASSIFICATION  BY  SERIES. 


511 


the  arrangement  most  appropriate  for  the  purposes  of  an  investigation  of 
the  laws  of  animal  life,  since  both  carnivorous  and  herbivorous  or  frugivo- 
rous  animals  are  found  at  almost  every  degree  in  the  scale  of  animal  per- 
fection. Blainville’s  classification  has  been  considered  by  high  authorities 
to  be  free  from  this  defect ; as  representing  correctly,  by  the  mere  order 
of  the  principal  groups,  the  successive  degeneracy  of  animal  nature  from 
its  highest  to  its  most  imperfect  exemplification. 

§ 5.  A classification  of  any  large  portion  of  the  field  of  nature  in  con- 
formity to  the  foregoing  principles,  has  hitherto  been  found  practicable 
only  in  one  great  instance,  that  of  animals.  In  the  case  even  of  vegetables, 
the  natural  arrangement  has  not  been  carried  beyond  the  formation  of  nat- 
ural groups.  Naturalists  have  found,  and  probably  will  continue  to  find  it 
impossible  to  form  those  groups  into  any  series,  the  terms  of  which  corre- 
spond to  real  gradations  in  the  phenomenon  of  vegetative  or  organic  life. 
Such  a difference  of  degree  may  be  traced  between  the  class  of  Vascular 
Plants  and  that  of  Cellular,  which  includes  lichens,  algae,  and  other  sub- 
stances whose  organization  is  simpler  and  more  rudimentary  than  that  of 
the  higher  order  of  vegetables,  and  which  therefore  approach  nearer  to 
mere  inorganic  nature.  But  when  we  rise  much  above  this  point,  we  do 
not  find  any  sufficient  difference  in  the  degree  in  which  different  plants 
possess  the  properties  of  organization  and  life.  The  dicotyledons  are  of 
more  complex  structure,  and  somewhat  more  perfect  organization,  than  the 
monocotyledons;  and  some  dicotyledonous  families,  such  as  the  Composite, 
are  rather  more  complex  in  their  organization  than  the  rest.  But  the  dif- 
ferences are  not  of  a marked  character,  and  do  not  promise  to  throw  any 
particular  light  upon  the  conditions  and  laws  of  vegetable  life  and  develop- 
ment. If  they  did,  the  classification  of  vegetables  would  have  to  be  made, 
like  that  of  animals,  with  reference  to  the  scale  or  series  indicated. 

Although  the  scientific  arrangements  of  organic  nature  afford  as  yet  the 
only  complete  example  of  the  true  principles  of  rational  classification, 
whether  as  to  the  formation  of  groups  or  of  series,  those  principles  are  ap- 
plicable to  all  cases  in  which  mankind  are  called  upon  to  bring  the  various 
parts  of  any  extensive  subject  into  mental  co-ordination.  They  are  as 
much  to  the  point  when  objects  are  to  be  classed  for  purposes  of  art  or 
business,  as  for  those  of  science.  The  proper  arrangement,  for  example,  of 
a code  of  laws,  depends  on  the  same  scientific  conditions  as  the  classifica- 
tions in  natural  history;  nor  could  there  be  a better  preparatory  discipline 
for  that  important  function,  than  the  study  of  the  principles  of  a natural 
arrangement,  not  only  in  the  abstract,  but  in  their  actual  application  to  the 
class  of  phenomena  for  which  they  were  first  elaborated,  and  which  are  still 
the  best  school  for  learning  their  use.  Of  this  the  great  authority  on  codi- 
fication, Bentham,  was  perfectly  aware ; and  his  early  Fragment  on  Gov- 
ernment, the  admirable  introduction  to  a series  of  writings  unequaled  in 
their  department,  contains  clear  and  just  views  (as  far  as  they  go)  on  the 
meaning  of  a natural  arrangement,  such  as  could  scarcely  have  occurred  to 
any  one  who  lived  anterior  to  the  age  of  Linnaeus  and  Bernard  de  Jussieu. 


BOOK  V. 

ON  FALLACIES. 


“ Errare  non  modo  nffirmando  et  negando,  sed  etiam  sentiendo,  et  in  tacita  hominum  cogi- 
tatione  contingit.” — Hobbes,  Computatio  sive  Logica,  chap.  v. 

“ II  leur  semble  qu'il  n’y  a qu’a  douter  par  fantaisie,  et  qn’il  n’y  a qu'a  dire  en  general  que 
notre  nature  est  infirme ; que  notre  esprit  est  plein  d’aveuglement : qu’il  taut  avoir  un  grand 
soin  de  se  de'faire  de  ses  prejuge's,  et  autres  choses  semblables.  Ils  pensent  que  cela  suffit 
pour  ne  plus  se  laisser  se'duire  a ses  sens,  et  pour  ne  plus  se  tromper  du  tout.  II  ne  suffit  pas 
de  dire  que  l’esprit  est  foible,  il  faut  lui  faire  sentir  ses  foiblesses.  Ce  n’est  pas  assez  de  dire 
qu’il  est  sujet  a l’erreur,  il  faut  lui  decouvrir  en  quoi  consistent  ses  erreurs.” — Malebranche, 
Recherche  de  la  Verite. 


CHAPTER  I. 

OF  FALLACIES  IN  GENERAL. 

§ 1.  It  is  a maxim  of  the  school-men,  that  “ contrariorum  eadem  est  sci- 
entia tve  never  really  know  what  a thing  is,  unless  we  are  also  able  to 
give  a sufficient  account  of  its  opposite.  Conformably  to  this  maxim,  one 
considerable  section,  in  most  treatises  on  Logic,  is  devoted  to  the  subject  of 
Fallacies ; and  the  practice  is  too  well  worthy  of  observance,  to  allow  of 
our  departing  from  it.  The  philosophy  of  reasoning,  to  be  complete,  ought 
to  comprise  the  theory  of  bad  as  well  as  of  good  reasoning. 

We  have  endeavored  to  ascertain  the  principles  by  which  the  sufficiency 
of  any  proof  can  be  tested,  and  by  which  the  nature  and  amount  of  evi- 
dence needful  to  prove  any  given  conclusion  can  be  determined  beforehand. 
If  these  principles  were  adhered  to,  then  although  the  number  and  value 
of  the  truths  ascertained  would  be  limited  by  the  opportunities,  or  by  the 
industry,  ingenuity,  and  patience,  of  the  individual  inquirer,  at  least  error 
would  not  be  embraced  instead  of  truth.  But  the  general  consent  of  man- 
kind, founded  on  their  experience,  vouches  for  their  being  far  indeed  from 
even  this  negative  kind  of  perfection  in  the  employment  of  their  reasoning 
powers. 

In  the  conduct  of  life — in  the  practical  business  of  mankind — wrong  infer- 
ences, incorrect  interpretations  of  experience,  unless  after  much  culture  of  the 
thinking  faculty,  are  absolutely  inevitable ; and  with  most  people,  after  the 
highest  degree  of  culture  they  ever  attain,  such  erroneous  inferences,  produ- 
cing corresponding  errors  in  conduct,  are  lamentably  frequent.  Even  in  the 
speculations  to  which  eminent  intellects  have  systematically  devoted  them- 
selves, and  in  reference  to  which  the  collective  mind  of  the  scientific  world  is 
always  at  hand  to  aid  the  efforts  and  correct  the  aberrations  of  individuals, 
it  is  only  from  the  more  perfect  sciences,  from  those  of  which  the  subject- 
matter  is  the  least  complicated,  that  opinions  not  resting  on  a correct  in- 
duction have  at  length,  generally  speaking,  been  expelled.  In  the  depart- 


FALLACIES  IN  GENERAL. 


513 


merits  of  inquiry  relating  to  the  more  complex  phenomena  of  nature,  and 
especially  those  of  which  the  subject  is  man,  whether  as  a moral  and  intel- 
lectual, a social,  or  even  as  a physical  being;  the  diversity  of  opinions  still 
prevalent  among  instructed  persons,  and  the  equal  confidence  with  which 
those  of  the  most  contrary  ways  of  thinking  cling  to  their  respective  ten- 
ets, are  proof  not  only  that  right  modes  of  philosophizing  are  not  yet  gen- 
erally adopted  on  those  subjects,  but  that  wrong  ones  are;  that  inquirers 
have  not  only  in  general  missed  the  truth,  but  have  often  embraced  error; 
that  even  the  most  cultivated  portion  of  our  species  have  not  yet  learned 
to  abstain  from  drawing  conclusions  which  the  evidence  does  not  warrant. 

The  only  complete  safeguard  against  reasoning  ill,  is  the  habit  of  reason- 
ing well ; familiarity  with  the  principles  of  correct  reasoning,  and  practice 
in  applying  those  principles.  It  is,  however,  not  unimportant  to  consider 
what  are  the  most  common  modes  of  bad  reasoning;  by  what  appearances 
the  mind  is  most  likely  to  be  seduced  from  the  observance  of  true  princi- 
ples of  induction ; what,  in  short,  are  the  most  common  and  most  danger- 
ous varieties  of  Apparent  Evidence,  whereby  persons  are  misled  into  opin- 
ions for  which  there  does  not  exist  evidence  really  conclusive. 

A catalogue  of  the  varieties  of  apparent  evidence  which  are  not  real  evi- 
dence, is  an  enumeration  of  Fallacies.  Without  such  an  enumeration,  there- 
fore, the  present  work  would  be  wanting  in  an  essential  point.  And  while 
writers  who  included  in  their  theory  of  reasoning  nothing  more  than  rati- 
ocination, have  in  consistency  with  this  limitation,  confined  their  remarks  to 
the  fallacies  which  have  their  seat  in  that  portion  of  the  process  of  investi- 
gation ; we,  who  profess  to  treat  of  the  whole  process,  must  add  to  our  di- 
rections for  performing  it  rightly,  warnings  against  performing  it  wrongly 
in  any  of  its  parts:  rvhether  the  ratiocinative  or  the  experimental  portion 
of  it  be  in  fault,  or  the  fault  lie  in  dispensing  with  ratiocination  and  induc- 
tion altogether. 

§ 2.  In  considering  the  sources  of  unfounded  inference,  it  is  unnecessa- 
ry to  reckon  the  errors  which  arise,  not  from  a wrong  method,  nor  even 
from  ignorance  of  the  right  one,  but  from  a casual  lapse,  through  hurry  or 
inattention,  in  the  application  of  the  true  principles  of  induction.  Such 
errors,  like  the  accidental  mistakes  in  casting  up  a sum,  do  not  call  for 
philosophical  analysis  or  classification  ; theoretical  considerations  can  throw 
no  light  upon  the  means  of  avoiding  them.  In  the  present  treatise  our  at- 
tention is  required,  not  to  mere  inexpertness  in  performing  the  operation 
in  the  right  way  (the  only  remedies  for  which  are  increased  attention  and 
more  sedulous  practice),  but  to  the  modes  of  performing  it  in  a way  fun- 
damentally wrong;  the  conditions  under  which  the  human  mind  persuades 
itself  that  it  has  sufficient  grounds  for  a conclusion  which  it  has  not  ar- 
rived at  by  any  of  the  legitimate  methods  of  induction — which  it  has  not, 
even  carelessly  or  overhastily,  endeavored  to  test  by  those  legitimate 
methods. 

§ 3.  There  is  another  branch  of  what  may  be  called  the  Philosophy  of 
Error,  which  must  be  mentioned  here,  though  only  to  be  excluded  from 
our  subject.  The  sources  of  erroneous  opinions  are  twofold,  moral  and  in- 
tellectual. Of  these,  the  moral  do  not  fall  within  the  compass  of  this  work. 
They  may  be  classed  under  two  general  heads : Indifference  to  the  attain- 
ment of  truth,  and  Bias;  of  which  last  the  most  common  case  is  that  in 
which  we  are  biased  by  our  wishes ; but  the  liability  is  almost  as  great  to 

33 


514 


FALLACIES. 


the  undue  adoption  of  a conclusion  which  is  disagreeable  to  us,  as  of  one 
which  is  agreeable,  if  it  be  of  a nature  to  bring  into  action  any  of  the 
stronger  passions.  Persons  of  timid  character  are  the  more  predisposed 
to  believe  any  statement,  the  more  it  is  calculated  to  alarm  them.  Indeed 
it  is  a psychological  law,  deducible  from  the  most  general  laws  of  the  men- 
tal constitution  of  man,  that  any  strong  passion  renders  us  credulous  as  to 
the  existence  of  objects  suitable  to  excite  it. 

But  the  moral  causes  of  opinions,  though  with  most  persons  the  most 
powerful  of  all,  are  but  remote  causes ; they  do  not  act  directly,  but  by 
means  of  the  intellectual  causes;  to  which  they  bear  the  same  relation  that 
the  circumstances  called,  in  the  theory  of  medicine,  predisposing  causes, 
bear  to  exciting  causes.  Indifference  to  truth  can  not,  in  and  by  itself, 
produce  erroneous  belief;  it  operates  by  preventing  the  mind  from  collect- 
ing the  proper  evidences,  or  from  applying  to  them  the  test  of  a legitimate 
and  rigid  induction ; by  which  omission  it  is  exposed  unprotected  to  the 
influence  of  any  species  of  apparent  evidence  which  offers  itself  sponta- 
neously, or  which  is  elicited  by  that  smaller  quantity  of  trouble  which  the 
mind  may  be  willing  to  take.  As  little  is  Bias  a direct  source  of  wrong 
conclusions.  We  can  not  believe  a proposition  only  by  wishing,  or  only 
by  dreading,  to  believe  it.  The  most  violent  inclination  to  find  a set  of 
propositions  true,  will  not  enable  the  weakest  of  mankind  to  believe  them 
without  a vestige  of  intellectual  grounds — without  any,  even  apparent,  evi- 
dence. It  acts  indirectly,  by  placing  the  intellectual  grounds  of  belief  in 
an  incomplete  or  distorted  shape  before  his  eyes.  It  makes  him  shrink 
from  the  irksome  labor  of  a rigorous  induction,  when  he  has  a misgiving 
that  its  result  may  be  disagreeable;  and  in  such  examination  as  he  does 
institute,  it  makes  him  exert  that  which  is  in  a certain  measure  voluntary, 
his  attention,  unfairly,  giving  a larger  share  of  it  to  the  evidence  which 
seems  favorable  to  the  desired  conclusion,  a smaller  to  that  which  seems 
unfavorable.  It  operates,  too,  by  making  him  look  out  eagerly  for  reasons, 
or  apparent  reasons,  to  support  opinions  which  are  conformable,  or  resist 
those  which  are  repugnant,  to  his  interests  or  feelings ; and  when  the  in- 
terests or  feelings  are  common  to  great  numbers  of  persons,  reasons  are 
accepted  and  pass  current,  which  would  not  for  a moment  be  listened  to  in 
that  character  if  the  conclusion  had  nothing  more  powerful  than  its  reasons 
to  speak  in  its  behalf.  The  natural  or  acquired  partialities  of  mankind  are 
continually  throwing  up  philosophical  theories,  the  sole  recommendation  of 
which  consists  in  the  premises  they  afford  for  proving  cherished  doctrines, 
or  justifying  favorite  feelings;  and  when  any  one  of  these  theories  has 
been  so  thoroughly  discredited  as  no  longer  to  serve  the  purpose,  another 
is  always  ready  to  takes  its  place.  This  propensity,  when  exercised  in  fa- 
vor of  any  widely-spread  persuasion  or  sentiment,  is  often  decorated  with 
complimentary  epithets;  and  the  contrary  habit  of  keeping  the  judgment 
in  complete  subordination  to  evidence,  is  stigmatized  bv  various  hard  names, 
as  skepticism,  immorality,  coldness,  hard-heartedness,  and  similar  expres- 
sions according  to  the  nature  of  the  case.  But  though  the  opinions  of  the 
generality  of  mankind,  when  not  dependent  on  mere  habit  and  inculcation, 
have  their  root  much  more  in  the  inclinations  than  in  the  intellect,  it  is  a 
necessary  condition  to  the  triumph  of  the  moral  bias  that  it  should  first 
pervert  the  understanding.  Every  erroneous  inference,  though  originating 
in  moral  causes,  involves  the  intellectual  operation  of  admitting  insufficient 
evidence  as  sufficient ; and  whoever  was  on  his  guard  against  all  kinds  of 
inconclusive  evidence  which  can  be  mistaken  for  conclusive,  would  be  in 


CLASSIFICATION  OF  FALLACIES. 


515 


no  danger  of  being  led  into  error  even  by  the  strongest  bias.  There  are 
minds  so  strongly  fortified  on  the  intellectual  side,  that  they  could  not 
blind  themselves  to  the  light  of  truth,  however  really  desirous  of  doing  so ; 
they  could  not,  with  all  the  inclination  in  the  world,  pass  off  upon  them- 
selves bad  arguments  for  good  ones.  If  the  sophisti’y  of  the  intellect  could 
be  rendered  impossible,  that  of  the  feelings,  having  no  instrument  to  work 
with,  would  be  powerless.  A comprehensive  classification  of  all  those 
things  which,  not  being  evidence,  are  liable  to  appear  such  to  the  under- 
standing, will,  therefore,  of  itself  include  all  errors  of  judgment  arising 
from  moral  causes,  to  the  exclusion  only  of  errors  of  practice  committed 
against  better  knowledge. 

To  examine,  then,  the  various  kinds  of  apparent  evidence  which  are  not 
evidence  at  all,  and  of  apparently  conclusive  evidence  which  do  not  really 
amount  to  conclusiveness,  is  the  object  of  that  part  of  our  inquiry  into 
which  we  are  about  to  enter. 

The  subject  is  not  beyond  the  compass  of  classification  and  comprehen- 
sive survey.  The  things,  indeed,  which  are  not  evidence  of  any  given  con- 
clusion, are  manifestly  endless,  and  this  negative  property,  having  no  de- 
pendence on  any  positive  ones,  can  not  be  made  the  groundwork  of  a real 
classification.  But  the  things  which,  not  being  evidence,  are  susceptible 
of  being  mistaken  for  it,  are  capable  of  a classification  having  reference  to 
the  positive  property  which  they  possess  of  appearing  to  be  evidence.  We 
may  arrange  them,  at  our  choice,  on  either  of  two  principles ; according 
to  the  cause  which  makes  them  appear  to  be  evidence,  not  being  so ; or 
according  to  the  particular  kind  of  evidence  which  they  simulate.  The 
Classification  of  Fallacies  which  will  be  attempted  in  the  ensuing  chapter, 
is  founded  on  these  considerations  jointly. 


CHAPTER  II. 

CLASSIFICATION  OF  FALLACIES. 

§ 1.  In  attempting  to  establish  certain  general  distinctions  which  shall 
mark  out  from  one  another  the  various  kinds  of  Fallacious  Evidence,  we 
propose  to  ourselves  an  altogether  different  aim  from  that  of  several  emi- 
nent thinkers,  who  have  given,  under  the  name  of  Political  or  other  Falla- 
cies, a mere  enumeration  of  a certain  number  of  erroneous  opinions ; false 
general  propositions  which  happen  to  be  often  met  with ; loci  communes 
of  bad  arguments  on  some  particular  subject.  Logic  is  not  concerned  with 
the  false  opinions  which  people  happen  to  entertain,  but  with  the  manner 
in  which  they  come  to  entertain  them.  The  question  is  not,  what  facts 
have  at  any  time  been  erroneously  supposed  to  be  proof  of  certain  other 
facts,  but  what  property  in  the  facts  it  was  which  led  any  one  to  this  mis- 
taken supposition. 

When  a fact  is  supposed,  though  incorrectly,  to  be  evidentiary  of,  or 
a mark  of,  some  other  fact,  there  must  be  a cause  of  the  error ; the  sup- 
posed evidentiary  fact  must  be  connected  in  some  particular  manner  with 
the  fact  of  which  it  is  deemed  evidentiary — must  stand  in  some  particular 
relation  to  it,  without  which  relation  it  would  not  be  regarded  in  that  light. 
The  relation  may  either  be  one  resulting  from  the  simple  contemplation  of 
the  two  facts  side  by  side  with  one  another,  or  it  may  depend  on  some 


51G 


FALLACIES. 


process  of  mind,  by  which  a previous  association  has  been  established  be- 
tween them.  Some  peculiarity  of  relation,  however,  there  must  be;  the 
fact  which  can,  even  by  the  wildest  aberration,  be  supposed  to  prove  an- 
other fact,  must  stand  in  some  special  position  with  regard  to  it;  and  if 
we  could  ascertain  and  define  that  special  position,  we  should  perceive  the 
origin  of  the  error. 

We  can  not  regard  one  fact  as  evidentiary  of  another,  unless  we  believe 
that  the  two  are  always,  or  in  the  majority  of  cases,  conjoined.  If  we  be- 
lieve A to  be  evidentiary  of  B,  if  when  we  see  A we  are  inclined  to  infer 
B from  it,  the  reason  is  because  we  believe  that  wherever  A is,  B also  ei- 
ther always  or  for  the  most  part  exists,  either  as  an  antecedent,  a conse- 
quent, or  a concomitant.  If  when  we  see  A we  are  inclined  not  to  expect 
B — if  we  believe  A to  be  evidentiary  of  the  absence  of  B — it  is  because  we 
believe  that  where  A is,  B either  is  never,  or  at  least  seldom,  found.  Er- 
roneous conclusions,  in  short,  no  less  than  correct  conclusions,  have  an  in- 
variable relation  to  a general  formula,  either  expressed  or  tacitly  implied. 
When  we  infer  some  fact  from  some  other  fact  which  does  not  really  prove 
it,  we  either  have  admitted,  or,  if  we  maintained  consistency,  ought  to  ad- 
mit, some  groundless  general  proposition  respecting  the  conjunction  of  the 
two  phenomena. 

For  every  property,  therefore,  in  facts,  or  in  our  mode  of  considering 
facts,  which  leads  us  to  believe  that  they  are  habitually  conjoined  when 
they  are  not,  or  that  they  are  not  when  in  reality  they  are,  there  is  a cor- 
responding kind  of  Fallacy;  and  an  enumeration  of  fallacies  would  consist 
in  a specification  of  those  properties  in  facts,  and  those  peculiarities  in  our 
mode  of  considering  them,  which  give  rise  to  this  erroneous 'opinion. 

§ 2.  To  begin,  then  ; the  supposed  connection,  or  repugnance,  between 
the  two  facts,  may  either  be  a conclusion  from  evidence  (that  is,  from  some 
other  proposition  or  propositions),  or  may  be  admitted  without  any  such 
ground  ; admitted,  as  the  phrase  is,  on  its  own  evidence ; embraced  as  self- 
evident,  as  an  axiomatic  truth.  This  gives  rise  to  the  first  great  distinc- 
tion, that  between  Fallacies  of  Inference  and  Fallacies  of  Simple  Inspec- 
tion. In  the  latter  division  must  be  included  not  only  all  cases  in  which 
a proposition  is  believed  and  held  for  true,  literally  without  any  extrinsic 
evidence,  either  of  specific  experience  or  general  reasoning;  but  those 
more  frequent  cases  in  which  simple  inspection  creates  a presumption  in 
favor  of  a proposition ; not  sufficient  for  belief,  but  sufficient  to  cause  the 
strict  principles  of  a regular  induction  to  be  dispensed  with,  and  creating 
a predisposition  to  believe  it  on  evidence  which  would  be  seen  to  be  in- 
sufficient if  no  such  presumption  existed.  This  class,  comprehending  the 
whole  of  what  may  be  termed  Natural  Prejudices,  and  which  I shall  call 
indiscriminately  Fallacies  of  Simple  Inspection  or  Fallacies  a priori , shall 
be  placed  at  the  head  of  our  list. 

Fallacies  of  Inference,  or  erroneous  conclusions  from  supposed  evidence, 
must  be  subdivided  according  to  the  nature  of  the  apparent  evidence  from 
which  the  conclusions  are  drawn ; or  (what  is  the  same  thing)  according 
to  the  particular  kind  of  sound  argument  which  the  fallacy  in  question 
simulates.  But  there  is  a distinction  to  be  first  drawn,  which  does  not 
answer  to  any  of  the  divisions  of  sound  arguments,  but  arises  out  of  the 
nature  of  bad  ones.  We  may  know  exactly  what  our  evidence  is,  and  yet 
draw  a false  conclusion  from  it;  we  may  conceive  precisely  what  our 
premises  are,  what  alleged  matters  of  fact,  or  general  principles,  are  the 


CLASSIFICATION  OF  FALLACIES. 


517 


foundation  of  our  inference ; and  yet,  because  the  premises  are  false,  or 
because  we  have  inferred  from  them  what  they  will  not  support,  our  con- 
clusion may  be  erroneous.  But  a case,  perhaps  even  more  frequent,  is  that 
in  which  the  error  arises  from  not  conceiving  our  premises  with  due  clear- 
ness, that  is  (as  shown  in  the  preceding  Booh*),  with  due  fixity:  form- 
ing one  conception  of  our  evidence  when  we  collect  or  receive  it,  and  an- 
other when  we  make  use  of  it;  or  unadvisedly, and  in  general  unconscious- 
ly, substituting,  as  we  proceed,  different  premises  in  the  place  of  those 
with  which  we  set  out,  or  a different  conclusion  for  that  which  we  under- 
took to  prove.  This  gives  existence  to  a class  of  fallacies  which  may  be 
justly  termed  (in  a phrase  borrowed  from  Bentliam)  Fallacies  of  Confu- 
sion; comprehending,  among  others,  all  those  which  have  their  source  in 
language,  whether  arising  from  the  vagueness  or  ambiguity  of  our  terms, 
or  from  casual  associations  with  them. 

When  the  fallacy  is  not  one  of  Confusion,  that  is,  when  the  proposition 
believed,  and  the  evidence  on  which  it  is  believed,  are  steadily  apprehended 
and  unambiguously  expressed,  there  remain  to  be  made  two  cross  divisions. 
The  Apparent  Evidence  may  be  either  particular  facts,  or  foregone  general- 
izations; that  is,  the  process  may  simulate  either  simple  Induction  or  De- 
duction; and  again,  the  evidence,  whether  consisting  of  supposed  facts  or 
of  general  propositions,  may  be  false  in  itself,  or,  being  true,  may  fail  to 
bear  out  the  conclusion  attempted  to  be  founded  on  it.  This  gives  us  first, 
Fallacies  of  Induction  and  Fallacies  of  Deduction,  and  then  a subdivision 
of  each  of  these,  according  as  the  supposed  evidence  is  false,  or  true  but  in- 
conclusive. 

Fallacies  of  Induction,  where  the  facts  on  which  the  induction  proceeds 
are  erroneous,  may  be  termed  Fallacies  of  Observation.  The  term  is  not 
strictly  accurate,  or,  rather,  not  accurately  co-extensive  with  the  class  of  fal- 
lacies which  I pi'opose  to  designate  by  it.  Induction  is  not  always  ground- 
ed on  facts  immediately  observed,  but  sometimes  on  facts  inferred ; and 
when  these  last  are  erroneous,  the  error  may  not  be,  in  the  literal  sense  of 
the  term,  an  instance  of  bad  observation,  but  of  bad  inference.  It  will  be 
convenient,  however,  to  make  only  one  class  of  all  the  inductions  of  which 
the  error  lies  in  not  sufficiently  ascertaining  the  facts  on  which  the  theory 
is  grounded  ; whether  the  cause  of  failure  be  malobservation,  or  simple  non- 
observation, and  whether  the  malobservation  be  direct,  or  by  means  of  in- 
termediate marks  which  do  not  prove  what  they  are  supposed  to  prove. 
And  in  the  absence  of  any  comprehensive  term  to  denote  the  ascertainment, 
by  whatever  means,  of  the  facts  on  which  an  induction  is  grounded,  I will 
venture  to  retain  for  this  class  of  fallacies,  under  the  explanation  now  given, 
the  title  of  Fallacies  of  Observation. 

The  other  class  of  inductive  fallacies,  in  which  the  facts  are  correct,  but 
the  conclusion  not  warranted  by  them,  are  properly  denominated  Fallacies 
of  Generalization;  and  these,  again, fall  into  various  subordinate  classes  or 
natural  groups,  some  of  which  will  be  enumerated  in  their  proper  place. 

When  we  now  turn  to  Fallacies  of  Deduction,  namely  those  modes  of  in- 
correct argumentation  in  which  the  premises,  or  some  of  them,  are  general 
propositions,  and  the  argument  a ratiocination ; we  may  of  course  subdi- 
vide these  also  into  two  species  similar  to  the  two  preceding,  namely,  those 
which  proceed  on  false  premises,  and  those  of  which  the  premises,  though 
true,  do  not  support  the  conclusion.  But  of  these  species,  the  first  must 


Supra,  p.  137. 


518 


FALLACIES. 


necessarily  fall  under  some  one  of  the  heads  already  enumerated.  For  the 
error  must  be  either  in  those  premises  which  are  general  propositions,  or  in 
those  which  assert  individual  facts.  In  the  former  case  it  is  an  Inductive 
Fallacy,  of  one  or  the  other  class;  in  the  latter  it  is  a Fallacy  of  Observa- 
tion ; unless,  in  either  case,  the  erroneous  premise  has  been  assumed  on 
simple  inspection,  in  which  case  the  fallacy  is  a priori.  Or,  finally,  the  prem- 
ises, of  whichever  kind  they  are,  may  never  have  been  conceived  in  so  dis- 
tinct a manner  as  to  produce  any  clear  consciousness  by  what  means  they 
were  arrived  at;  as  in  the  case  of  what  is  called  reasoning  in  a circle;  and 
then  the  fallacy  is  one  of  Confusion. 

There  remain,  therefore,  as  the  only  class  of  fallacies  having  properly 
their  seat  in  deduction,  those  in  which  the  premises  of  the  ratiocination  do 
not  bear  out  its  conclusion ; the  various  cases,  in  short,  of  vicious  argu- 
mentation, provided  against  by  the  rules  of  the  syllogism.  We  shall  call 
these,  Fallacies  of  Ratiocination. 

We  have  thus  five  distinguishable  classes  of  fallacy,  which  may  be  ex- 
pressed in  the  following  synoptic  table : 


Fallacies 


of  Simple  Inspection 1.  Fallacies  a priori. 

f Inductive  ( 2.  Fallacies  of  Observation. 


rfrom  evidence  dis 

tinctly  conceived.,  'j  Deductive|  4 

of  Inference  <|  h Fallacies) 


j Fallacies  ( 3.  Fallacies  of  Generalization. 

Fallacies  of  Ratiocination. 


from  evidence  indis 
tinctly  conceived 


-} 


.5.  Fallacies  of  Confusion. 


§ 3.  We  must  not,  however,  expect  to  find  that  men’s  actual  errors  al- 
ways, or  even  commonly,  fall  so  unmistakably  under  some  one  of  these 
classes,  as  to  be  incapable  of  being  referred  to  any  other.  Erroneous  ar- 
guments do  not  admit  of  such  a sharply  cut  division  as  valid  arguments 
do.  An  argument  fully  stated,  with  all  its  steps  distinctly  set  out,  in  lan- 
guage not  susceptible  of  misunderstanding,  must,  if  it  be  erroneous,  be  so 
in  some  one  of  these  five  modes  unequivocally ; or  indeed  of  the  first  four, 
since  the  fifth,  on  such  a supposition,  would  vanish.  But  it  is  not  in  the 
nature  of  bad  reasoning  to  express  itself  thus  unambiguously.  When  a 
sophist,  whether  he  is  imposing  on  himself  or  attempting  to  impose  on  oth- 
ers; can  be  constrained  to  throw  his  sophistry  into  so  distinct  a form,  it 
needs,  in  a large  proportion  of  cases,  no  further  exposure. 

In  all  arguments,  everywhere  but  in  the  schools,  some  of  the  links  are 
suppressed  ; a fortiori  when  the  arguer  either  intends  to  deceive,  or  is  a 
lame  and  inexpert  thinker,  little  accustomed  to  bring  his  reasoning  proc- 
esses to  any  test;  and  it  is  in  those  steps  of  the  reasoning  which  are  made 
in  this  tacit  and  half-conscious,  or  even  wholly  unconscious  manner,  that 
the  error  oftenest  lurks.  In  order  to  detect  the  fallacy,  the  proposition 
thus  silently  assumed  must  be  supplied;  but  the  reasoner, most  likely, has 
never  really  asked  himself  what  he  was  assuming;  his  confuter,  unless  per- 
mitted to  extort  it  from  him  by  the  Socratic  mode  of  interrogation,  must 
himself  judge  what  the  suppressed  premise  ought  to  be  in  order  to  support 
the  conclusion.  And  hence,  in  the  words  of  Archbishop  Whately,  “ it  must 
be  often  a matter  of  doubt,  or,  rather,  of  arbitrary  choice,  not  only  to  which 
genus  each  lcind  of  fallacy  should  be  referred,  but  even  to  which  kind  to 
refer  any  one  individual  fallacy ; for  since,  in  any  course  of  argument,  one 
premise  is  usually  suppressed,  it  frequently  happens  in  the  case  of  a fallacy, 
that  the  hearers  are  left  to  the  alternative  of  supplying  either  a premise 


CLASSIFICATION  OF  FALLACIES. 


519 


which  is  not  true , or  else,  one  which  does  not  prove  the  conclusion  ; e.  g.,  if 
a man  expatiates  on  the  distress  of  the  country,  and  thence  argues  that  the 
government  is  tyrannical, we  must  suppose  him  to  assume  either  that  ‘ev- 
ery distressed  country  is  under  a tyranny,’  which  is  a manifest  falsehood, 
or  merely  that  ‘every  country  under  a tyranny  is  distressed,’  which,  how- 
ever true,  proves  nothing,  the  middle  term  being  undistributed.”  The  for- 
mer would  be  ranked,  in  our  distribution,  among  fallacies  of  generalization, 
the  latter  among  those  of  ratiocination.  “ Which  are  wtc  to  suppose  the 
speaker  meant  us  to  understand  ? Surely  ” (if  he  understood  himself)  “ just 
whichever  each  of  his  hearers  might  happen  to  prefer:  some  might  assent 
to  the  false  premise;  others  allow  the  unsound  syllogism.” 

Almost  all  fallacies,  therefore,  might  in  strictness  be  brought  under  our 
fifth  class,  Fallacies  of  Confusion.  A fallacy  can  seldom  be  absolutely  re- 
ferred to  any  of  the  other  classes ; we  can  only  say,  that  if  all  the  links 
were  filled  up  which  should  be  capable  of  being  supplied  in  a valid  argu- 
ment, it  would  either  stand  thus  (forming  a fallacy  of  one  class),  or  thus  (a 
fallacy  of  another) ; or  at  furthest  we  may  say,  that  the  conclusion  is  most 
likely  to  have  originated  in  a fallacy  of  such  and  such  a class.  Thus,  in 
the  illustration  just  quoted,  the  error  committed  may  be  traced  with  most 
probability  to  a fallacy  of  generalization  ; that  of  mistaking  an  uncertain 
mark,  or  piece  of  evidence,  for  a certain  one ; concluding  from  an  effect  to 
some  one  of  its  possible  causes,  wdien  there  are  others  which  would  have 
been  equally  capable  of  producing  it. 

Yet,  though  the  five  classes  run  into  each  other,  and  a particular  error 
often  seems  to  be  arbitrarily  assigned  to  one  of  them  rather  than  to  any 
of  the  rest,  there  is  considerable  use  in  so  distinguishing  them.  We  shall 
find  it  convenient  to  set  apart,  as  Fallacies  of  Confusion,  those  of  which 
confusion  is  the  most  obvious  characteristic ; in  which  no  other  cause  can 
be  assigned  for  the  mistake  committed,  than  neglect  or  inability  to  state 
the  question  properly,  and  to  apprehend  the  evidence  with  definiteness  and 
precision.  In  the  remaining  four  classes  I shall  place  not  only  the  cases  in 
which  the  evidence  is  clearly  seen  to  be  what  it  is,  and  yet  a wrong  conclu- 
sion drawn  from  it,  but  also  those  in  which,  although  there  be  confusion, 
the  confusion  is  not  the  sole  cause  of  the  error,  but  there  is  some  shadow 
of  a ground  for  it  in  the  nature  of  the  evidence  itself.  And  in  distribu- 
ting these  cases  of  partial  confusion  among  the  four  classes,  I shall,  when 
there  can  be  any  hesitation  as  to  the  precise  seat  of  the  fallacy,  suppose  it 
to  be  in  that  part  of  the  process  in  which,  from  the  nature  of  the  case,  and 
the  tendencies  of  the  human  mind,  an  error  would  in  the  particular  circum- 
stances be  the  most  probable. 

After  these  observations  we  shall  proceed,  without  further  pi’eamble,  to 
consider  the  five  classes  in  their  order. 


520 


FALLACIES. 


CHAPTER  III. 

FALLACIES  OF  SIMPLE  INSPECTION;  OR  A PRIORI  FALLACIES. 

§ 1.  The  tribe  of  errors  of  which  we  are  to  treat  in  the  first  instance, 
are  those  in  which  no  actual  inference  takes  place  at  all;  the  proposition 
(it  can  not  in  such  cases  be  called  a conclusion)  being  embraced,  not  as 
proved,  but  as  requiring  no  proof  ; as  a self-evident  truth  ; or  else  as  hav- 
ing such  intrinsic  verisimilitude,  that  external  evidence  not  in  itself  amount- 
ing to  proof,  is  sufficient  in  aid  of  the  antecedent  presumption. 

An  attempt  to  treat  this  subject  comprehensively  would  be  a trails 
gression  of  the  bounds  prescribed  to  this  work,  since  it  would  necessitate 
the  inquiry  which,  more  than  any  other,  is  the  grand  question  of  what  is 
called  metaphysics,  viz.,  What  are  the  propositions  which  may  reasonably 
be  received  without  proof  ? That  there  must  be  some  such  propositions 
all  are  agreed,  since  there  can  not  be  an  infinite  series  of  proof,  a chain  sus- 
pended from  nothing.  But  to  determine  what  these  propositions  are,  is 
the  opus  magnum  of  the  more  recondite  mental  philosophy.  Two  prin- 
cipal divisions  of  opinion  on  the  subject  have  divided  the  schools  of  phi- 
losophy from  its  first  dawn.  The  one  recognizes  no  ultimate  premises  but 
the  facts  of  our  subjective  consciousness;  our  sensations,  emotions,  intellect- 
ual states  of  mind,  and  volitions.  These,  and  whatever  by  strict  rules  of 
induction  can  be  derived  from  these,  it  is  possible,  according  to  this  theory, 
for  us  to  know ; of  all  else  we  must  remain  in  ignorance.  The  opposite 
school  hold  that  there  are  other  existences,  suggested  indeed  to  our  minds 
by  these  subjective  phenomena,  but  not  inferable  from  them,  by  any  proc- 
ess either  of  deduction  or  of  induction;  which,  however,  we  must,  by  the 
constitution  of  our  mental  nature,  recognize  as  realities;  and  realities,  too, 
of  a higher  order  than  the  phenomena  of  our  consciousness,  being  the  ef- 
ficient causes  and  necessary  substrata  of  all  Phenomena.  Among  these 
entities  they  reckon  Substances,  whether  matter  or  spirit;  from  the  dust 
under  our  feet  to  the  soul,  and  from  that  to  Deity.  All  these,  according  to 
them,  are  preternatural  or  'supernatural  beings,  having  no  likeness  in  expe- 
rience, though  experience  is  entirely  a manifestation  of  their  agency.  Their 
existence,  together  with  more  or  less  of  the  laws  to  which  they  conform  in 
their  operations,  are,  on  this  theory,  apprehended  and  recognized  as  real  by 
the  mind  itself  intuitively;  experience  (whether  in  the  form  of  sensation 
or  of  mental  feeling)  having  no  other  part  in  the  matter  than  as  affording 
facts  which  are  consistent  with  these  necessary  postulates  of  reason,  and 
which  are  explained  and  accounted  for  by  them. 

As  it  is  foreign  to  the  purpose  of  the  present  treatise,  to  decide  between 
these  conflicting  theories,  we  are  precluded  from  inquiring  into  the  exist- 
ence, or  defining  the  extent  and  limits,  of  knowledge  a priori,  and  from 
characterizing  the  kind  of  correct  assumption  which  the  fallacy  of  incorrect 
assumption,  now  under  consideration,  simulates.  Yet  since  it  is  allowed 
on  botli  sides  that  such  assumptions  are  often  made  improperly,  we  may 
find  it  practicable,  without  entering  into  the  ultimate  metaphysical  grounds 
of  the  discussion,  to  state  some  speculative  propositions,  and  suggest  some 


FALLACIES  OF  SIMPLE  INSPECTION. 


521 


practical  cautions,  respecting  the  forms  in  which  such  unwarranted  assump- 
tions are  most  likely  to  be  made. 

§ 2.  In  the  cases  in  which,  according  to  the  thinkers  of  the  ontological 
school,  the  mind  apprehends,  by  intuition,  things,  and  the  laws  of  things, 
not  cognizable  by  our  sensitive  faculty;  those  intuitive,  or  supposed  intui- 
tive, perceptions  are  undistinguishable  from  what  the  opposite  school  are 
accustomed  to  call  ideas  of  the  mind.  When  they  themselves  say  that  they 
perceive  the  things  by  an  immediate  act  of  a faculty  given  for  that  purpose 
by  their  Creator,  it  would  be  said  of  them  by  their  opponents  that  they 
find  an  idea  or  conception  in  their  own  minds,  and  from  the  idea  or  concep- 
tion,-infer  the  existence  of  a corresponding  objective  reality.  Nor  would 
this  be  an  unfair  statement,  but  a mere  version  into  other  words  of  the  ac- 
count given  by  many  of  themselves  ; and  one  to  which  the  more  clear- 
sighted of  them  might,  and  generally  do,  without  hesitation,  subscribe. 
Since,  therefore,  in  the  cases  which  lay  the  strongest  claims  to  be  examples 
of  knowledge  a priori,  the  mind  proceeds  from  the  idea  of  a thing  to  the 
reality  of  the  thing  itself,  we  can  not  be  surprised  by  finding  that  illicit 
assumptions  a priori  consist  in  doing  the  same  thing  erroneously;  in  mis- 
taking subjective  facts  for  objective,  laws  of  the  percipient  mind  for  laws 
of  the  perceived  object,  properties  of  the  ideas  or  conceptions  for  proper- 
ties of  the  things  conceived. 

Accordingly,  a large  proportion  of  the  erroneous  thinking  which  exists 
in  the  world  proceeds  on  a tacit  assumption,  that  the  same  order  must  ob- 
tain among  the  objects  in  nature  which  obtains  among  our  ideas  of  them. 
That  if  we  always  think  of  two  things  together,  the  two  things  must  al- 
ways exist  together.  That  if  one  thing  makes  us  think  of  another  as  pre- 
ceding or  following  it,  that  other  must  precede  it  or  follow  it  in  actual 
fact.  And  conversely,  that  when  we  can  not  conceive  two  things  together 
they  can  not  exist  together,  and  that  their  combination  may,  without  fur- 
ther evidence,  be  rejected  from  the  list  of  possible  occurrences. 

Few  persons,  I am  inclined  to  think,  have  reflected  on  the  great  extent 
to  which  this  fallacy  has  prevailed,  and  prevails,  in  the  actual  beliefs  and 
actions  of  mankind.  For  a first  illustration  of  it  we  may  refer  to  a large 
class  of  popular  superstitions.  If  any  one  will  examine  in  what  circum- 
stances most  of  those  things  agree,  which  in  different  ages  and  by  differ- 
ent portions  of  the  human  race  have  been  considered  as  omens  or  prognos- 
tics of  some  interesting  event,  whether  calamitous  or  fortunate;  they  will 
be  found  very  generally  characterized  by  this  peculiarity,  that  they  cause 
the  mind  to  think  of  that,  of  which  they  are  therefore  supposed  to  forbode 
the  actual  occurrence.  “Talk  of  the  devil  and  he  will  appear,”  has  passed 
into  a proverb.  Talk  of  the  devil,  that  is,  raise  the  idea,  and  the  reality 
will  follow.  In  times  when  the  appearance  of  that  personage  in  a visible 
form  was  thought  to  be  no  unfrequent  occurrence,  it  has  doubtless  often 
happened  to  persons  of  vivid  imagination  and  susceptible  nerves,  that  talk- 
ing of  the  devil  has  caused  them  to  fancy  they  saw  him ; as,  even  in  our 
more  incredulous  days,  listening  to  ghost  stories  predisposes  us  to  see 
ghosts ; and  thus,  as  a prop  to  the  a priori  fallacy,  there  might  come  to  be 
added  an  auxiliary  fallacy  of  malobservation,  with  one  of  false  generaliza- 
tion grounded  on  it.  Fallacies  of  different  orders  often  herd  or  cluster  to- 
gether in  this  fashion,  one  smoothing  the  way  for  another.  But  the  origin 
of  the  superstition  is  evidently  that  which  we  have  assigned.  In  like  man- 
ner, it  has  been  universally  considered  unlucky  to  speak  of  misfortune. 


522 


FALLACIES. 


The  day  on  which  any  calamity  happened  lias  been  considered  an  unfor- 
tunate day,  and  there  has  been  a feeling  everywhere,  and  in  some  nations 
a religious  obligation,  against  transacting  any  important  business  on  that 
day.  For  on  such  a day  our  thoughts  are  likely  to  be  of  misfortune.  For 
a similar  reason,  any  untoward  occurrence  in  commencing  an  undertaking 
has  been  considered  ominous  of  failure ; and  often,  doubtless,  has  really 
contributed  to  it  by  putting  the  persons  engaged  in  the  enterprise  more  or 
less  out  of  spirits  ; but  the  belief  has  equally  prevailed  where  the  disagree- 
able circumstance  was,  independently  of  superstition,  too  insignificant  to 
depress  the  spirits  by  any  influence  of  its  own.  All  know  the  story  of 
Ctesar’s  accidentally  stumbling  in  the  act  of  landing  on  the  African  coast; 
and  the  presence  of  mind  with  which  he  converted  the  direful  presage  into 
a favorable  one  by  exclaiming,  “Africa,  I embrace  thee.”  Such  omens,  it 
is  true,  were  often  conceived  as  warnings  of  the  future,  given  by  a friendly 
or  a hostile  deity;  but  this  very  superstition  grew  out  of  a pre-existing 
tendency;  the  god  was  supposed  to  send,  as  an  indication  of  what  was  to 
come,  something  which  people  were  already  disposed  to  consider  in  that 
light.  So  in  the  case  of  lucky  or  unlucky  names.  Herodotus  tells  us  how 
the  Greeks,  on  the  way  to  Mycale,  were  encouraged  in  their  enterprise  by 
the  arrival  of  a deputation  from  Samos,  one  of  the  members  of  which  was 
named  Hegesistratus,  the  leader  of  armies. 

Cases  may  be  pointed  out  in  which  something  which  could  have  no  real 
effect  but  to  make  persons  think  of  misfortune,  was  regarded  not  merely 
as  a prognostic,  but  as  something  approaching  to  an  actual  cause  of  it. 
The  £vfpi)i.iEi  of  the  Greeks,  and  favete  Unguis , or  bona  verba  queeso,  of  the 
Romans,  evince  the  care  with  which  they  endeavored  to  repress  the  utter- 
ance of  any  word  expressive  or  suggestive  of  ill  fortune ; not  from  notions 
of  delicate  politeness,  to  which  their  general  mode  of  conduct  and  feeling 
had  very  little  reference,  but  from  bona  fide  alarm  lest  the  event  so  sug- 
gested to  the  imagination  should  in  fact  occur.  Some  vestige  of  a similar 
superstition  has  been  known  to  exist  among  uneducated  persons  even  in 
our  own  day : it  is  thought  an  unchristian  thing  to  talk  of,  or  suppose,  the 
death  of  any  person  while  he  is  alive.  It  is  known  how  careful  the  Ro- 
mans were  to  avoid,  by  an  indirect  mode  of  speech,  the  utterance  of  any 
word  directly  expressive  of  death  or  other  calamity;  how  instead  of  mor- 
tuns  est  they  said  vixit / and  “be  the  event  fortunate  or  otherwise''’'  instead 
of  adverse.  The  name  Maleventum,  of  which  Salmasius  so  sagaciously  de- 
tected the  Thessalian  origin  (MaXbae,  MaXoAroe),  they  changed  into  the 
highly  propitious  denomination,  Beneventum ; Egesta  into  Segesta;  and 
Epidanmus,  a name  so  interesting  in  its  associations  to  the  reader  of  Thu- 
cydides, they  exchanged  for  Dyrrhachium,  to  escape  the  perils  of  a word 
suggestive  of  damnum  or  detriment. 

“ If  a hare  cross  the  highway,”  says  Sir  Thomas  Browne,*  “ there  are 
few  above  threescore  that  are  not  perplexed  thereat;  which  notwithstand- 
ing is  but  an  augurial  terror,  according  to  that  received  expression,  Inau- 
spicatum  dot  iter  oblatus  lepus.  And  the  ground  of  the  conceit  was  prob- 
ably no  greater  than  this,  that  a fearful  animal  passing  by  us  portended 
unto  us  something  to  be  feared;  as  upon  the  like  consideration  the  meet- 
ing of  a fox  presaged  some  future  imposture.”  Such  superstitions  as  these 
last  must  be  the  result  of  study  ; they  are  too  recondite  for  natural  or  spon- 
taneous growth.  But  when  the  attempt  was  once  made  to  construct  a 


Vulgar  Errors , book  v.,  chap.  21. 


FALLACIES  OF  SIMPLE  INSPECTION. 


523 


science  of  predictions,  any  association,  though  ever  so  faint  or  remote,  by 
which  an  object  could  be  connected  in  however  far-fetched  a manner  with 
ideas  either  of  prosperity  or  of  danger  and  misfortune,  was  enough  to  de- 
termine its  being  classed  among  good  or  evil  omens. 

An  example  of  rather  a different  kind  from  any  of  these,  but  falling  un- 
der the  same  principle,  is  the  famous  attempt  on  which  so  much  labor  and 
ingenuity  were  expended  by  the  alchemists,  to  make  gold  potable.  The 
motive  to  this  was  a conceit  that  potable  gold  could  be  no  other  than  the 
universal  medicine ; and  why  gold  ? Because  it  was  so  precious.  It  must 
have  all  marvelous  properties  as  a physical  substance,  because  the  mind 
was  already  accustomed  to  marvel  at  it. 

From  a similar  feeling,  “every  substance,”  says  Dr.  Paris,*  “whose  ori- 
gin is  involved  in  mystery,  has  at  different  times  been  eagerly  applied  to 
the  purposes  of  medicine.  Not  long  since,  one  of  those  showers  which  are 
now  known  to  consist  of  the  excrements  of  insects,  fell  in  the  north  of 
Italy ; the  inhabitants  regarded  it  as  manna,  or  some  supernatural  panacea, 
and  they  swallowed  it  with  such  avidity,  that  it  was  only  by  extreme  ad- 
dress that  a small  quantity  was  obtained  for  a chemical  examination.” 
The  superstition,  in  this  instance,  though  doubtless  partly  of  a religious 
character,  probably  in  part  also  arose  from  the  prejudice  that  a 'wonderful 
thing  must  of  course  have  wonderful  properties. 

§ 3.  The  instances  of  a priori  fallacy  which  we  have  hitherto  cited  be- 
long to  the  class  of  vulgar  errors,  and  do  not  now,  nor  in  any  but  a rude 
age  ever  could,  impose  upon  minds  of  any  considerable  attainments.  But 
those  to  which  we  are  about  to  proceed,  have  been,  and  still  are,  all  but 
universally  prevalent  among  thinkers.  The  same  disposition  to  give  ob- 
jectivity to  a law  of  the  mind — to  suppose  that  what  is  true  of  our  ideas 
of  things  must  be  true  of  the  things  themselves — exhibits  itself  in  many  of 
the  most  accredited  modes  of  philosophical  investigation,  both  on  physical 
and  on  metaphysical  subjects.  In  one  of  its  most  undisguised  manifesta- 
tions, it  embodies  itself  in  two  maxims,  which  lay  claim  to  axiomatic  truth  : 
Things  w’hich  we  can  not  think  of  together,  can  not  co-exist ; and  Things 
which  we  can  not  help  thinking  of  together,  must  co-exist.  I am  not  sure 
that  the  maxims  were  ever  expressed  in  these  precise  words,  but  the  his- 
tory both  of  philosophy  and  of  popular  opinions  abounds  with  exemplifica- 
tions of  both  forms  of  the  doctrine. 

To  begin  with  the  latter  of  them : Things  which  we  can  not  think  of 
except  together,  must  exist  together.  This  is  assumed  in  the  generally 
received  and  accredited  mode  of  reasoning  which  concludes  that  A must 
accompany  B in  point  of  fact,  because  “ it  is  involved  in  the  idea.”  Such 
thinkers  do  not  reflect  that  the  idea,  being  a result  of  abstraction,  ought  to 
conform  to  the  facts,  and  can  not  make  the  facts  conform  to  it.  The  ar- 
gument is  at  most  admissible  as  an  appeal  to  authority ; a surmise,  that 
what  is  now  part  of  the  idea,  must,  before  it  became  so,  have  been  found 
by  previous  inquirers  in  the  facts.  Nevertheless,  the  philosopher  who 
more  than  all  others  made  professions  of  rejecting  authority,  Descartes, 
constructed  his  system  on  this  very  basis.  His  favorite  device  for  arriving 
at  truth,  even  in  regard  to  outward  things,  was  by  looking  into  his  own 
mind  for  it.  “ Credidi  me,”  says  his  celebrated  maxim,  “ pro  regula  ge- 
nerali  sumere  posse,  omne  id  quod  valde  dilucide  et  distincte  concipiebam. 


Pharmacologia,  Historical  Introduction,  p.  16. 


524 


FALLACIES. 


verum  osse whatever  can  be  very  clearly  conceived  must  certainly  exist ; 
that  is,  as  he  afterward  explains  it,  if  the  idea  includes  existence.  And  on 
this  ground  he  infers  that  geometrical  figures  really  exist,  because  they 
can  be  distinctly  conceived.  Whenever  existence  is  “ involved  in  an  idea,” 
a thing  conformable  to  the  idea  must  really  exist;  which  is  as  much  as  to 
say,  whatever  the  idea  contains  must  have  its  equivalent  in  the  thing;  and 
what  we  are  not  able  to  leave  out  of  the  idea  can  not  be  absent  from  the 
reality.*  This  assumption  pervades  the  philosophy  not  only  of  Descartes, 
but  of  all  the  thinkers  who  received  their  impulse  mainly  from  him,  in  par- 
ticular the  two  most  remarkable  among  them,  Spinoza  and  Leibnitz,  from 
whom  the  modern  German  metaphysical  philosophy  is  essentially  an  ema- 
nation. I am  indeed  disposed  to  think  that  the  fallacy  now  under  consid- 
eration has  been  the  cause  of  two-thirds  of  the  bad  philosophy,  and  espe- 
cially of  the  bad  metaphysics,  which  the  human  mind  has  never  ceased  to 
produce.  Our  general  ideas  contain  nothing  but  what  has  been  put  into 
them,  either  by  our  passive  experience,  or  by  our  active  habits  of  thought; 
and  the  metaphysicians  in  all  ages,  who  have  attempted  to  construct  the 
laws  of  the  universe  by  reasoning  from  our  supposed  necessities  of  thought, 
have  always  proceeded,  and  only  could  proceed,  by  laboriously  finding  in 
their  own  minds  what  they  themselves  had  formerly  put  there,  and  evolv- 
ing from  their  ideas  of  things  what  they  had  first  involved  in  those  ideas. 
In  this  way  all  deeply-rooted  opinions  and  feelings  are  enabled  to  create 
apparent  demonstrations  of  their  truth  and  reasonableness,  as  it  were,  out 
of  their  own  substance. 

The  other  form  of  the  fallacy:  Things  which  we  can  not  think  of  to- 
gether can  not  exist  together — including  as  one  of  its  branches,  that  what 
we  can  not  think  of  as  existing  can  not  exist  at  all — may  thus  be  briefly 
expressed  : Whatever  is  inconceivable  must  be  false. 

Against  this  prevalent  doctrine  I have  sufficiently  argued  in  a former 
Book,f  and  nothing  is  required  in  this  place  but  examples.  It  was  long 
held  that  Antipodes  were  impossible  because  of  the  difficulty  which  was 
found  in  conceiving  persons  with  their  heads  in  the  same  direction  as  our 
feet.  And  it  was  one  of  the  received  arguments  against  the  Copernican 
system,  that  we  can  not  conceive  so  great  a void  space  as  that  system  sup- 
poses to  exist  in  the  celestial  regions.  When  men’s  imaginations  had  al- 
ways been  used  to  conceive  the  stars  as  firmly  set  in  solid  spheres,  they 
naturally  found  much  difficulty  in  imagining  them  in  so  different,  and,  as 
it  doubtless  appeared  to  them,  so  precarious  a situation.  But  they  had  no 
right  to  mistake  the  limitation  (whether  natural,  or,  as  it  in  fact  proved, 
only  artificial)  of  their  own  faculties,  for  an  inherent  limitation  of  the  pos- 
sible modes  of  existence  in  the  universe. 

It  may  be  said  in  objection,  that  the  error  in  these  cases  was  in  the 
minor  premise,  not  the  major;  an  error  of  fact,  not  of  principle;  that  it 
did  not  consist  in  supposing  that  what  is  inconceivable  can  not  be  true,  but 

* The  author  of  one  of  the  Bridgewater  Treatises  has  fallen,  ns  it  seems  to  me,  into  a simi- 
lar fallacy  when,  after  arguing  in  rather  a curious  way  to  prove  that  matter  may  exist  with- 
out any  of  the  known  properties  of  matter,  and  may  therefore  be  changeable,  he  concludes 
that  it  can  not  be  eternal,  because  “eternal  (passive)  existence  necessarily  involves  incapa- 
bility of  change.”  I believe  it  would  be  difficult  to  point  out  any  other  connection  between 
the  facts  of  eternity  and  unchangeableness,  than  a strong  association  between  the  two  ideas. 
Most  of  the  a priori  arguments,  both  religious  and  anti-religious,  on  the  origin  of  things,  are 
fallacies  drawn  from  the  same  source. 

t Supra,  book  ii. , chap,  v.,  § 6,  and  chap,  vii.,  § 1,  2,  3,  4.  See  also  Examination  of  Sir 
William  Hamilton  s Philosophy,  chap.  vi.  and  elsewhere. 


FALLACIES  OF  SIMPLE  INSPECTION. 


525 


in  supposing  antipodes  to  be  inconceivable,  when  present  experience  proves 
that  they  can  be  conceived.  Even  if  this  objection  were  allowed,  and  the 
proposition  that  what  is  inconceivable  can  not  be  true  were  suffered  to 
remain  unquestioned  as  a speculative  truth,  it  would  be  a truth  on  which 
no  practical  consequence  could  ever  be  founded,  since,  on  this  showing, 
it  is  impossible  to  affirm  of  any  proposition,  not  being  a contradiction  in 
terms,  that  it  is  inconceivable.  Antipodes  were  really,  not  fictitiously,  in- 
conceivable to  our  ancestors:  they  are  indeed  conceivable  to  us;  and  as 
the  limits  of  our  power  of  conception  have  been  so  largly  extended,  by  the 
extension  of  our  experience  and  the  more  varied  exercise  of  our  imagina- 
tion, so  may  posterity  find  many  combinations  perfectly  conceivable  to 
them  which  are  inconceivable  to  us.  But,  as  beings  of  limited  experience, 
we  must  always  and  necessarily  have  limited  conceptive  powers ; while  it 
does  not  by  any  means  follow  that  the  same  limitation  obtains  in  the  pos- 
sibilities of  Nature,  nor  even  in  her  actual  manifestations. 

Rather  more  than  a century  and  a half  ago  it  was  a scientific  maxim, 
disputed  by  no  one,  and  which  no  one  deemed  to  require  any  proof,  that 
“a  thing  can  not  act  where  it  is  not.”*  With  this  weapon  the  Cartesians 
waged  a formidable  war  against  the  theory  of  gravitation,  which,  accord- 
ing to  them,  involving  so  obvious  an  absurdity, must  be  rejected  in  limine: 
the  sun  could  not  possibly  act  upon  the  earth,  not  being  there.  It  was  not 
surprising  that  the  adherents  of  the  old  systems  of  astronomy  should  urge 
this  objection  against  the  new;  but  the  false  assumption  imposed  equally 
on  Newton  himself,  who,  in  order  to  turn  the  edge  of  the  objection,  im- 
agined a subtle  ether  which  filled  up  the  space  between  the  sun  and  the 
earth,  and  by  its  intermediate  agency  was  the  proximate  cause  of  the  phe- 
nomena of  gravitation.  “ It  is  inconceivable,”  said  Newton,  in  one  of  his 
letters  to  Dr.  Bentley, f “that  inanimate  brute  matter  should,  without  the 
mediation  of  something  else,  which  is  not  material,  operate  upon  and  affect 

other  matter  without  mutual  contact That  gravity  should  be  innate, 

inherent,  and  essential  to  matter,  so  that  one  body  may  act  on  another,  at 
a distance,  through  a vacuum,  without  the  mediation  of  any  thing  else,  by 
and  through  which  their  action  and  force  may  be  conveyed  from  one  to 
another,  is  to  me  so  great  an  absurdity,  that  I believe  no  man,  who  in  phil- 
osophical matters  has  a competent  faculty  of  thinking,  can  ever  fall  into 
it.”  This  passage  should  be  hung  up  in  the  cabinet  of  every  cultivator  of 
science  who  is  ever  tempted  to  pronounce  a fact  impossible  because  it 
appears  to  him  inconceivable.  In  our  own  day  one  would  be  more  tempt- 
ed, though  with  equal  injustice,  to  reverse  the  concluding  observation,  and 
consider  the  seeing  any  absurdity  at  all  in  a thing  so  simple  and  natural, 
to  be  what  really  marks  the  absence  of  “ a competent  faculty  of  thinking.” 
No  one  now  feels  any  difficulty  in  conceiving  gravity  to  be,  as  much  as 
any  other  property  is,  “ inherent  and  essential  to  matter,”  nor  finds  the 
comprehension  of  it  facilitated  in  the  smallest  degree  by  the  supposition 
of  an  ether  (though  some  recent  inquirers  do  give  this  as  an  explanation 
of  it) ; nor  thinks  it  at  all  incredible  that  the  celestial  bodies  can  and  do 
act  where  they,  in  actual  bodily  presence,  are  not.  To  us  it  is  not  more 
wonderful  that  bodies  should  act  upon  one  another  “ without  mutual  con- 
tact,” than  that  they  should  do  so  when  in  contact ; we  are  familiar  with 

* It  seems  that  this  doctrine  was,  before  the  time  I have  mentioned,  disputed  by  some 
thinkers.  Dr.  Ward  mentions  Scotus,  Yasquez,  Biel,  Francis  Lugo,  and  Valentia. 

t I quote  this  passage  from  Playfair’s  celebrated  Dissertation  on  the  Progress  of  Mathemat- 
ical and  Physical  Science. 


526 


FALLACIES. 


both  these  facts,  and  we  find  them  equally  inexplicable,  but  equally  easy  to 
believe.  To  Newton,  the  one,  because  his  imagination  was  familiar  with  it, 
appeared  natural  and  a matter  of  course,  while  the  other,  for  the  contrary 
reason,  seemed  too  absurd  to  be  credited. 

It  is  strange  that  any  one,  after  such  a warning,  should  rely  implicitly 
on  the  evidence  a 'priori  of  such  propositions  as  these,  that  matter  can  not 
think;  that  space,  or  extension,  is  infinite;  that  nothing  can  be  made  out 
of  nothing  (ex  nihilo  nihil  Jit).  Whether  these  propositions  are  true  or 
not  this  is  not  the  place  to  determine,  nor  even  whether  the  questions  are 
soluble  by  the  human  faculties.  But  such  doctrines  are  no  more  self-evi- 
dent truths,  than  the  ancient  maxim  that  a thing  can  not  act  where  it  is 
not,  which  probably  is  not  now  believed  by  any  educated  person  in  Eu- 
rope.* Matter  can  not  think;  why?  because  we  can  not  conceive  thought 
to  be  annexed  to  any  arrangement  of  material  particles.  Space  is  infinite, 
because  having  never  known  any  part  of  it  which  had  not  other  parts  be- 
yond it,  we  can  not  conceive  an  absolute  termination.  Ex  nihilo  nihil  Jit, 
because  having  never  known  any  physical  product  without  a pre-existing 
physical  material,  we  can  not,  or  think  we  can  not,  imagine  a creation  out 
of  nothing.  But  these  things  may  in  themselves  be  as  conceivable  as 
gravitation  without  an  intervening  medium,  which  Newton  thought  too 
great  an  absurdity  for  any  person  of  a competent  faculty  of  philosophical 
thinking  to  admit:  and  even  supposing  them  not  conceivable,  this,  for 
aught  we  know,  may  be  merely  one  of  the  limitations  of  our  very  limited 
minds,  and  not  in  nature  at  all. 

No  writer  has  more  directly  identified  himself  with  the  fallacy  now  un- 
der consideration,  or  has  embodied  it  in  more  distinct  terms,  than  Leibnitz. 
In  his  view,  unless  a thing  was  not  merely  conceivable,  but  even  explaina- 
ble, it  could  not  exist  in  nature.  All  natural  phenomena,  according  to  him, 
must  be  susceptible  of  being  accounted  for  a priori.  The  only  facts  of 
which  no  explanation  could  be  given  but  the  will  of  God,  were  miracles 
properly  so  called.  “ Je  reconnais,”  says  he,f  “ qu’il  n’est  pas  permis  de 
nier  ce  qu’on  n’entend  pas ; mais  j’ajoute  qu’on  a droit  de  nier  (au  moins 
dans  l’ordre  naturel)  ce  que  absolument  n’est  point  intelligible  ni  explicable. 
Je  soutiens  aussi  ....  qu’enfin  la  conception  des  creatures  n’est  pas  la  me- 
sure  du  pouvoir  de  Dieu,  mais  que  leur  conceptivite,  ou  force  de  concevoir, 
est  la  mesure  du  pouvoir  de  la  nature,  tout  ce  qui  est  conforme  a l’ordre 
naturel  pouvant  etre  conju  ou  entendu  par  quelque  creature.” 

Not  content  with  assuming  that  nothing  can  be  true  which  we  are  unable 
to  conceive,  scientific  inquirers  have  frequently  given  a still  further  exten- 
sion to  the  doctrine,  and  held  that,  even  of  things  not  altogether  inconceiv- 
able, that  which  we  can  conceive  with  the  greatest  ease  is  likeliest  to  be 
true.  It  was  long  an  admitted  axiom,  and  is  not  yet  entirely  discredited, 
that  “nature  always  acts  by  the  simplest  means,”  i.e.,  by  those  which  are 
most  easily  conceivable.];  A large  proportion  of  all  the  errors  ever  commit- 
ted in  the  investigation  of  the  laws  of  nature,  have  arisen  from  the  assump- 
tion that  the  most  familiar  explanation  or  hypothesis  must  be  the  truest. 


* This  statement  I must  now  correct,  as  too  unqualified.  The  maxim  in  question  was 
maintained  with  full  conviction  by  no  less  an  authority  than  Sir  William  Hamilton.  See  my 
Examination , chap.  xxiv. 

t Nouveaux  Essais  sur  V Entendement  Humain — Avant-propos.  (CEuvres,  Paris  ed.,  1842, 
vol.  i.,  p.  19.) 

t This  doctrine  also  was  accepted  as  true,  and  conclusions  were  grounded  on  it,  by  Sir 
William  Hamilton.  See  Examination , chap.  xxiv. 


FALLACIES  OF  SIMPLE  INSPECTION. 


527 


One  of  the  most  instructive  facts  in  scientific  history  is  the  pertinacity  with 
which  the  human  mind  clung  to  the  belief  that  the  heavenly  bodies  must 
move  in  circles,  or  be  carried  round  by  the  revolution  of  spheres ; merely 
because  those  were  in  themselves  the  simplest  suppositions:  though,  to 
make  them  accord  with  the  facts  which  were  ever  contradicting  them  more 
and  more,  it  became  necessary  to  add  sphere  to  sphere  and  circle  to  circle, 
until  the  original  simplicity  was  converted  into  almost  inextricable  compli- 
cation. 

§ 4.  We  pass  to  another  a 'priori  fallacy  or  natui-al  prejudice,  allied  to 
the  former,  and  originating,  as  that  does,  in  the  tendency  to  presume  an  ex- 
act correspondence  between  the  laws  of  the  mind  and  those  of  things  ex- 
ternal to  it.  The  fallacy  may  be  enunciated  in  this  general  form — What- 
ever can  be  thought  of  apart  exists  apart:  and  its  most  remarkable  mani- 
festation consists  in  the  personification  of  abstractions.  Mankind  in  all 
ages  have  had  a strong  propensity  to  conclude  that  wherever  there  is  a 
name,  there  must  be  a distinguishable  separate  entity  corresponding  to  the 
name;  and  every  complex  idea  which  the  mind  has  formed  for  itself  by 
operating  upon  its  conceptions  of  individual  things,  was  considered  to  have 
an  outward  objective  reality  answering  to  it.  Fate,  Chance,  Nature,  Time, 
Space,  were  real  beings,  nay,  even  gods.  If  the  analysis  of  qualities  in  the 
earlier  part  of  this  work  be  correct,  names  of  qualities  and  names  of  sub- 
stances stand  for  the  very  same  sets  of  facts  or  phenomena ; whiteness  and 
a white  thing  are  only  different  phrases,  required  by  convenience  for  speak- 
ing of  the  same  external  fact  under  different  relations.  Not  such,  how- 
ever, was  the  notion  which  this  verbal  distinction  suggested  of  old,  either 
to  the  vulgar  or  to  the  scientific.  Whiteness  was  an  entity,  inhering  or 
sticking  in  the  white  substance:  and  so  of  all  other  qualities.  So  far  was 
this  carried,  that  even  concrete  general  terms  were  supposed  to  be,  not 
names  of  indefinite  numbers  of  individual  substances,  but  names  of  a pe- 
culiar kind  of  entities  termed  Universal  Substances.  Because  we  can  think 
and  speak  of  man  in  general,  that  is,  of  all  persons  in  so  far  as  possessing 
the  common  attributes  of  the  species,  without  fastening  our  thoughts  per- 
manently on  some  one  individual  person;  therefore  man  in  general  was 
supposed  to  be,  not  an  aggregate  of  individual  persons,  but  an  abstract  or 
universal  man,  distinct  from  these. 

It  may  be  imagined  what  havoc  metaphysicians  trained  in  these  habits 
made  with  philosophy,  when  they  came  to  the  largest  generalizations  of  all. 
Substantiae  Secundce  of  any  kind  were  bad  enough,  but  such  Substantiae  Se- 
cundae  as  -o  by,  for  example,  and  -b  'ey,  standing  for  peculiar  entities  supposed 
to  be  inherent  in  all  things  which  exist,  or  in  all  which  are  said  to  be  one, 
were  enough  to  put  an  end  to  all  intelligible  discussion ; especially  since, 
with  a just  perception  that  the  truths  which  philosophy  pursues  are  gener- 
al truths,  it  was  soon  laid  down  that  these  general  substances  were  the  only 
subjects  of  science,  being  immutable,  while  individual  substances  cogniza- 
ble by  the  senses,  being  in  a perpetual  flux,  could  not  be  the  subject  of  real 
knowledge.  This  misapprehension  of  the  import  of  general  language  con- 
stitutes Mysticism,  a word  so  much  oftener  written  and  spoken  than  under- 
stood. Whether  in  the  Vedas,  in  the  Platonists,  or  in  the  Hegelians,  mysti- 
cism is  neither  more  nor  less  than  ascribing  objective  existence  to  the  sub- 
jective creations  of  our  own  faculties,  to  ideas  or  feelings  of  the  mind ; 
and  believing  that  by  watching  and  contemplating  these  ideas  of  its  own 
making,  it  can  read  in  them  what  takes  place  in  the  world  without. 


528 


FALLACIES. 


§ 5.  Proceeding  with  the  enumeration  of  a priori  fallacies,  and  endeav- 
oring to  arrange  them  with  as  much  reference  as  possible  to  their  natural 
affinities,  we  come  to  another,  which  is  also  nearly  allied  to  the  fallacy  pre- 
ceding the  last,  standing  in  the  same  relation  to  one  variety  of  it  as  the 
fallacy  last  mentioned  does  to  the  other.  This,  too,  represents  nature  as 
under  incapacities  corresponding  to  those  of  our  intellect;  but  instead  of 
only  asserting  that  nature  can  not  do  a thing  because  we  can  not  conceive 
it  done,  goes  the  still  greater  length  of  averring  that  nature  does  a particu- 
lar thing,  on  the  sole  ground  that  we  can  see  no  reason  why  she  should  not. 
Absurd  as  this  seems  when  so  plainly  stated,  it  is  a received  principle 
among  scientific  authorities  for  demonstrating  a priori  the  laws  of  physical 
phenomena.  A phenomenon  must  follow  a certain  law,  because  we  see  no 
reason  why  it  should  deviate  from  that  law  in  one  way  rather  than  in  an- 
other. This  is  called  the  Principle  of  the  Sufficient  Reason  ;*  and  by 
means  of  it  philosophers  often  flatter  themselves  that  they  are  able  to  es- 
tablish, without  any  appeal  to  experience,  the  most  general  truths  of  ex- 
perimental physics. 

Take,  for  example,  two  of  the  most  elementary  of  all  laws,  the  law  of  in- 
ertia and  the  first  law  of  motion.  A body  at  rest  can  not,  it  is  affirmed, 
begin  to  move  unless  acted  upon  by  some  external  force ; because,  if  it 
did,  it  must  either  move  up  or  down,  forward  or  backward,  and  so  forth ; 
but  if  no  outward  force  acts  upon  it,  there  can  be  no  reason  for  its  mov- 
ing up  rather  than  down,  or  down  rather  than  up,  etc.,  ergo,  it  will  not 
move  at  all. 

This  reasoning  I conceive  to  be  entirely  fallacious,  as  indeed  Dr.  Brown, 
in  his  treatise  on  Cause  and  Effect,  has  shown  with  great  acuteness  and 
justness  of  thought.  We  have  before  remarked,  that  almost  every  fallacy 
may  be  referred  to  different  genera  by  different  modes  of  filling  up  the 
suppressed  steps ; and  this  particular  one  may,  at  our  option,  be  brought 
under petitio principii.  It  supposes  that  nothing  can  be  a “sufficient  rea- 
son” for  a body’s  moving  in  one  particular  direction,  except  some  external 
force.  But  this  is  the  very  thing  to  be  proved.  Why  not  some  internal 
force?  Why  not  the  law  of  the  thing’s  own  nature?  Since  these  philoso- 
phers think  it  necessary  to  prove  the  law  of  inertia,  they  of  course  do  not 
suppose  it  to  be  self-evident;  they  must,  therefore,  be  of  opinion  that  pre- 
viously to  all  proof,  the  supposition  of  a body’s  moving  by  internal  impulse 
is  an  admissible  hypothesis;  but  if  so,  why  is  not  the  hypothesis  also  ad- 
missible, that  the  internal  impulse  acts  naturally  in  some  one  particular  di- 
rection, not  in  another?  If  spontaneous  motion  might  have  been  the  law 
of  matter,  why  not  spontaneous  motion  toward  the  sun,  toward  the  earth, 
or  toward  the  zenith  ? Why  not,  as  the  ancients  supposed,  toward  a par- 
ticular place  in  the  universe,  appropriated  to  each  particular  kind  of  sub- 
stance ? Surely  it  is  not  allowable  to  say  that  spontaneity  of  motion  is 
credible  in  itself,  but  not  credible  if  supposed  to  take  place  in  any  deter- 
minate direction. 

Indeed,  if  any  one  chose  to  assert  that  all  bodies  when  uncontrolled  set 
out  in  a direct  line  toward  the  North  Pole,  he  might  equally  prove  his  point 
by  the  principle  of  the  Sufficient  Reason.  By  what  right  is  it  assumed 
that  a state  of  rest  is  the  particular  state  which  can  not  be  deviated  from 
without  special  cnuse?  Why  not  a state  of  motion,  and  of  some  particular 
sort  of  motion?  Why  may  we  not  say  that  the  natural  state  of  a horse 

* Not  that  of  Leibnitz,  but  the  principle  commonly  appealed  to  under  that  name  by  mathe- 
maticians. 


FALLACIES  OF  SIMPLE  INSPECTION. 


529 


left  to  himself  is  to  amble,  because  otherwise  he  must  either  trot,  gallop,  or 
stand  still,  and  because  we  know  no  reason  why  he  should  do  one  of  these 
rather  than  another  ? If  this  is  to  be  called  an  unfair  use  of  the  “ sufficient 
reason,”  and  the  other  a fair  one,  there  must  be  a tacit  assumption  that  a 
state  of  rest  is  more  natural  to  a horse  than  a state  of  ambling.  If  this 
means  that  it  is  the  state  which  the  animal  will  assume  when  left  to  him- 
self, that  is  the  very  point  to  be  proved;  and  if  it  does  not  mean  this,  it 
can  only  mean  that  a state  of  rest  is  the  simplest  state,  and  therefore  the 
most  likely  to  prevail  in  nature,  which  is  one  of  the  fallacies  or  natural 
prejudices  we  have  already  examined. 

So  again  of  the  First  Law  of  Motion ; that  a body  once  moving  will,  if 
left  to  itself,  continue  to  move  uniformly  in  a straight  line.  An  attempt 
is  made  to  prove  this  law  by  saying,  that  if  not,  the  body  must  deviate 
either  to  the  right  or  to  the  left,  and  that  there  is  no  reason  why  it  should 
do  one  more  than  the  other.  But  who  could  know,  antecedently  to  experi- 
ence, whether  there  was  a reason  or  not  ? Might  it  not  be  the  nature  of 
bodies,  or  of  some  particular  bodies,  to  deviate  toward  the  right?  or  if  the 
supposition  is  preferred,  toward  the  east,  or  south  ? It  was  long  thought 
that  bodies,  terrestrial  ones  at  least,  hftd  a natural  tendency  to  deflect  down- 
ward ; and  there  is  no  shadow  of. any  thing  objectionable  in  the  supposition, 
except  that  it  is  not  true.  The  pretended  proof  of  the  law  of  motion  is  even 
more  manifestly  untenable  than  that  of  the  law  of  inertia,  for  it  is  flagrantly 
inconsistent;  it  assumes  that  the  continuance  of  motion  in  the  direction  first 
taken  is  more  natural  than  deviation  either  to  the  l ight  or  to  the  left,  but 
denies  that  one  of  these  can  possibly  be  more  natural  than  the  other.  All 
these  fancies  of  the  possibility  of  knowing  what  is  natural  or  not  natural 
by  any  other  means  than  experience,  are,  in  truth,  entirely  futile.  The  real 
and  only  proof  of  the  laws  of  motion,  or  of  any  other  law  of  the  universe,  is 
experience  ; it  is  simply  that  no  other  suppositions  explain  or  are  consistent 
with  the  facts  of  universal  nature. 

Geometers  have,  in  all  ages,  been  open  to  the  imputation  of  endeavoring 
to  prove  the  most  general  facts  of  the  outward  world  by  sophistical  reason- 
ing, in  order  to  avoid  appeals  to  the  senses.  Archimedes,  says  Professor 
Playfair,*  established  some  of  the  elementary  propositions  of  statics  by  a 
process  in  which  he  “borrows  no  principle  from  experiment,  but  establish- 
es his  conclusion  entirely  by  reasoning  a priori.  He  assumes,  indeed,  that 
equal  bodies,  at  the  ends  of  the  equal  arms  of  a lever,  will  balance  one  an- 
other; and  also  that  a cylinder  or  parallelopiped  of  homogeneous  matter, 
will  be  balanced  about  its  centre  of  magnitude.  These,  however,  are  not  in- 
ferences from  experience;  they  are,  properly  speaking,  conclusions  deduced 
from  the  principle  of  the  Sufficient  Reason.”  And  to  this  day  there  are 
few  geometers  who  would  not  think  it  far  more  scientific  to  establish  these 
or  any  other  premises  in  this  way,  than  to  rest  their  evidence  on  that  fa- 
miliar experience  which  in  the  case  in  question  might  have  been  so  safely 
appealed  to. 

§ 6.  Another  natural  prejudice,  of  most  extensive  prevalence,  and  which 
had  a great  share  in  producing  the  errors  fallen  into  by  the  ancients  in 
their  physical  inquiries,  was  this : That  the  differences  in  nature  must  cor- 
respond to  our  received  distinctions : that  effects  which  we  are  accustom- 
ed, in  popular  language,  to  call  by  different  names,  and  arrange  in  different 


* Dissertation , p.  27. 
34 


530 


FALLACIES. 


classes,  must  be  of  different  natures,  and  have  different  causes.  This  prej- 
udice, so  evidently  of  the  same  origin  with  those  already  treated  of,  marks 
more  especially  the  earliest  stage  of  science,  when  it  has  not  yet  broken 
loose  from  the  trammels  of  every  - day  phraseology.  The  extraordinary 
prevalence  of  the  fallacy  among  the  Greek  philosophers  may  be  accounted 
tor  by  their  generally  knowing  no  other  language  than  their  own;  from 
which  it  was  a consequence  that  their  ideas  followed  the  accidental  or  ar- 
bitrary combinations  of  that  language,  more  completely  than  can  happen 
among  the  moderns  to  any  but  illiterate  persons.  They  had  great  difficulty 
in  distinguishing  between  things  which  their  language  confounded,  or  in 
putting  mentally  together  things  which  it  distinguished;  and  could  hardly 
combine  the  objects  in  nature,  into  any  classes  but  those  which  were  made 
for  them  by  the  popular  phrases  of  their  own  country;  or  at  least  could 
not  help  fancying  those  classes  to  be  natural  and  all  others  arbitrary  and 
artificial.  Accordingly,  scientific  investigation  among  the  Greek  schools 
of  speculation  and  their  followers  in  the  Middle  Ages,  was  little  more  than 
a mere  sifting  and  analyzing  of  the  notions  attached  to  common  language. 
They  thought  that  by  determining  the  meaning  of  words,  they  could  be- 
come acquainted  with  facts.  “They  took  for  granted,”  says  Dr.Whewell,* 
“that  philosophy  must  result  from  the  relations  of  those  notions  which  are 
involved  in  the  common  use  of  language,  and  they  proceeded  to  seek  it  by 
studying  such  notions.”  In  his  next  chapter,  Dr.  Whewell  has  so  well 
illustrated  and  exemplified  this  error,  that  I shall  take  the  liberty  of  quot- 
ing him  at  some  length. 

“The  propensity  to  seek  for  principles  in  the  common  usages  of  lan- 
guage may  be  discerned  at  a very  early  period.  Thus  we  have  an  example 
of  it  in  a saying  which  is  reported  of  Thales,  the  founder  of  Greek  philoso- 
phy. When  he  was  asked,4  What  is  the  greatest  thing?’  he  replied  4 Place ; 
for  all  other  things  are  in  the  world,  but  the  world  is  in  it.’  In  Aristotle 
we  have  the  consummation  of  this  mode  of  speculation.  The  usual  point 
from  which  he  starts  in  his  inquiries  is,  that  we  say  thus  or  thus  in  common 
language.  Thus,  when  he  has  to  discuss  the  question  whether  there  be,  in 
any  part  of  the  universe,  a void,  or  space  in  which  there  is  nothing,  he  in- 
quires first  in  how  many  senses  we  say  that  one  thing  is  in  another.  He 
enumerates  many  of  these;  we  say  the  part  is  in  the  whole,  as  the  finger  is 
in  the  hand ; again  we  say,  the  species  is  in  the  genus,  as  man  is  included 
in  animal;  again,  the  government  of  Greece  is  in  the  king;  and  various 
■other  senses  are  described  and  exemplified,  but  of  all  these  the  most  proper 
is  when  we  say  a thing  is  in  a vessel,  and  generally  in  place.  He  next  ex- 
amines what  place  is,  and  comes  to  this  conclusion,  that  4 if  about  a body 
there  be  another  body  including  it,  it  is  in  place,  and  if  not,  not.’  A body 
moves  when  it  changes  its  place;  but  he  adds,  that  if  water  be  in  a vessel, 
the  vessel  being  at  rest,  the  parts  of  the  water  may  still  move,  for  they  are 
included  by  each  other;  so  that  while  the  whole  does  not  change  its  place, 
the  parts  may  change  their  place  in  a circular  order.  Proceeding  then  to 
the  question  of  a void,  he  as  usual  examines  the  different  senses  in  which 
the  term  is  used,  and  adopts  as  the  most  proper,  place  without  matter , 
with  no  useful  result. 

44  Again,  in  a question  concerning  mechanical  action,  he  says, ‘When  a 
man  moves  a stone  by  pushing  it  with  a stick,  we  say  both  that  the  man 
moves  the  stone,  and  that  the  stick  moves  the  stone,  but  the  latter  more 
properly .’ 


Hist.  lnd.  Sc.,  Book  i.,  chap.  i. 


FALLACIES  OF'  SIMPLE  INSPECTION. 


531 


“Again,  we  find  the  Greek  philosophers  applying  themselves  to  extract 
their  dogmas  from  the  most  general  and  abstract  notions  which  they  could 
detect;  for  example,  from  the  conception  of  the  Universe  as  One  or  as 
Many  things.  They  tried  to  determine  how  far  we  may,  or  must,  combine 
with  these  conceptions  that  of  a whole,  of  parts,  of  number,  of  limits,  of 
place,  of  beginning  or  end,  of  full  or  void,  of  rest  or  motion,  of  cause  and 
effect,  and  the  like.  The  analysis  of  such  conceptions  with  such  a view, 
occupies,  for  instance,  almost  the  whole  of  Aristotle’s  Treatise  on  the 
Heavens.” 

The  following  paragraph  merits  particular  attention:  “Another  mode 
of  reasoning,  very  widely  applied  in  these  attempts,  was  the  doctrine  of 
contrarieties , in  which  it  was  assumed  that  adjectives  or  substances  which 
are  in  common  language,  or  in  some  abstract  mode  of  conception,  opposed 
to  each  other,  must  point  at  some  fundamental  antithesis  in  nature,  which 
it  is  important  to  study.  Thus  Aristotle  says  that  the  Pythagoreans,  from 
the  contrasts  which  number  suggests,  collected  ten  principles  — Limited 
and  Unlimited,  Odd  and  Even,  One  and  Many,  Right  and  Left,  Male  and 
Female,  Rest  and  Motion,  Straight  and  Curved,  Light  and  Darkness,  Good 
and  Evil,  Square  and  Oblong..  . . Aristotle  himself  deduced  the  doctrine 
of  four  elements  and  other  dogmas  by  oppositions  of  the  same  kind.” 

Of  the  manner  in  which,  from  premises  obtained  in  this  way,  the  ancients 
attempted  to  deduce  laws  of  nature,  an  example  is  given  in  the  same  work 
a few  pages  further  on.  “Aristotle  decides  that  there  is  no  void  on  such 
arguments  as  this.  In  a void  there  could  be  no  difference  of  up  and  down  ; 
for  as  in  nothing  there  are  no  differences,  so  there  are  none  in  a privation 
or  negation  ; but  a void  is  merely  a privation  or  negation  of  matter;  there- 
fore, in  a void,  bodies  could  not  move  up  and  down,  which  it  is  in  their 
nature  to  do.  It  is  easily  seen”  (Dr. Whewell  very  justly  adds)  “that 
such  a mode  of  reasoning  elevates  the  familiar  forms  of  language,  and 
the  intellectual  connections  of  terms,  to  a supremacy  over  facts ; making 
truth  depend  upon  whether  terms  are  or  are  not  privative,  and  whether  we 
say  that  bodies  fall  naturally .” 

The  propensity  to  assume  that  the  same  relations  obtain  between  ob- 
jects themselves,  which  obtain  between  our  ideas  of  them,  is  here  seen  in 
the  extreme  stage  of  its  development.  For  the  mode  of  philosophizing, 
exemplified  in  the  foregoing  instances,  assumes  no  less  than  that  the  prop- 
er way  of  arriving  at  knowledge  of  nature,  is  to  study  nature  itself  sub- 
jectively; to  apply  our  observation  and  analysis  not  to  the  facts,  but  to 
the  common  notions  entertained  of  the  facts. 

Many  other  equally  striking  examples  may  be  given  of  the  tendency  to 
assume  that  things  which  for  the  convenience  of  common  life  are  placed  in 
different  classes,  must  differ  in  every  respect.  Of  this  nature  was  the  uni- 
versal and  deeply-rooted  prejudice  of  antiquity  and  the  Middle  Ages,  that 
celestial  and  terrestrial  phenomena  must  be  essentially  different,  and  could 
in  no  manner  or  degree  depend  on  the  same  laws.  Of  the  same  kind,  also, 
was  the  prejudice  against  which  Bacon  contended,  that  nothing  produced 
by  nature  could  be  successfully  imitated  by  man : “ Calorem  solis  et  ignis 
toto  genere  differre ; ne  scilicet  homines  putent  se  per  opera  ignis,  aliquid 
simile  iis  quae  in  Natura  fiunt,  educere  et  formare  posse ;”  and  again,  “ Com- 
positionem  tantum  opus  Hominis,  Mistionem  vero  opus  solius  Naturae  esse: 
ne  scilicet  homines  sperent  aliquam  ex  arte  Corporum  naturalium  genera- 
tionem  aut  transformationem.”*  The  grand  distinction  in  the  ancient  sci- 
* Novum  Organum , Aph.  75. 


532 


FALLACIES. 


entilic  speculations,  between  natural  and  violent  motions,  though  not  with- 
out a plausible  foundation  in  the  appearances  themselves,  was  doubtless 
greatly  recommended  to  adoption  by  its  conformity  to  this  prejudice. 

§ 7.  From  the  fundamental  error  of  the  scientific  inquirers  of  antiquity, 
we  pass,  by  a natural  association,  to  a scarcely  less  fundamental  one  of 
their  great  rival  and  successor,  Bacon.  It  has  excited  the  surprise  of  phi- 
losophers that  the  detailed  system  of  inductive  logic,  which  this  extraor- 
dinary man  labored  to  construct,  has  been  turned  to  so  little  direct  use  by 
subsequent  inquirers,  having  neither  continued,  except  in  a few  of  its  gen- 
eralities, to  be  recognized  as  a theory,  nor  having  conducted  in  practice  to 
any  great  scientific  results.  But  this,  though  not  uufrequently  remarked, 
has  scarcely  received  any  plausible  explanation ; and  some,  indeed,  have 
preferred  to  assert  that  all  rules  of  induction  are  useless,  rather  than  sup- 
pose that  Bacon’s  rules  are  grounded  on  an  insufficient  analysis  of  the  in- 
ductive process.  Such,  however,  will  be  seen  to  be  the  fact,  as  soon  as  it 
is  considered,  that  Bacon  entirely  overlooked  Plurality  of  Causes.  All  his 
rules  tacitly  imply  the  assumption,  so  contrary  to  all  we  now  know  of  na- 
ture, that  a phenomenon  can  not  have  more  than  one  cause. 

When  he  is  inquiring  into  what  he  terms  the  forma  calidi  aut  frigidi, 
gravis  aut  levis,  sicci  aut  liumidi , and  the  like,  he  never  for  an  instant 
doubts  that  there  is  some  one  thing,  some  invariable  condition  or  set  of 
conditions,  which  is  present  in  all  cases  of  heat,  or  cold,  or  whatever  other 
phenomenon  he  is  considering;  the  only  difficulty  being  to  find  what  it  is; 
which  accordingly  he  tries  to  do  by  a process  of  elimination,  rejecting  or 
excluding,  by  negative  instances,  whatever  is  not  th e forma  or  cause,  in  or- 
der to  arrive  at  what  is.  But,  that  this  forma  or  cause  is  one  thing,  and 
that  it  is  the  same  in  all  hot  objects,  he  has  no  more  doubt  of,  than  anoth- 
er person  has  that  there  is  always  some  cause  or  other.  In  the  present 
state  of  knowledge  it  could  not  be  necessary,  even  if  we  had  not  already 
treated  so  fully  of  the  question,  to  point  out  how  widely  this  supposition 
is  at  variance  with  the  truth.  It  is  particularly  unfortunate  for  Bacon 
that,  falling  into  this  error,  he  should  have  fixed  almost  exclusively  upon  a 
class  of  inquiries  in  which  it  was  especially  fatal ; namely,  inquiries  into 
the  causes  of  the  sensible  qualities  of  objects.  For  his  assumption,  ground- 
less in  every  case,  is  false  in  a peculiar  degree  with  respect  to  those  sensi- 
ble qualities.  In  regard  to  scarcely  any  of  them  has  it  been  found  possible 
to  trace  any  unity  of  cause,  any  set  of  conditions  invariably  accompanying 
the  quality.  The  conjunctions  of  such  qualities  with  one  another  consti- 
tute the  variety  of  Kinds,  in  which,  as  already  remarked,  it  has  not  been 
found  possible  to  trace  any  law.  Bacon  was  seeking  for  what  did  not  ex- 
ist. The  phenomenon  of  which  he  sought  for  the  one  cause  has  oftenest  no 
cause  at  all,  and  when  it  has,  depends  (as  far  as  hitherto  ascertained)  on 
an  unassignable  variety  of  distinct  causes. 

And  on  this  rock  every  one  must  split,  who  represents  to  himself  as  the 
first  and  fundamental  problem  of  science  to  ascertain  what  is  the  cause  of 
a given  effect,  rather  than  what  are  the  effects  of  a given  cause.  It  was 
shown,  in  an  early  stage  of  our  inquiry  into  the  nature  of  Induction,*  how 
muck  more  ample  are  the  resources  which  science  commands  for  the  latter 
than  for  the  former  inquiry,  since  it  is  upon  the  latter  only  that  we  can 
throw  any  direct  light  by  means  of  experiment ; the  power  of  artificially 


Supra,  book  iii.,  chap,  vii.,  § 4. 


FALLACIES  OF  SIMPLE  INSPECTION. 


533 


producing  an  effect,  implying  a previous  knowledge  of  at  least  one  of  its 
causes.  If  we  discover  the  causes  of  effects,  it  is  generally  by  having  pre- 
viously discovered  the  effects  of  causes ; the  greatest  skill  in  devising  cru- 
cial instances  for  the  former  purpose  may  only  end,  as  Bacon’s  physical  in- 
quiries did,  in  no  result  at  all.  Was  it  that  his  eagerness  to  acquire  the 
power  of  producing  for  man’s  benefit  effects  of  practical  importance  to  hu- 
man life,  rendering  him  impatient  of  pursuing  that  end  by  a circuitous 
route,  made  even  him,  the  champion  of  experiment,  prefer  the  direct  mode, 
though  one  of  mere  observation,  to  the  indirect,  in  which  alone  experiment 
was  possible?  Or  had  even  Bacon  not  entirely  cleared  his  mind  from  the 
notion  of  the  ancients,  that  “rerum  cognoscere  causas ” was  the  sole  ob- 
ject of  philosophy,  and  that  to  inquire  into  the  effects  of  things  belonged 
to  servile  and  mechanical  arts  ? 

It  is  worth  remarking  that,  while  the  only  efficient  mode  of  cultivating 
speculative  science  was  missed  from  an  undue  contempt  of  manual  opera- 
tions, the  false  speculative  views  thus  engendered  gave  in  their  turn  a false 
direction  to  such  practical  and  mechanical  aims  as  were  suffered  to  exist. 
The  assumption  universal  among  the  ancients  and  in  the  Middle  Ages,  that 
there  were  principles  of  heat  and  cold,  dryness  and  moisture,  etc.,  led  di- 
rectly to  a belief  in  alchemy;  in  a transmutation  of  substances,  a change 
from  one  Kind  into  another.  Why  should  it  not  be  possible  to  make 
gold?  Each  of  the  characteristic  properties  of  gold  has  its  forma , its 
essence,  its  set  of  conditions,  which  if  we  could  discover,  and  learn  how  to 
realize,  we  could  superinduce  that  particular  property  upon  any  other  sub- 
stance, upon  wood,  or  iron,  or  lime,  or  clay.  If,  then,  we  could  effect  this 
with  respect  to  every  one  of  the  essential  properties  of  the  precious  metal, 
we  should  have  converted  the  other  substance  into  gold.  Nor  did  this,  if 
once  the  premises  were  granted,  appear  to  transcend  the  real  powers  of 
mankind.  For  daily  experience  showed  that  almost  every  one  of  the  dis- 
tinctive sensible  properties  of  any  object,  its  consistence,  its  color,  its  taste, 
its  smell,  its  shape,  admitted  of  being  totally  changed  by  tire,  or  water,  or 
some  other  chemical  agent.  The  formce  of  all  those  qualities  seeming, 
therefore,  to  be  within  human  power  either  to  produce  or  to  annihilate, 
not  only  did  the  transmutation  of  substances  appear  abstractedly  possible, 
but  the  employment  of  the  power,  at  our  choice,  for  practical  ends,  seemed 
by  no  means  hopeless.* 

A prejudice,  universal  in  the  ancient  world,  and  from  which  Bacon  was 
so  far  from  being  free,  that  it  pervaded  and  vitiated  the  whole  practical 
part  of  his  system  of  logic,  may  with  good  reason  be  ranked  high  in  the 
order  of  Fallacies  of  which  we  are  now  treating. 

§ 8.  There  remains  one  a priori  fallacy  or  natural  prejudice,  the  most 
deeply-rooted,  perhaps,  of  all  which  we  have  enumerated ; one  which  not 
only  reigned  supreme  in  the  ancient  world,  but  still  possesses  almost  undis- 
puted dominion  over  many  of  the  most  cultivated  minds;  and  some  of  the 
most  remarkable  of  the  numerous  instances  by  which  I shall  think  it  neces- 
sary to  exemplify  it,  will  be  taken  from  recent  thinkers.  This  is,  that  the 
conditions  of  a phenomenon  must,  or  at  least  probably  will,  resemble  the 
phenomenon  itself. 

* It  is  hardly  needful  to  remark  that  nothing  is  here  intended  to  be  said  against  the  possi- 
bility at  some  future  period  of  making  gold — by  first  discovering  it  to  be  a compound,  and 
putting  together  its  different  elements  or  ingredients.  But  this  is  a totally  different  idea  from 
that  of  the  seekers  of  the  grand  arcanum. 


534 


FALLACIES. 


* 

Conformably  to  what  we  have  before  remarked  to  be  of  frequent  occur- 
rence, this  fallacy  might  without  much  impropriety  have  been  placed  in  a 
different  class,  among  Fallacies  of  Generalization;  for  experience  does  af- 
ford a certain  degree  of  countenance  to  the  assumption.  The  cause  does, 
in  very  many  cases,  resemble  its  effect;  like  produces  like.  Many  phe- 
nomena have  a direct  tendency  to  perpetuate  their  own  existence,  or  to 
give  rise  to  other  phenomena  similar  to  themselves.  Not  to  mention 
forms  actually  moulded  on  one  another,  as  impressions  on  wax  and  the 
like,  in  which  the  closest  resemblance' between  the  effect  and  its  cause  is 
the  very  law  of  the  phenomenon ; all  motion  tends  to  continue  itself,  with 
its  own  velocity,  and  in  its  own  original  direction ; and  the  motion  of  one 
body  tends  to  set  others  in  motion,  which  is  indeed  the  most  common  of 
the  modes  in  which  the  motions  of  bodies  originate.  We  need  scarcely 
refer  to  contagion,  fermentation,  and  the  like ; or  to  the  production  of  ef- 
fects by  the  growth  or  expansion  of  a germ  or  rudiment  resembling  on  a 
smaller  scale  the  completed  phenomenon,  as  in  the  growth  of  a plant  or 
animal  from  an  embryo,  that  embryo  itself  deriving  its  origin  from  another 
plant  or  animal  of  the  same  kind.  Again,  the  thoughts  or  reminiscences, 
which  are  effects  of  our  past  sensations,  resemble  those  sensations;  feel- 
ings produce  similar  feelings  by  way  of  sympathy ; acts  produce  similar 
acts  by  involuntary  or  voluntary  imitation.  With  so  many  appearances  in 
its  favor,  no  wonder  if  a presumption  naturally  grew  up,  that  causes  must 
necessarily  resemble  their  effects,  and  that  like  could  only  be  produced  by 
like. 

This  principle  of  fallacy  has  usually  presided  over  the  fantastical  at- 
tempts to  influence  the  course  of  nature  by  conjectural  means,  the  choice 
of  which  was  not  directed  by  previous  observation  and  experiment.  The 
guess  almost  always  fixed  upon  some  means  which  possessed  features  of 
real  or  apparent  resemblance  to  the  end  in  view.  If  a charm  was  wanted, 
as  by  Ovid’s  Medea,  to  prolong  life,  all  long-lived  animals,  or  what  were 
esteemed  such,  were  collected  and  brewed  into  a broth  : 

nec  defuit  illic 

Squamea  Cinyphii  tenuis  membrana  chelydri 
Vivacisque  jecur  cervi : quibus  insuper  addit 
Ora  caputque  novem  cornicis  scecula  passtc. 

A similar  notion  was  embodied  in  the  celebrated  medical  theory  called 
the  “ Doctrine  of  Signatures,”  “ which  is  no  less,”  says  Dr.  Paris,*  “ than 
a belief  that  every  natural  substance  which  possesses  any  medicinal  virtue 
indicates  by  an  obvious  and  well-marked  external  character  the  disease  for 
which  it  is  a remedy,  or  the  object  for  which  it  should  be  employed.” 
This  outward  character  was  generally  some  feature  of  resemblance,  real  or 
fantastical,  either  to  the  effect  it  was  supposed  to  produce,  or  to  the  phe- 
nomenon over  which  its  power  was  thought  to  be  exercised.  “Thus  the 
lungs  of  a fox  must  be  a specific  for  asthma,  because  that  animal  is  re- 
markable for  its  strong  powers  of  respiration.  Turmeric  has  a brilliant 
yellow  color,  which  indicates  that  it  has  the  power  of  curing  the  jaundice; 
for  the  same  reason,  poppies  must  relieve  diseases  of  the  head  ; Agaricus 
those  of  the  bladder;  Cassia  fistula  the  affections  of  the  intestines,  and 
Aristolochia  the  disorders  of  the  uterus  : the  polished  surface  and  stony 
hardness  which  so  eminently  characterize  the  seeds  of  the  Lithospermum 
officinale  (common  gromwell)  were  deemed  a certain  indication  of  their 


Pharmacologia,  pp.  43— 15. 


FALLACIES  OF  SIMPLE  INSPECTION. 


535 


efficacy  in  calculous  and  gravelly  disorders;  for  a similar  reason,  the  roots 
of  the  Saxifraga  granulata  (white  saxifrage)  gained  reputation  in  the  cure 
of  the  same  disease;  and  the  Euphrasia  (eye-bright)  acquired  fame,  as  an 
application  in  complaints  of  the  eye,  because  it  exhibits  a black  spot  in  its 
corolla  resembling  the  pupil.  The  blood-stone,  the  Heliotropium  of  the 
ancients,  from  the  occasional  small  specks  or  points  of  a blood-red  color 
exhibited  on  its  green  surface,  is  even  at  this  very  day  employed  in  many 
parts  of  England  and  Scotland  to  stop  a bleeding  from  the  nose ; and  net- 
tle tea  continues  a popular  remedy  for  the  cure  of  Urticaria.  It  is  also 
asserted  that  some  substances  bear  the  signatures  of  the  humors,  as  the 
petals  of  the  red  rose  that  of  the  blood,  and  the  roots  of  rhubarb  and  the 
flowers  of  saffron  that  of  the  bile.” 

The  early  speculations  respecting  the  chemical  composition  of  bodies 
were  rendered  abortive  by  no  circumstance  more  than  by  their  invariably 
taking  for  granted  that  the  properties  of  the  elements  must  resemble  those 
of  the  compounds  which  were  formed  from  them. 

To  descend  to  more  modern  instances;  it  was  long  thought,  and  was 
stoutly  maintained  by  the  Cartesians  and  even  by  Leibnitz  against  the 
Newtonian  system  (nor  did  Newton  himself,  as  we  have  seen,  contest  the 
assumption,  but  eluded  it  by  an  arbitrary  hypothesis),  that  nothing  (of  a 
physical  nature  at  least)  could  account  for  motion,  except  previous  motion; 
the  impulse  or  impact  of  some  other  body.  It  was  very  long  before  the 
scientific  world  could  prevail  upon  itself  to  admit  attraction  and  repulsion 
(i.  e.,  spontaneous  tendencies  of  particles  to  approach  or  recede  from  one 
another)  as  ultimate  laws,  no  more  requiring  to  be  accounted  for  than 
impulse  itself,  if  indeed  the  latter  were  not,  in  truth,  resolvable  into  the 
former.  From  the  same  source  arose  the  innumerable  hypotheses  devised 
to  explain  those  classes  of  motion  which  appeared  more  mysterious  than 
others  because  there  was  no  obvious  mode  of  attributing  them  to  impulse, 
as  for  example  the  voluntary  motions  of  the  human  body.  Such  were  the 
interminable  systems  of  vibrations  propagated  along  the  nerves,  or  animal 
spirits  rushing  up  and  down  between  the  muscles  and  the  brain;  which,  if 
the  facts  could  have  been  proved,  would  have  been  an  important  addition 
to  our  knowledge  of  physiological  laws ; but  the  mere  invention,  or  arbi- 
trary supposition  of  them,  could  not  unless  by  the  strongest  delusion  be 
supposed  to  render  the  phenomena  of  animal  life  more  comprehensible,  or 
less  mysterious.  Nothing,  however,  seemed  satisfactory,  but  to  make  out 
that  motion  was  caused  by  motion  ; by  something  like  itself.  If  it  was 
not  one  kind  of  motion,  it  must  be  another.  In  like  manner  it  was  sup- 
posed that  the  physical  qualities  of  objects  must  arise  from  some  similar 
quality,  or  perhaps  only  some  quality  bearing  the  same  name,  in  the  parti- 
cles or  atoms  of  which  the  objects  were  composed  ; that  a sharp  taste,  for 
example,  must  arise  from  sharp  particles.  And  reversing  the  inference,  the 
effects  produced  by  a phenomenon  must,  it  was  supposed,  resemble  in  their 
physical  attributes  the  phenomenon  itself.  The  influences  of  the  planets 
were  supposed  to  be  analogous  to  their  visible  peculiarities  : Mars,  being  of 
a red  color,  portended  fire  and  slaughter;  and  the  like. 

Passing  from  physics  to  metaphysics,  we  may  notice  among  the  most  re- 
markable fruits  of  this  a priori  fallacy  two  closely  analogous  theories,  em- 
ployed in  ancient  and  modern  times  to  bridge  over  the  chasm  between  the 
world  of  mind  and  that  of  matter  ; the  species  sensibiles  of  the  Epicureans, 
and  the  modern  doctrine  of  perception  by  means  of  ideas.  These  theories 
are  indeed,  probably,  indebted  for  their  existence  not  solely  to  the  fallacy  in 


53G 


FALLACIES. 


question,  but  to  that  fallacy  combined  with  another  natural  prejudice  already 
adverted  to,  that  a thing  can  not  act  where  it  is  not.  In  both  doctrines 
it  is  assumed  that  the  phenomenon  which  takes  place  in  us  when  we  see 
or  touch  an  object,  and  which  we  regard  as  an  effect  of  that  object,  or  rath- 
er of  its  presence  to  our  organs,  must  of  necessity  resemble  very  closely  the 
outward  object  itself.  To  fulfill  this  condition,  the  Epicureans  supposed 
that  objects  were  constantly  projecting  in  all  directions  impalpable  images 
of  themselves,  which  entered  at  the  eyes  and  penetrated  to  the  mind;  while 
modern  metaphysicians,  though  they  rejected  this  hypothesis,  agreed  in 
deeming  it  necessary  to  suppose  that  not  the  thing  itself, but  a mental  im- 
age or  representation  of  it,  was  the  direct  object  of  perception.  Dr.  Reid 
had  to  employ  a world  of  argument  and  illustration  to  familiarize  people 
with  the  truth,  that  the  sensations  or  impressions  on  our  minds  need  not 
necessarily  be  copies  of,  or  bear  any  resemblance  to,  the  causes  which  pro- 
duce them;  in  opposition  to  the  natural  prejudice  which  led  people  to  as- 
similate the  action  of  bodies  upon  our  senses,  and  through  them  upon  our 
minds,  to  the  transfer  of  a given  form  from  one  object  to  another  by  actual 
moulding.  The  works  of  Dr.  Reid  are  even  now  the  most  effectual  course  of 
study  for  detaching  the  mind  from  the  prejudice  of  which  this  was  an  exam- 
ple. And  the  value  of  the  service  which  he  thus  rendered'to  popular  philos- 
ophy is  not  much  diminished,  although  we  may  hold,  with  Brown,  that  he 
went  too  far  in  imputing  the  “ideal  theory”  as  an  actual  tenet,  to  the  gen- 
eralitv  of  the  philosophers  who  preceded  him,  and  especially  to  Locke  and 
If  ume ; for  if  they  did  not  themselves  consciously  fall  into  the  error,  unques- 
tionably they  often  led  their  readers  into  it. 

The  prejudice,  that  the  conditions  of  a phenomenon  must  resemble  the 
phenomenon,  is  occasionally  exaggerated,  at  least  verbally,  into  a still  more 
palpable  absurdity ; the  conditions  of  the  thing  are  spoken  of  as  if  they 
were  the  very  thing  itself.  In  Bacon’s  model  inquiry,  which  occupies  so 
great  a space  in  the  Novum  Organum , the  inquisitio  informant  calidi,  the 
conclusion  which  he  favors  is  that  heat  is  a kind  of  motion;  meaning  of 
course  not  the  feeling  of  heat, but  the  conditions  of  the  feeling;  meaning, 
therefore,  only  that  wherever  there  is  heat,  there  must  first  be  a particu- 
lar kind  of  motion  ; but  he  makes  no  distinction  in  his  language  between 
these  two  ideas,  expressing  himself  as  if  heat,  and  the  conditions  of  heat, 
were  one  and  the  same  thing.  So  the  elder  Darwin,  in  the  beginning  of 
his  Zoonomia , says,  “ The  word  idea  has  various  meanings  in  the  writers  of 
metaphysics;  it  is  here  used  simply  for  those  notions  of  external  things 
which  our  organs  of  sense  bring  us  acquainted  with  originally”  (thus  far 
the  proposition,  though  vague,  is  unexceptionable  in  meaning),  “and  is  de- 
fined a contraction,  a motion,  or  configuration,  of  the  fibres  which  constitute 
the  immediate  organ  of  sense.”  Our  notions , a configuration  of  the  fibres  ! 
What  kind  of  logician  must  he  be  who  thinks  that  a phenomenon  is  defined 
to  be  the  condition  on  which  ho  supposes  it  to  depend  ? Accordingly  he 
says  soon  after,  not  that  our  ideas  are  caused  by,  or  consequent  on,  certain 
organic  phenomena,  but  “ our  ideas  are  animal  motions  of  the  organs  of 
sense.”  And  this  confusion  runs  through  the  four  volumes  of  the  Zoono- 
mia; the  reader  never  knows  whether  the  writer  is  speaking  of  the  effect, 
or  of  its  supposed  cause;  of  the  idea,  a state  of  mental  consciousness,  or  of 
the  state  of  the  nerves  and  brain  which  he  considers  it  to  presuppose. 

I have  given  a variety  of  instances  in  which  the  natural  prejudice,  that 
causes  and  their  effects  must  resemble  one  another,  has  operated  in  practice 
so  as  to  give  rise  to  serious  errors.  I shall  now  go  further,  and  produce 


FALLACIES  OF  SIMPLE  INSPECTION. 


537 


from  writings  even  of  the  present  or  very  recent  times,  instances  in  which 
this  prejudice  is  laid  down  as  an  established  principle.  M.  Victor  Cousin, 
in  the  last  of  his  celebrated  lectures  on  Locke,  enunciates  the  maxim  in  the 
following  unqualified  terms:  “Tout  ce  qui  est  vrai  de  l’effet,  est  vrai  de  la 
cause.”  A doctrine  to  which,  unless  in  some  peculiar  and  technical  mean- 
ing of  the  words  cause  and  effect,  it  is  not  to  be  imagined  that  any  person 
would  literally  adhere;  but  he  who  could  so  write  must  be  far  enough  from 
seeing  that  the  very  reverse  might  be  the  effect;  that  there  is  nothing  im- 
possible in  the  supposition  that  no  one  property  which  is  true  of  the  effect 
might  be  true  of  the  cause.  Without  going  quite  so  far  in  point  of  ex- 
pression, Coleridge,  in  his  Diographia  Literciria*  affirms  as  an  “evident 
truth,”  that  “ the  law  of  causality  holds  only  between  homogeneous  things, 
i.  e.,  things  having  some  common  property,”  and  therefore  “ can  not  extend 
from  one  world  into  another,  its  opposite  ;”  hence,  as  mind  and  matter 
have  no  common  property,  mind  can  not  act  upon  matter,  nor  matter 
upon  mind.  What  is  this  but  the  a priori  fallacy  of  which  we  are  speak- 
ing? The  doctrine,  like  many  others  of  Coleridge,  is  taken  from  Spinoza, 
in  the  first  book  of  whose  Ethicci  ( De  Deo ) it  stands  as  the  Third  Propo- 
sition, “Quae  res  nihil  commune  inter  se  habent,  earum  una  alterius  causa 
esse  non  potest,”  and  is  there  proved  from  two  so-called  axioms,  equally 
gratuitous  with  itself ; but  Spinoza  ever  systematically  consistent,  pursued 
the  doctrine  to  its  inevitable  consequence,  the  materiality  of  God. 

The  same  conception  of  impossibility  led  the  ingenious  and  subtle  mind 
of  Leibnitz  to  his  celebrated  doctrine  of  a pre-established  harmony.  He, 
too,  thought  that  mind  could  not  act  upon  matter,  nor  matter  upon  mind, 
and  that  the  two,  therefore,  must  have  been  arranged  by  their  Maker  like 
two  clocks,  which,  though  unconnected  with  one  another,  strike  simultane- 
ously, and  always  point  to  the  same  hour.  Malebranche’s  equally  famous 
theory  of  Occasional  Causes  was  another  form  of  the  same  conception ; in- 
stead of  supposing  the  clocks  originally  arranged  to  strike  together,  he  held 
that  when  the  one  strikes,  God  interposes,  and  makes  the  other  strike  in 
correspondence  with  it. 

Descartes,  in  like  manner,  whose  works  are  a rich  mine  of  almost  every 
description  of  a priori  fallacy,  says  that  the  Efficient  Cause  must  at  least 
have  all  the  perfections  of  the  effect,  and  for  this  singular  reason  : “ Si  enim 
ponamus  aliquid  in  idea  reperiri  quod  non  fuerit  in  ejus  causa,  hoc  igitur 
habet  a nihilo ;”  of  which  it  is  scarcely  a parody  to  say,  that  if  there  be 
pepper  in  the  soup  there  must  be  pepper  in  the  cook  who  made  it,  since 
otherwise  the  pepper  would  be  without  a cause.  A similar  fallacy  is  com- 
mitted by  Cicero,  in  his  second  book  De  Finibus,  where,  speaking  in  his 
own  person  against  the  Epicureans,  he  charges  them  with  inconsistency  in 
saying  that  the  pleasures  of  the  mind  had  their  origin  from  those  of  the 
body,  and  yet  that  the  former  were  more  valuable,  as  if  the  effect  could  sur- 
pass the  cause.  “Animi  voluptas  oritur  propter  voluptatem  corporis,  et 
major  est  animi  voluptas  quam  corporis?  ita  fit  ut  gratulator,  lastior  sit 
quam  is  cui  gratulatur.”  Even  that,  surely,  is  not  an  impossibility;  a per- 
son’s good  fortune  has  often  given  more  pleasure  to  others  than  it  gave  to 
the  person  himself. 

Descartes,  with  no  less  readiness,  applies  the  same  principle  the  converse 
way,  and  infers  the  nature  of  the  effects  from  the  assumption  that  they 
must,  in  this  or  that  property  or  in  all  their  properties,  resemble  their 


Yol.  i.,  chap.  8. 


538 


FALLACIES. 


cause.  To  this  class  belong  his  speculations,  and  those  of  so  many  others 
after  him,  tending  to  infer  the  order  of  the  universe,  not  from  observation, 
but  by  a priori  reasoning  from  supposed  qualities  of  the  Godhead.  This 
sort  of  inference  was  probably  never  carried  to  a greater  length  than  it 
was  in  one  particular  instance  by  Descartes,  when,  as  a proof  of  one  of  his 
physical  principles,  that  the  quantity  of  motion  in  the  universe  is  invaria- 
ble, he  had  recourse  to  the  immutability  of  the  Divine  Nature.  Reason- 
ing of  a very  similar  character  is,  however,  nearly  as  common  now  as  it 
was  in  his  time,  and  does  duty  largely  as  a means  of  fencing  off  disagree- 
able conclusions.  Writers  have  not  yet  ceased  to  oppose  the  theory  of 
divine  benevolence  to  the  evidence  of  physical  facts,  to  the  principle  of 
population  for  example.  And  people  seem  in  general  to  think  that  they 
have  used  a very  powerful  argument,  when  they  have  said,  that  to  suppose 
some  proposition  true,  would  be  a reflection  on  the  goodness  or  wisdom  of 
the  Deity.  Put  into  the  simplest  possible  terms,  their  argument  is,  “If  it 
had  depended  on  me,  I would  not  have  made  the  proposition  true,  there- 
fore it  is  not  true.”  Put  into  other  words,  it  stands  thus:  “God  is  perfect, 
therefore  (what  I think)  perfection  must  obtain  in  nature.”  But  since  in 
reality  every  one  feels  that  nature  is  very  far  from  perfect,  the  doctrine  is 
never  applied  consistently.  It  furnishes  an  argument  which  (like  many 
others  of  a similar  character)  people  like  to  appeal  to  when  it  makes  for 
their  own  side.  Nobody  is  convinced  by  it,  but  each  appears  to  think 
that  it  puts  religion  on  his  side  of  the  question,  and  that  it  is  a useful 
weapon  of  offense  for  wounding  an  adversary. 

Although  several  other  varieties  of  a priori  fallacy  might  probably  be 
added  to  those  here  specified,  these  are  all  against  which  it  seems  neces- 
sary to  give  any  special  caution.  Our  object  is  to  open,  without  attempt- 
ing or  affecting  to  exhaust,  the  subject.  Having  illustrated,  therefore,  this 
first  class  of  Fallacies  at  sufficient  length,  I shall  proceed  to  the  second. 


CHAPTER  IV. 

FALLACIES  OF  OBSERVATION. 

§ 1.  From  the  Fallacies  which  are  properly  Prejudices,  or  presumptions 
antecedent  to,  and  superseding,  proof,  we  pass  to  those  which  lie  in  the  in- 
correct performance  of  the  proving  process.  And  as  Proof,  in  its  widest 
extent,  embraces  one  or  more,  or  all,  of  three  processes,  Observation,  Gen- 
eralization, and  Deduction,  we  shall  consider  in  their  order  the  errors  ca- 
pable of  being  committed  in  these  three  operations.  And  first,  of  the  first 
mentioned. 

A fallacy  of  misobservation  may  be  either  negative  or  positive ; either 
Non -observation  or  Mai- observation.  It  is  non-observation,  when  all  the 
error  consists  in  overlooking,  or  neglecting,  facts  or  particulars  which 
ought  to  have  been  observed.  It  is  mal-observation,  when  something  is 
not  simply  unseen,  but  seen  wrong;  when  the  fact  or  phenomenon,  instead 
of  being  recognized  for  what  it  is  in  reality,  is  mistaken  for  something  else. 

§ 2.  Non-observation  may  either  take  place  by  overlooking  instances,  or 
by  overlooking  some  of  the  circumstances  of  a given  instance.  If  we  were 
to  conclude  that  a fortune-teller  was  a true  prophet,  from  not  adverting 
to  the  cases  in  which  his  predictions  had  been  falsified  by  the  event,  this 


FALLACIES  OF  OBSERVATION. 


539 


would  be  non-observation  of  instances ; but  if  we  overlooked  or  remained 
ignorant  of  the  fact  that  in  cases  where  the  predictions  had  been  fulfilled, 
he  had  been  in  collusion  with  some  one  who  had  given  him  the  informa- 
tion on  which  they  were  grounded,  this  would  be  non-observation  of  cir- 
cumstances. 

The  former  case,  in  so  far  as  the  act  of  induction  from  insufficient  evi- 
dence is  concerned,  does  not  fall  under  this  second  class  of  Fallacies,  but 
under  the  third,  Fallacies  of  Generalization.  In  every  such  case,  however, 
there  are  two  defects  or  errors  instead  of  one  ; there  is  the  error  of  treat- 
ing the  insufficient  evidence  as  if  it  were  sufficient,  which  is  a Fallacy  of 
the  third  class;  and  there  is  the  insufficiency  itself;  the  not  having  better 
evidence  ; which,  when  such  evidence,  or,  in  other  words,  when  other  in- 
stances, were  to  be  had,  is  Non-observation;  and  the  erroneous  inference, 
so  far  as  it  is  to  be  attributed  to  this  cause,  is  a Fallacy  of  the  second 
class. 

It  belongs  not  to  our  purpose  to  treat  of  non-observation  as  arising  from 
casual  inattention,  from  general  slovenliness  of  mental  habits,  want  of  due 
practice  in  the  use  of  the  observing  faculties,  or  insufficient  interest  in 
the  subject.  The  question  pertinent  to  logic  is — Granting  the  want  of 
complete  competency  in  the  observer,  on  what  point  is  that  insufficiency 
on  his  part  likely  to  lead  him  wrong?  or  rather,  what  sorts  of  instances, 
or  of  circumstances  in  any  given  instance,  are  most  likely  to  escape  the 
notice  of  observers  generally ; of  mankind  at  large. 

§ 3.  First,  then,  it  is  evident  that  when  the  instances  on  one  side  of  a 
question  are  more  likely  to  be  remembered  and  recorded  than  those  on 
the  other;  especially  if  there  be  any  strong  motive  to  preserve  the  memory 
of  the  first,  but  not  of  the  latter;  these  last  are  likely  to  be  overlooked, 
and  escape  the  observation  of  the  mass  of  mankind.  This  is  the  recog- 
nized explanation  of  the  credit  given,  in  spite  of  reason  and  evidence,  to 
many  classes  of  impostors;  to  quack -doctors,  and  fortune-tellers  in  all 
ages;  to  the  “cunning  man”  of  modern  times,  and  the  oracles  of  old. 
Few  have  considered  the  extent  to  which  this  fallacy  operates  in  practice, 
even  in  the  teeth  of  the  most  palpable  negative  evidence.  A striking  ex- 
ample of  it  is  the  faith  which  the  uneducated  portion  of  the  agricultural 
classes,  in  this  and  other  countries,  continue  to  repose  in  the  prophecies  as 
to  weather  supplied  by  almanac-makers  ; though  every  season  affords  to 
them  numerous  cases  of  completely  erroneous  prediction  ; but  as  every 
season  also  furnishes  some  cases  in  which  the  prediction  is  fulfilled,  this  is 
enough  to  keep  up  the  credit  of  the  prophet,  with  people  who  do  not  re' 
fleet  on  the  number  of  instances  requisite  for  what  we  have  called,  in  our 
inductive  terminology,  the  Elimination  of  Chance ; since  a certain  number 
of  casual  coincidences  not  only  may  but  will  happen,  between  any  two  un- 
connected events. 

Coleridge,  in  one  of  the  essays  in  the  Friend , has  illustrated  the  matter 
we  are  now  considering,  in  discussing  the  origin  of  a proverb,  “ which,  dif- 
ferently worded,  is  to  be  found  in  all  the  languages  of  Europe,”  viz.,  “For- 
tune favors  fools.”  He  ascribes  it  partly  to  the  “ tendency  to  exaggerate 
all  effects  that  seem  disproportionate  to  their  visible  cause,  and  all  circum- 
stances that  are  in  any  way  strongly  contrasted  with  our  notions  of  the 
persons  under  them.”  Omitting  some  explanations  which  would  refer  the 
error  to  mal-observation,  or  to  the  other  species  of  non-observation  (that 
of  circumstances),  I take  up  the  quotation  further  on.  “ Unforeseen  coinci- 


540 


FALLACIES. 


tlences  may  have  greatly  helped  a man,  yet  if  they  have  done  for  him  only 
what  possibly  from  his  own  abilities  he  might  have  effected  for  himself, 
his  good  luck  will  excite  less  attention,  and  the  instances  be  less  remem- 
bered. That  clever  men  should  attain  their  objects  seems  natural,  and  we 
neglect  the  circumstances  that  perhaps  produced  that  success  of  themselves 
without  the  intervention  of  skill  or  foresight ; but  we  dwell  on  the  fact  and 
remember  it,  as  something  strange,  when  the  same  happens  to  a weak  or 
ignorant  man.  So  too,  though  the  latter  should  fail  in  his  undertakings 
from  concurrences  that  might  have  happened  to  the  wisest  man,  yet  his 
failure  being  no  more  than  might  have  been  expected  and  accounted  for 
from  his  folly,  it  lays  no  hold  on  our  attention,  but  fleets  away  among  the 
other  undistinguished  waves  in  which  the  stream  of  ordinary  life  murmurs 
by  us,  and  is  forgotten.  Had  it  been  as  true  as  it  was  notoriously  false, 
that  those  all-embracing  discoveries,  which  have  shed  a dawn  of  science 
on  the  art  of  chemistry,  and  give  no  obscure  promise  of  some  one  great 
constitutive  law,  in  the  light  of  which  dwell  dominion  and  the  power  of 
prophecy  ; if  these  discoveries,  instead  of  having  been,  as  they  really  were, 
preconcerted  by  meditation,  and  evolved  out  of  his  own  intellect,  had  oc- 
curred by  a set  of  lucky  accidents  to  the  illustrious  father  and  founder  of 
philosophic  alchemy ; if  they  had  presented  themselves  to  Professor  Davy 
exclusively  in  consequence  of  his  luck  in  possessing  a particular  galvanic 
battery  ; if  this  battery,  as  far  as  Davy  was  concerned,  had  itself  been  an 
accident , and  not  (as  in  point  of  fact  it  was)  desired  and  obtained  by  him 
for  the  purpose  of  insuring  the  testimony  of  experience  to  his  principles, 
and  in  order  to  bind  down  material  nature  under  the  inquisition  of  reason, 
and  force  from  her,  as  by  torture,  unequivocal  answers  to  prepared  and 
preconceived  questions — yet  still  they  would  not  have  been  talked  of  or 
described  as  instances  of  luck,  but  as  the  natural  results  of  his  admitted 
genius  and  known  skill.  But  should  an  accident  have  disclosed  similar 
discoveries  to  a mechanic  at  Birmingham  or  Sheffield,  and  if  the  man 
should  grow  rich  in  consequence,  and  partly  by  the  envy  of  his  neighbors 
and  partly  with  good  reason,  be  considered  by  them  as  a man  below  par  in 
the  general  powers  of  his  understanding;  then,  ‘ Oh,  what  a lucky  fellow! 
Well,  Fortune  does  favor  fools — that’s  for  certain  ! It  is  always  so  !’  And 
forthwith  the  exclaimer  relates  half  a dozen  similar  instances.  Thus  ac- 
cumulating the  one  sort  of  facts  and  never  collecting  the  other,  we  do,  as 
poets  in  their  diction,  and  quacks  of  all  denominations  do  in  their  reason- 
ing, put  a part  for  the  whole.” 

This  passage  very  happily  sets  forth  the  manner  in  which,  under  the 
loose  mode  of  induction  which  proceeds  per  enumerationem  simplicem , 
not  seeking  for  instances  of  such  a kind  as  to  be  decisive  of  the  question, 
but  generalizing  from  any  which  occur,  or  rather  which  are  remembered, 
opinions  grow  up  with  the  apparent  sanction  of  experience,  which  have  no 
foundation  in  the  laws  of  nature  at  all.  “Itaquo  recte  respondit  ille”  (we 
may  say  with  Bacon*),  “ qui  cum  suspensa  tabula  in  templo  ei  monstrare- 
tur  eoruru,  qui  vota  solverant,  quod  naufragii  periculo  elapsi  sint,  atque 
interrogando  premeretur,  anno  turn  quidem  Deorum  numen  agnosceret, 
quassivitdenuo,  At  ubi  sunt  illi  depicti  qui  post  vota  nuncupata  perierunt? 
Eadem  ratio  est  fere  omnis  superstitionis,  ut  in  Astrologicis,  in  Sonmiis, 
Ominibns,  Nemesibus,  et  hujusmodi;  in  quibus,  homines  delectati  hujus- 
modi  vanitatibus,  advertunt  eventus,  ubi  implentur ; ast  ubi  fallunt,  licet 


Nov.  Org.,  Aph.  46. 


FALLACIES  OF  OBSERVATION. 


541 


multo  frequentius,  tamen  negligunt,  et  prsetereunt.”  And  he  proceeds  to 
say  that,  independently  of  the  love  of  the  marvelous,  or  any  other  bias  in 
the  inclinations,  there  is  a natural  tendency  in  the  intellect  itself  to  this 
kind  of  fallacy ; since  the  mind  is  more  moved  by  affirmative  instances, 
though  negative  ones  are  of  most  use  in  philosophy : “ Is  tamen  humano 
intellectui  error  est  proprius  et  perpetuus,  ut  magis  moveatur  et  excitetur 
Affirmativis  quam  Negativis ; cum  rite  et  ordine  sequum  so  utrique  p in- 
here debeat;  quin  contra,  in  omni  Axiomate  vero  constituendo,  major  vis 
est  instantise  negative.” 

But  the  greatest  of  all  causes  of  non-observation  is  a preconceived  opin- 
ion. This  it  is  which,  in  all  ages,  has  made  the  whole  race  of  mankind, 
and  every  separate  section  of  it,  for  the  most  part  unobservant  of  all  facts, 
however  abundant,  even  when  passing  under  their  own  eyes,  which  are  con- 
tradictory to  any  first  appearance,  or  any  received  tenet.  It  is  worth 
while  to  recall  occasionally  to  the  oblivious  memory  of  mankind  some  of 
the  striking  instances  in  which  opinions  that  the  simplest  experiment 
would  have  shown  to  be  erroneous,  continued  to  be  entertained  because 
nobody  ever  thought  of  trying  that  experiment.  One  of  the  most  remark- 
able of  these  was  exhibited  in  the  Copernican  controversy.  The  opponents 
of  Copernicus  argued  that  the  earth  did  not  move,  because  if  it  did,  a 
stone  let  fall  from  the  top  of  a high  tower  would  not  reach  the  ground  at 
the  foot  of  the  tower,  but  at  a little  distance  from  it,  in  a contrary  direc- 
tion to  the  earth’s  course  ; in  the  same  manner  (said  they)  as,  if  a ball  is 
let  drop  from  the  mast-head  while  the  ship  is  in  full  sail,  it  does  not  fall 
exactly  at  the  foot  of  the  mast,  but  nearer  to  the  stern  of  the  vessel.  The 
Copernicans  would  have  silenced  these  objectors  at  once  if  they  had  tried 
dropping  a ball  from  the  mast-head,  since  they  would  have  found  that  it 
does  fall  exactly  at  the  foot,  as  the  theory  requires ; but  no  ; they  admitted 
the  spurious  fact,  and  struggled  vainly  to  make  out  a difference  between 
the  two  cases.  “The  ball  was  no  part  of  the  ship — and  the  motion  for- 
ward was  not  natural , either  to  the  ship  or  to  the  ball.  The  stone,  on  the 
other  hand,  let  fall  from  the  top  of  the  tower,  was  a part  of  the  earth ; and 
therefore,  the  diurnal  and  annular  revolutions  which  were  natural  to  the 
earth,  were  also  natural  to  the  stone ; the  stone  would,  therefore,  retain 
the  same  motion  with  the  tower,  and  strike  the  ground  precisely  at  the 
bottom  of  it.”* 

Other  examples,  scarcely  less  striking,  are  recorded  by  Dr.  Whewell,f 
where  imaginary  laws  of  nature  have  continued  to  be  received  as  real, 
merely  because  no  person  had  steadily  looked  at  facts  which  almost  every 
one  had  the  opportunity  of  observing.  “A  vague  and  loose  mode  of  look- 
ing at  facts  very  easily  observable,  left  men  for  a long  time  under  the  be- 
lief that  a body  ten  times  as  heavy  as  another  falls  ten  times  as  fast ; that 
objects  immersed  in  water  are  always  magnified,  without  regard  to  the 
form  of  the  surface  ; that  the  magnet  exerts  an  irresistible  force ; that  crys- 
tal is  always  found  associated  with  ice;  and  the  like.  These  and  many 
others  are  examples  how  blind  and  careless  man  can  be  even  in  observation 
of  the  plainest  and  commonest  appearances ; and  they  show  us  that  the 
mere  faculties  of  perception,  although  constantly  exercised  upon  innumer- 
able objects,  may  long  fail  in  leading  to  any  exact  knowledge.” 

If  even  on  physical  facts,  and  these  of  the  most  obvious  character,  the 
observing  faculties  of  mankind  can  be  to  this  degree  the  passive  slaves  of 


Playfair’s  Dissertation , sect.  4. 


t Nov.  Orff.  Renov.,  p.  61. 


542 


FALLACIES. 


their  preconceived  impressions,  we  need  not  be  surprised  that  this  should 
be  so  lamentably  true  as  all  experience  attests  it  to  be,  on  things  more 
nearly  connected  with  their  stronger  feelings — on  moral,  social,  and  relig- 
ious subjects.  The  information  which  an  ordinary  traveler  brings  back 
from  a foreign  country,  as  the  result  of  the  evidence  of  his  senses,  is  almost 
always  such  as  exactly  confirms  the  opinions  with  which  he  set  out.  He 
has  had  eyes  and  ears  for  such  things  only  as  he  expected  to  see.  Men  read 
the  sacred  books  of  their  religion,  and  pass  unobserved  therein  multitudes 
of  things  utterly  irreconcilable  with  even  their  own  notions  of  moral  ex- 
cellence. With  the  same  authorities  before  them,  different  historians,  alike 
innocent  of  intentional  misrepresentation,  see  only  what  is  favorable  to 
Protestants  or  Catholics,  royalists  or  republicans,  Charles  I.  or  Cromwell; 
while  others,  having  set  out  with  the  preconception  that  extremes  must 
be  in  the  wrong,  are  incapable  of  seeing  truth  and  justice  when  these  are 
wholly  on  one  side. 

The  influence  of  a preconceived  theory  is  well  exemplified  in  the  super- 
stitions of  barbarians  respecting  the  virtues  of  medicaments  and  charms. 
The  negroes,  among  whom  corai,  as  of  old  among  ourselves,  is  worn  as  an 
amulet,  affirm,  according  to  Dr.  Paris,*  that  its  color  “is  always  affected 
by  the  state  of  health  of  the  wearer,  it  becoming  paler  in  disease.”  On  a 
matter  open  to  universal  observation,  a general  proposition  which  has  not 
the  smallest  vestige  of  truth  is  received  as  a result  of  experience ; the  pre- 
conceived opinion  preventing,  it  would  seem,  any  observation  whatever  on 
the  subject. 

§ 4.  For  illustration  of  the  first  species  of  non-observation,  that  of  In- 
stances, what  has  now  been  stated  may  suffice.  But  there  may  also  be 
non-observation  of  some  material  circumstances,  in  instances  which  have 
not  been  altogether  overlooked — nay,  which  may  be  the  very  instances  on 
which  the  whole  superstructure  of  a theory  has  been  founded.  As,  in  the 
cases  hitherto  examined,  a general  proposition  was  too  rashly  adopted,  on 
the  evidence  of  particulars,  true  indeed,  but  insufficient  to  support  it;  so 
in  the  cases  to  which  we  now  turn,  the  particulars  themselves  have  been 
imperfectly  observed,  and  the  singular  propositions  on  which  the  generali- 
zation is  grounded,  or  some  at  least  of  those  singular  propositions,  are 
false. 

Such,  for  instance,  was  one  of  the  mistakes  committed  in  the  celebrated 
phlogistic  theory ; a doctrine  which  accounted  for  combustion  by  the  ex- 
trication of  a substance  called  phlogiston,  supposed  to  be  contained  in  all 
combustible  matter.  The  hypothesis  accorded  tolerably  well  with  super- 
ficial appearances ; the  ascent  of  flame  naturally  suggests  the  escape  of  a 
substance ; and  the  visible  residuum  of  ashes,  in  bulk  and  weight,  generally 
falls  extremely  short  of  the  combustible  material.  The  error  was,  non-ob- 
servation of  an  important  portion  of  the  actual  residue,  namely,  the  gaseous 
products  of  combustion.  When  these  were  at  last  noticed  and  brought 
into  account,  it  appeared  to  be  a universal  law,  that  all  substances  gain  in- 
stead of  losing  weight  by  undergoing  combustion;  and  after  the  usual  at- 
tempt to  accommodate  the  old  theory  to  the  new  fact  by  means  of  an  ar- 
bitrary hypothesis  (that  phlogiston  had  the  quality  of  positive  levity  in- 
stead of  gravity),  chemists  were  conducted  to  the  true  explanation,  namely, 
that  instead  of  a substance  separated,  there  was,  on  the  contrary,  a substance 
absorbed. 


P harmacologia,  p.  21. 


FALLACIES  OF  OBSERVATION. 


543 


Many  of  the  absurd  practices  which  have  been  deemed  to  possess  medic- 
inal efficacy,  have  been  indebted  for  their  reputation  to  non-observance  of 
some  accompanying  circumstance  which  was  the  real  agent  in  the  cures 
ascribed  to  them.  Thus,  of  the  sympathetic  powder  of  Sir  Kenelm  Digbv : 
“ Whenever  any  wound  had  been  inflicted,  this  powder  was  applied  to  the 
weapon  that  had  inflicted  it,  which  was,  moreover,  covered  with  ointment, 
and  dressed  two  or  three  times  a day.  The  wound  itself,  in  the  mean  time, 
was  directed  to  be  brought  together,  and  carefully  bound  up  with  clean 
linen  rags,  but , -above  all , to  be  let  alone  for  seven  days,  at  the  end  of  which 
period  the  bandages  were  removed,  when  the  wound  was  generally  found 
perfectly  united.  The  triumph  of  the  cure  was  decreed  to  the  mysterious 
agency  of  the  sympathetic  powder  which  had  been  so  assiduously  applied 
to  the  weapon,  whereas  it  is  hardly  necessary  to  observe  that  the  prompt- 
ness of  the  cure  depended  on  the  total  exclusion  of  air  from  the  wound, 
and  upon  the  sanative  operations  of  nature  not  having  received  any  dis- 
turbance from  the  officious  interference  of  art.  The  result,  beyond  all 
doubt,  furnished  the  first  hint  which  led  surgeons  to  the  improved  practice 
of  healing  wounds  by  what  is  technically  called  the  first  intention “In 
all  records,”  adds  Dr.  Paris,  of  “ extraordinary  cures  performed  by  mysteri- 
ous agents,  there  is  a great  desire  to  conceal  the  remedies  and  other  curative 
means  which  were  simultaneously  administered  with  them;  thus  Oribasius 
commends  in  high  terms  a necklace  of  Paeony  root  for  the  cure  of  epilepsy ; 
but  we  learn  that  he  always  took  care  to  accompany  its  use  with  copious 
evacuations,  although  he  assigns  to  them  no  share  of  credit  in  the  cure. 
In  later  times  we  have  a good  specimen  of  this  species  of  deception,  pre- 
sented to  us  in  a work  on  scrofula  by  Mr.  Morley,  written,  as  we  are  in- 
formed, for  the  sole  purpose  of  restoring  the  much-injured  character  and 
use  of  the  Vervain;  in  which  the  author  directs  the  root  of  this  plant  to 
be  tied  with  a yard  of  white  satin  ribbon  around  the  neck,  where  it  is  to 
remain  until  the  patient  is  cured;  but  mark — during  this  interval  he  calls 
to  his  aid  the  most  active  medicines  in  the  materia  medica.”f 

In  other  cases,  the  cures  really  produced  by  rest,  regimen,  and  amuse- 
ment have  been  ascribed  to  the  medicinal,  or  occasionally  to  the  supernatu- 
ral, means  which  were  put  in  requisition.  “The  celebrated  John  Wesley, 
while  he  commemorates  the  triumph  of  sulphur  and  supplication  over  his 
bodily  infirmity,  forgets  to  appreciate  the  resuscitating  influence  of  four 
months’  repose  from  his  apostolic  labors  ; and  such  is  the  disposition  of 
the  human  mind  to  place  confidence  in  the  operation  of  mysterious  agents, 
that  we  find  him  more  disposed  to  attribute  his  cure  to  a brown  paper 
plaster  of  egg  and  brimstone,  than  to  Dr.  Fothergill’s  salutary  prescription 
of  country  air,  rest,  asses’  milk,  and  horse  exercise.”! 

In  the  following  example,  the  circumstance  overlooked  was  of  a some- 
what different  character.  “When  the  yellow  fever  raged  in  America,  the 
practitioners  trusted  exclusively  to  the  copious  use  of  mercury ; at  first 
this  plan  was  deemed  so  universally  efficacious,  that,  in  the  enthusiasm  of  the 
moment,  it  was  triumphantly  proclaimed  that  death  never  took  place  after 
the  mercury  had  evinced  its  effect  upon  the  system  : all  this  was  very  true, 
but  it  furnished  no  proof  of  the  efficacy  of  that  metal,  since  the  disease  in  its 
aggravated  form  was  so  rapid  in  its  career,  that  it  swept  away  its  victims 
long  before  the  system  could  be  brought  under  mercurial  influence,  while  in 
its  milder  shap'e  it  passed  off  equally  well  without  any  assistance  from  art.”§ 


Pharmacologia,  pp.  23,  24. 


t Ibid.,  p.  28. 


X Ibid.,  p.  62.  § Ibid.,  pp.  61,  62. 


544 


FALLACIES. 


In  those  examples  the  circumstance  overlooked  was  cognizable  by  the 
senses.  In  other  cases,  it  is  one  the  knowledge  of  which  could  only  be  ar- 
rived at  by  reasoning ; but  the  fallacy  may  still  be  classed  under  the  head 
to  which,  for  want  of  a more  appropriate  name,  we  have  given  the  appel- 
lation Fallacies  of  Non-observation.  It  is  not  the  nature  of  the  facul- 
ties which  ought  to  have  been  employed,  but  the  non-employment  of  them, 
which  constitutes  this  Natural  Order  of  Fallacies.  Wherever  the  error  is 
negative,  not  positive ; wherever  it  consists  especially  in  overlooking , in 
being  ignorant  or  unmindful  of  some  fact  which,  if  known  and  attended  to, 
would  have  made  a difference  in  the  conclusion  arrived  at;  the  error  is 
properly  placed  in  the  Class  which  we  are  considering.  In  this  Class,  there 
is  not,  as  in  all  other  fallacies  there  is,  a positive  misestimate  of  evidence 
actually  had.  The  conclusion  would  be  just,  if  the  portion  which  is  seen 
of  the  case  were  the  whole  of  it;  but  there  is  another  portion  overlooked, 
which  vitiates  the  result. 

For  instance,  there  is  a remarkable  doctrine  which  has  occasionally  found 
a vent  in  the  public  speeches  of  unwise  legislators,  but  which  only  in  one 
instance  that  I am  aware  of  has  received  the  sanction  of  a philosophical 
writer,  namely,  M.  Cousin,  who  in  his  preface  to  the  Gorgias  of  Plato,  con- 
tending that  punishment  must  have  some  other  and  higher  justification 
than  the  prevention  of  crime,  makes  use  of  this  argument — that  if  punish- 
ment were  only  for  the  sake  of  example,  it  would  be  indifferent  whether 
we  punished  the  innocent  or  the  guilty,  since  the  punishment,  considered  as 
an  example,  is  equally  efficacious  in  either  case.  Now  we  must,  in  order 
to  go  along  with  this  reasoning,  suppose,  that  the  person  who  feels  himself 
under  temptation,  observing  somebody  punished,  concludes  himself  to  be 
in  danger  of  being  punished  likewise,  and  is  terrified  accordingly.  But  it 
is  forgotten  that  if  the  person  punished  is  supposed  to  be  innocent,  or  even 
if  there  be  any  doubt  of  his  guilt,  the  spectator  will  reflect  that  his  own 
danger,  whatever  it  may  be,  is  not  contingent  on  his  guiltiness,  but  threat- 
ens him  equally  if  he  remains  innocent,  and  how,  therefore,  is  he  deterred 
from  guilt  by  the  apprehension  of  such  punishment?  M.  Cousin  supposes 
that  people  will  be  dissuaded  from  guilt  by  whatever  renders  the  condi- 
tion of  the  guilty  more  perilous,  forgetting  that  the  condition  of  the  inno- 
cent (also  one  of  the  elements  in  the  calculation)  is,  in  the  case  supposed, 
made  perilous  in  precisely  an  equal  degree.  This  is  a fallacy  of  overlook- 
ing; or  of  non-observation,  within  the  intent  of  our  classification. 

Fallacies  of  this  description  are  the  great  stumbling-block  to  correct 
thinking  in  political  economy.  The  economical  workings  of  society  afford 
numerous  cases  in  which  the  effects  of  a cause  consist  of  two  sets  of  phe- 
nomena: the  one  immediate,  concentrated,  obvious  to  all  eyes,  and  passing, 
in  common  apprehension, for  the  whole  effect;  the  other  widely  diffused, 
or  lying  deeper  under  the  surface,  and  which  is  exactly  contrary  to  the 
former.  Take,  for  instance,  the  common  notion  so  plausible  at  the  first 
glance,  of  the  encouragement  given  to  industry  by  lavish  expenditure.  A, 
who  spends  his  whole  income,  and  even  his  capital,  in  expensive  living,  is 
supposed  to  give  great  employment  to  labor.  B,  who  lives  on  a small  por- 
tion, and  invests  the  remainder  in  the  funds,  is  thought  to  give  little  or 
no  employment.  For  every  body  sees  the  gains  which  are  made  by  A’s 
tradesmen,  servants,  and  others,  while  his  money  is  spending.  B’s  sav- 
ings, on  the  contrary,  pass  into  the  hands  of  the  person  w'hose  stock  he 
purchased,  who  with  it  pays  a debt  he  owed  to  some  banker,  who  lends  it 
again  to  some  merchant  or  manufacturer;  and  the  capital  being  laid  out 


FALLACIES?  OF  OBSERVATION. 


545 


in  hiring  spinners  and  weavers,  or  carriers  and  the  crews  of  merchant  ves- 
sels, not  only  gives  immediate  employment  to  at  least  as  much  industry  as 
A employs  during  the  whole  of  his  career,  but  coming  back  with  increase 
by  the  sale  of  the  goods  which  have  been  manufactured  or  imported,  forms 
a fund  for  the  employment  of  the  same  and  perhaps  a greater  quantity  of 
labor  in  perpetuity.  But  the  observer  does  not  see,  and  therefore  does 
not  consider,  what  becomes  of  B’s  money;  he  does  see  what  is  done  with 
A’s ; he  observes  the  amount  of  industry  which  A’s  profusion  feeds;  he 
observes  not  the  far  greater  quantity  which  it  prevents  from  being  fed; 
and  thence  the  prejudice,  universal  to  the  time  of  Adam  Smith,  that  prodi- 
gality encourages  industry,  and  parsimony  is  a discouragement  to  it. 

The  common  argument  against  free  trade  was  a fallacy  of  the  same  na- 
ture. The  purchaser  of  British  silk  encourages  British  industry ; the  pur- 
chaser of  Lyons  silk  encourages  only  French  ; the  former  conduct  is  patri- 
otic, the  latter  ought  to  be  prevented  by  law.  The  circumstance  is  over- 
looked, that  the  purchaser  of  any  foreign  commodity  necessarily  causes,  di- 
rectly or  indirectly,  the  export  of  an  equivalent  value  of  some  article  of 
home  production  (beyond  what  would  otherwise  be  exported),  either  to 
the  same  foreign  country  or  to  some  other;  which  fact,  though  from  the 
complication  of  the  circumstances  it  can  not  always  be  verified  by  specific 
observation,  no  observation  can  possibly  be  brought  to  contradict,  while  the 
evidence  of  reasoning  on  which  it  rests  is  irrefragable.  The  fallacy  is, 
therefore,  the  same  as  in  the  preceding  case, .that  of  seeing  a part  only  of 
the  phenomena,  and  imagining  that  part  to  be  the  whole;  and  may  be 
ranked  among  Fallacies  of  Non-observation. 

§ 5.  To  complete  the  examination  of  the  second  of  our  five  classes,  we 
have  now  to  speak  of  Mal-observation ; in  which  the  error  does  not  lie  in 
the  fact  that  something  is  unseen,  but  that  something  seen  is  seen  wrong. 

Perception  being  infallible  evidence  of  whatever  is  really  perceived,  the 
error  now  under  consideration  can  be  committed  no  otherwise  than  by 
mistaking  for  conception  what  is,  in  fact,  inference.  We  have  formerly 
shown  how  intimately  the  two  are  blended  in  almost  every  thing  which  is 
called  observation,  and  still  more  in  every  Description.*  What  is  actually 
on  any  occasion  perceived  by  our  senses  being  so  minute  in  amount,  and 
generally  so  unimportant  a portion  of  the  state  of  facts  which  we  wish  to 
ascertain  or  to  communicate;  it  would  be  absurd  to  say  that  either  in  our 
observations,  or  in  conveying  their  result  to  others,  we  ought  not  to  mingle 
inference  with  fact;  all  that  can  be  said  is,  that  when  we  do  so  we  ought 
to  be  aware  of  what  we  are  doing,  and  to  know  what  part  of  the  assertion 
rests  on  consciousness,  and  is  therefore  indisputable,  what  part  on  inference, 
and  is  therefore  questionable. 

One  of  the  most  celebrated  examples  of  a universal  error  produced  by 
mistaking  an  inference  for  the  direct  evidence  of  the  senses,  was  the  resist- 
ance made,  on  the  ground  of  common  sense,  to  the  Copernican  system. 
People  fancied  they  saio  the  sun  rise  and  set,  the  stars  revolve  in  circles 
round  the  pole.  We  now  know  that  they  saw  no  such  thing;  what  they 
really  saw  was  a set  of  appearances,  equally  reconcilable  with  the  theory 
they  held  and  with  a totally  different  one.  It  seems  strange  that  such  an 
instance  as  this  of  the  testimony  of  the  senses  pleaded  with  the  most  en- 
tire conviction  in  favor  of  something  which  was  a mere  inference  of  the 


* Suvra,  p.  450. 
35 


546 


FALLACIES. 


judgment,  and,  as  it  turned  out,  a false  inference,  should  not  have  opened 
tlie  eyes  of  the  bigots  of  common  sense,  and  inspired  them  with  a more 
modest  distrust  of  the  competency  of  mere  ignorance  to  judge  the  conclu- 
sions of  cultivated  thought. 

In  proportion  to  any  person’s  deficiency  of  knowledge  and  mental  culti- 
vation is,  generally,  his  inability  to  discriminate  between  his  inferences  and 
the  perceptions  on  which  they  were  grounded.  Many  a marvelous  tale, 
many  a scandalous  anecdote,  owes  its  origin  to  this  incapacity.  The  nar- 
rator relates,  not  what  he  saw  or  heard,  but  the  impression  which  he  de- 
rived from  what  he  saw  or  heard,  and  of  which  perhaps  the  greater  part 
consisted  of  inference,  though  the  whole  is  related  not  as  inference  but  as 
matter  of  fact.  The  difficulty  of  inducing  witnesses  to  restrain  within  any 
moderate  limits  the  intermixture  of  their  inferences  with  the  narrative  of 
their  perceptions,  is  well  known  to  experienced  cross-examiners;  and  still 
more  is  this  the  case  when  ignorant  persons  attempt  to  describe  any  natu- 
ral phenomenon.  “The  simplest  nai native,”  says  Dugald  Stewart,*  “of 
the  most  illiterate  observer  involves  more  or  less  of  hypothesis;  nay,  in 
general,  it  will  be  found  that,  in  proportion  to  his  ignorance,  the  greater  is 
the  number  of  conjectural  principles  involved  in  his  statements.  A village 
apothecary  (and,  if  possible,  in  a still  greater  degree,  an  experienced  nurse) 
is  seldom  able  to  describe  the  plainest  case,  without  employing  a phraseol- 
ogy of  which  every  word  is  a theory:  whereas  a simple  and  genuine  speci- 
fication of  the  phenomena  which  mark  a particular  disease  ; a specification 
unsophisticated  by  fancy,  or  by  preconceived  opinions,  may  be  regarded  as 
unequivocal  evidence  of  a mind  trained  by  long  and  successful  study  to  the 
most  difficult  of  all  arts,  that  of  the  faithful  interpretation  of  nature.” 

The  universality  of  the  confusion  between  perceptions  and  the  inferences 
drawm  from  them,  and  the  rarity  of  the  power  to  discriminate  the  one  from 
the  other,  ceases  to  surprise  us  when  we  consider  that  in  the  far  greater 
number  of  instances  the  actual  perceptions  of  our  senses  are  of  no  impor- 
tance or  interest  to  us  except  as  marks  from  which  wTe  infer  something  be- 
yond them.  It  is  not  the  color  and  superficial  extension  perceived  by  the 
eye  that  are  important  to  us,  but  the  object,  of  w'hich  those  visible  appear- 
ances testify  the  presence;  and  wdiere  the  sensation  itself  is  indifferent,  as 
it  generally  is,  we  have  no  motive  to  attend  particularly  to  it,  but  acquire  a 
habit  of  passing  it  over  without  distinct  consciousness,  and  going  on  at 
once  to  the  inference.  So  that  to  know  w'hat  the  sensation  actually  was,  is 
a study  in  itself,  to  which  painters,  for  example,  have  to  train  themselves 
by  special  and  long-continued  discipline  and  application.  In  things  farther 
removed  from  the  dominion  of  the  outward  senses,  no  one  who  has  not 
great  experience  in  pyschologie.nl  analysis  is  competent  to  break  this  in- 
tense association  ; and  when  such  analytic  habits  do  not  exist  in  the  requi- 
site degree,  it  is  hardly  possible  to  mention  any  of  the  habitual  judgments 
of  mankind  on  subjects  of  a high  degree  of  abstraction,  from  the  being  of 
a God  and  the  immortality  of  the  soul  down  to  the  multiplication  table, 
which  are  not,  or  have  not  been,  considered  as  matter  of  direct  intuition. 
So  strong  is  the  tendency  to  ascribe  an  intuitive  character  to  judgments 
which  are  mere  inferences,  and  often  false  ones.  No  one  can  doubt  that 
many  a deluded  visionary  has  actually  believed  that  he  was  directly  in- 
spired from  Heaven,  and  that  the  Almighty  had  conversed  with  him  face 
to  face;  which  yet  was  only,  on  his  part,  a conclusion  drawn  from  appear 


Elements  of  the  Philosophy  of  the  Mind , vol.  ii. , chap.  4,  sect.  5. 


FALLACIES  OF  GENERALIZATION. 


547 


ances  to  his  senses,  or  feelings  in  his  internal  consciousness,  which  afforded 
no  warrant  for  any  such  belief.  A caution,  therefore,  against  this  class  of 
errors,  is  not  only  needful  but  indispensable ; though  to  determine  wheth- 
er, on  any  of  the  great  questions  of  metaphysics,  such  errors  are  actually 
committed,  belongs  not  to  this  place,  but,  as  I have  so  often  said,  to  a dif- 
ferent science. 


CHAPTER  V. 

FALLACIES  OF  GENERALIZATION. 

§ 1.  The  class  of  Fallacies  of  which  we  are  now  to  speak,  is  the  most 
extensive  of  all ; embracing  a greater  number  and  variety  of  unfounded 
inferences  than  any  of  the  other  classes,  and  which  it  is  even  more  difficult 
to  reduce  to  sub-classes  or  species.  If  the  attempt  made  in  the  preceding- 
books  to  define  the  principles  of  well-grounded  generalization  has  been 
successful,  all  generalizations  not  conformable  to  those  principles  might, 
in  a certain  sense,  be  brought  under  the  present  class;  when,  however,  the 
rules  are  known  and  kept  in  view,  but  a casual  lapse  committed  in  the  ap- 
plication of  them,  this  is  a blunder,  not  a fallacy.  To  entitle  an  error  of 
generalization  to  the  latter  epithet,  it  must  be  committed  on  principle; 
there  must  lie  in  it  some  erroneous  general  conception  of  the  inductive 
process ; the  legitimate  mode  of  drawing  conclusions  from  observation  and 
experiment  must  be  fundamentally  misconceived. 

Without  attempting  any  thing  so  chimerical  as  an  exhaustive  classifica- 
tion of  all  the  misconceptions  which  can  exist  on  the  subject,  let  us  con- 
tent ourselves  with  noting,  among  the  cautions  which  might  be  suggested, 
a few  of  the  most  useful  and  needful. 

§ 2.  In  the  first  place,  there  are  certain  kinds  of  generalization  which, 
if  the  principles  already  laid  down  be  correct,  must  be  groundless;  expe- 
rience can  not  afford  the  necessary  conditions  for  establishing  them  by  a 
correct  induction.  Such,  for  instance,  are  all  inferences  from  the  order  of 
nature  existing  on  the  earth,  or  in  the  solar  system,  to  that  which  may 
exist  in  remote  parts  of  the  universe;  where  the  phenomena,  for  aught  we 
know,  may  be  entirely  different,  or  may  succeed  one  another  according  to 
different  laws,  or  even  according  to  no  fixed  law  at  all.  Such,  again,  in 
matters  dependent  on  causation,  are  all  universal  negatives,  all  propositions 
that  assert  impossibility.  The  non-existence  of  any  given  phenomenon, 
however  uniformly  experience  may  as  yet  have  testified  to  the  fact,  proves 
at  most  that  no  cause,  adequate  to  its  production,  has  yet  manifested  itself ; 
but  that  no  such  causes  exist  in  nature  can  only  be  inferred  if  we  are  so 
foolish  as  to  suppose  that  we  know  all  the  forces  in  nature.  The  supposi- 
tion would  at  least  be  premature  while  our  acquaintance  with  some  even 
of  those  which  we  do  know  is  so  extremely  recent.  And  however  much 
our  knowledge  of  nature  may  hereafter  be  extended,  it  is  not  easy  to  see 
how  that  knowledge  could  ever  be  complete,  or  how,  if  it  were,  we  could 
ever  be  assured  of  its  being  so. 

The  only  laws  of  nature  which  afford  sufficient  warrant  for  attributing 
impossibility  (even  with  reference  to  the  existing  order  of  nature,  and  to 
our  own  region  of  the  universe)  are,  first,  those  of  number  and  extension, 
which  are  paramount  to  the  laws  of  the  succession  of  phenomena,  and  not 
exposed  to  the  agency  of  counteracting  causes ; and,  secondly,  the  universal 


545 


FALLACIES. 


law  of  causality  itself.  That  no  variation  in  any  effect  or  consequent  will 
take  place  while  the  whole  of  the  antecedents  remain  the  same,  may  be 
affirmed  with  full  assurance.  But,  that  the  addition  of  some  new  anteced- 
ent might  not  entirely  alter  and  subvert  the  accustomed  consequent,  or  that 
antecedents  competent  to  do  I his  do  not  exist  in  nature,  we  are  in  no  case 
empowered  positively  to  conclude. 

§ 3.  It  is  next  to  be  remarked  that  all  generalizations  which  profess, 
like  the  theories  of  Thales,. Democritus,  and  others  of  the  early  Greek 
speculators,  to  resolve  all  things  into  some  one  element,  or  like  many  mod- 
ern theories,  to  resolve  phenomena  radically  different  into  the  same,  are 
necessarily  false.  By  radically  different  phenomena  I mean  impressions 
on  our  senses  which  differ  in  quality,  and  not  merely  in  degree.  On  this 
subject  what  appeared  necessary  was  said  in  the  chapter  on  the  Limits  to 
the  Explanation  of  Laws  of  Nature;  but  as  the  fallacy  is  even  in  our  own 
times  a common  one,  I shall  touch  on  it  somewhat  further  in  this  place. 

When  we  say  that  the  force  which  retains  the  planets  in  their  orbits  is 
resolved  into  gravity,  or  that  the  force  which  makes  substances  combine 
chemically  is  resolved  into  electricity,  we  assert  in  the  one  case  what  is, 
and  in  the  other  case  what  might,  and  probably  will  ultimately,  be  a legiti- 
mate result  of  induction.  In  both  these  cases  motion  is  resolved  into  mo- 
tion. The  assertion  is,  that  a case  of  motion,  which  was  supposed  to  be 
special,  and  to  follow  a distinct  law  of  its  own,  conforms  to  and  is  included 
in  the  general  law  which  regulates  another  class  of  motions.  But,  from 
these  and  similar  generalizations,  countenance  and  currency  have  been 
given  to  attempts  to  resolve,  not  motion  into  motion,  but  heat  into  motion, 
light  into  motion,  sensation  itself  into  motion  ; states  of  consciousness  into' 
states  of  the  nervous  system,  as  in  the  ruder  forms  of  the  materialist  phi- 
losophy; vital  phenomena  into  mechanical  or  chemical  processes,  as  in 
some  schools  of  physiology. 

Now  I am  far  from  pretending  that  it  may  not  be  capable  of  proof,  or 
that  it  is  not  an  important  addition  to  our  knowledge  if  proved,  that  cer- 
tain motions  in  the  particles  of  bodies  are  the  conditions  of  the  production 
of  heat  or  light;  that  certain  assignable  physical  modifications  of  the  nerves 
may  be  the  conditions  not  only  of  our  sensations  or  emotions,  but  even  of 
our  thoughts;  that  certain  mechanical  and  chemical  conditions  may,  in  the 
order  of  nature,  be  sufficient  to  determine  to  action  the  physiological  laws 
of  life.  All  I insist  upon,  in  common  with  every  thinker  who  entertains 
any  clear  idea  of  the  logic  of  science,  is,  that  it  shall  not  be  supposed  that 
by  proving  these  things  one  step  would  be  made  toward  a real  explanation 
of  heat,  light,  or  sensation ; or  that  the  generic  peculiarity  of  those  phe- 
nomena can  be  in  the  least  degree  evaded  by  any  such  discoveries,  how- 
ever well  established.  Let  it  be  shown,  for  instance,  that  the  most  com- 
plex series  of  physical  causes  and  effects  succeed  one  another  in  the  eye 
and  in  the  brain  to  produce  a sensation  of  color;  rays  falling  on  the  eye, 
refracted,  converging,  crossing  one  another,  making  an  inverted  image  on 
the  retina,  and  after  this  a motion — let  it  be  a vibration,  or  a rush  of  nerv- 
ous fluid,  or  whatever  else  you  are  pleased  to  suppose,  along  the  optic 
nerve — a propagation  of  this  motion  to  the  brain  itself,  and  as  many  more 
different  motions  as  you  choose ; still,  at  the  end  of  these  motions,  there  is 
something  which  is  not  motion,  there  is  a feeling  or  sensation  of  color. 
Whatever  number  of  motions  we  may  be  able  to  interpolate,  and  whether 
they  be  real  or  imaginary,  we  shall  still  find,  at  the  end  of  the  series,  a mo- 


FALLACIES  OF  GENERALIZATION. 


549 


tion  antecedent  and  a color  consequent.  The  mode  in  which  any  one  of 
the  motions  produces  the  next,  may  possibly  be  susceptible  of  explanation 
by  some  general  law  of  motion : but  the  mode  in  which  the  last  motion 
produces  the  sensation  of  color,  can  not  be  explained  by  any  law  of  mo- 
tion ; it  is  the  law  of  color : which  is,  and  must  always  remain,  a peculiar 
thing.  Where  our  consciousness  recognizes  between  two  phenomena  an 
inherent  distinction ; where  we  are  sensible  of  a difference  which  is  not 
merely  of  degree,  and  feel  that  no  adding  one  of  the  phenomena  to  itself 
would  produce  the  other;  any  theory  which  attempts  to  bring  either  un- 
der the  laws  of  the  other  must  be  false ; though  a theory  which  merely 
treats  the  one  as  a cause  or  condition  of  the  other,  may  possibly  be  true. 

§ 4.  Among  the  remaining  forms  of  erroneous  generalization,  several  of 
those  most  worthy  of  and  most  requiring  notice  have  fallen  under  our  ex- 
amination in  former  places,  where,  in  investigating  the  rules  of  correct  in- 
duction, we  have  had  occasion  to  advert  to  the  distinction  between  it  and 
some  common  mode  of  the  incorrect.  In  this  number  is  what  I have  for- 
merly called  the  natural  Induction  of  uninquiring  minds,  the  induction  of 
the  ancients,  which  proceeds  per  enumerationem  simplicem : “This,  that, 
and  the  other  A are  B,  I can  not  think  of  any  A which  is  not  B,  therefore 
every  A is  B.”  As  a final  condemnation  of  this  rude  and  slovenly  mode 
of  generalization,  I will  quote  Bacon’s  emphatic  denunciation  of  it ; the 
most  important  part,  as  I have  more  than  once  ventured  to  assert,  of  the 
permanent  service  rendered  by  him  to  philosophy.  “Inductio  quae  pro- 
cedit  per  enumerationem  simplicem,  res  puerilis  est,  et  precario  concludit” 
(concludes  only  by  your  leave,  or  provisionally),  “ et  periculo  exponitur  ab 
instantia  contradictoria,  et  plerumque  secundum  pauciora  quam  par  est,  et 
ex  his  tantummodo  qua ? pnesto  sunt pronunciat.  At  Inductio  quae  ad  in- 
ventionem  et  demonstrationem  Scientiarum  et  Artiom  erit  utilis,  Naturam 
separate  debet,  per  rejectiones  et  exclusiones  debitas;  ac  deinde  post  nega- 
tivas  tot  quot  sufficiunt,  super  affirmativas  concludere.” 

I have  already  said  that  the  mode  of  Simple  Enumeration  is  still  the 
common  and  received  method  of  Induction  in  whatever  relates  to  man  and 
society.  Of  this  a very  few  instances,  more  by  way  of  memento  than  of 
instruction,  may  suffice.  What,  for  example,  is  to  be  thought  of  all  the 
“common-sense”  maxims  for  which  the  following  may  serve  as  the  uni- 
versal formula,  “Whatsoever  has  never  been,  will  never  be.”  As  for  ex- 
ample : negroes  have  never  been  as  civilized  as  whites  sometimes  are, 
therefore  itT  is  impossible  they  should  be  so.  Women,  as  a class,  are  sup- 
posed not  to  have  hitherto  been  equal  in  intellect  to  men,  therefore  they 
are  necessarily  inferior.  Society  can  not  prosper  without  this  or  the  other 
institution ; e.  y.,  in  Aristotle’s  time,  without  slavery ; in  later  times,  with- 
out an  established  priesthood,  without  artificial  distinctions  of  rank,  etc. 
One  poor  person  in  a thousand,  educated,  while  the  nine  hundred  and  nine- 
ty-nine remain  uneducated,  has  usually  aimed  at  raising  himself  out  of  his 
class,  therefore  education  makes  people  dissatisfied  with  the  condition  of  a 
laborer.  Bookish  men,  taken  from  speculative  pursuits  and  set  to  work 
on  something  they  know  nothing  about,  have  generally  been  found  or 
thought  to  do  it  ill ; therefore  philosophers  are  unfit  for  business,  etc., 
etc.  All  these  are  inductions  by  simple  enumeration.  Reasons  having- 
some  reference  to  the  canons  of  scientific  investigation  have  been  attempt- 
ed to  be  given,  hoAvever  unsuccessfully,  for  some  of  these  propositions ; 
but  to  the  multitude  of  those  who  parrot  them,  the  enumeratio  simplex,  ex 


550 


FALLACIES. 


his  tantummodo  quce  prcesto  sunt pronuncians,  is  the  sole  evidence.  Their 
fallacy  consists  in  this,  that  they  are  inductions  without  elimination  : there 
has  been  no  real  comparison  of  instances,  nor  even  ascertainment  of  the 
material  facts  in  any  given  instance.  There  is  also  the  further  error,  of 
forgetting  that  such  generalizations,  even  if  well  established,  could  not  be 
ultimate  truths,  but  must  be  results  of  laws  much  more  elementary ; and 
therefore,  until  deduced  from  such,  could  at  most  be  admitted  as  empirical 
laws,  holding  good  within  the  limits  of  space  and  time  by  which  the  partic- 
ular observations  that  suggested  the  generalization  were  bounded. 

This  error,  of  placing  mere  empirical  laws,  and  laws  in  which  there  is  no 
direct  evidence  of  causation,  on  the  same  footing  of  certainty  as  laws  of 
cause  and  effect,  an  error  which  is  at  the  root  of  perhaps  the  greater  num- 
ber of  bad  inductions,  is  exemplified  only  in  its  grossest  form  in  the  kind 
of  generalizations  to  which  we  have  now  referred.  These,  indeed,  do  not 
possess  even  the  degree  of  evidence  which  pertains  to  a well-ascertained 
empirical  law;  but  admit  of  refutation  on  the  empirical  ground  itself,  with- 
out ascending  to  casual  laws.  A little  reflection,  indeed,  will  show  that 
mere  negations  can  only  form  the  ground  of  the  lowest  and  least  valuable 
kind  of  empirical  law.  A phenomenon  has  never  been  noticed  ; this  only 
proves  that  the  conditions  of  that  phenomenon  have  not  yet  occurred  in  ex- 
perience, but  does  not  prove  that  they  may  not  occur  hereafter.  There  is 
a better  kind  of  empirical  law  than  this,  namely,  when  a phenomenon  which 
is  observed  presents  within  the  limits  of  observation  a series  of  gradations, 
in  which  a regularity,  or  something  like  a mathematical  law, is  perceptible; 
from  which,  therefore,  something  may  be  rationally  presumed  as  to  those 
terms  of  the  series  which  are  beyond  the  limits  of  observation.  But  in  ne- 
gation there  are  no  gradations,  and  no  series ; the  generalizations,  therefore, 
which  deny  the  possibility  of  any  given  condition  of  man  and  society  merely 
because  it  has  never  yet  been  witnessed,  can  not  possess  this  higher  degree 
of  validity  even  as  empirical  laws.  What  is  more,  the  minuter  examination 
which  that  higher  order  of  empirical  laws  presupposes,  being  applied  to 
the  subject-matter  of  these,  not  only  does  not  confirm  but  actually  refutes 
them.  For  in  reality  the  past  history  of  Man  and  Society,  instead  of  ex- 
hibiting them  as  immovable,  unchangeable,  incapable  of  ever  presenting 
new  phenomena,  shows  them,  on  the  contrary,  to  be,  in  many  most  impor- 
tant particulars,  not  only  changeable,  but  actually  undergoing  a progressive 
change.  The  empirical  law,  therefore,  best  expressive,  in  most  cases,  of  the 
genuine  result  of  observation,  would  be,  not  that  such  and  such  a phenom- 
enon will  continue  unchanged,  but  that  it  will  continue  to  change  in  some 
particular  manner. 

Accordingly,  while  almost  all  generalizations  relating  to  Man  and  Society, 
antecedent  to  the  last  fifty  or  sixty  years,  have  erred  in  the  gross  way  which 
we  have  attempted  to  characterize,  namely,  by  implicitly  assuming  that  na- 
ture and  society  will  forever  revolve  in  the  same  orbit,  and  exhibit  essential- 
ly the  same  phenomena ; which  is  also  the  vulgar  error  of  the  ostentatiously 
practical,  the  votaries  of  so-called  common  sense,  in  our  day,  especially  in 
Great  Britain  ; the  more  thinking  minds  of  the  present  age,  having  applied 
a more  minute  analysis  to  the  past  records  of  our  race,  have  for  the  most 
part  adopted  a contrary  opinion,  that  the  human  species  is  in  a state  of  neces- 
sary progression,  and  that  from  the  terms  of  the  series  which  are  past  we 
may  infer  positively  those  which  are  yet  to  come.  Of  this  doctrine,  consid- 
ered as  a philosophical  tenet,  we  shall  have  occasion  to  speak  more  fully  in 
the  concluding  Book.  If  not,  in  all  its  forms,  free  from  error,  it  is  at  least 


FALLACIES  OF  GENERALIZATION. 


551 


free  from  the  gross  and  stupid  error  which  we  previously  exemplified.  But, 
in  all  except  the  most  eminently  philosophical  minds,  it  is  infected  with  pre- 
cisely the  same  kind  of  fallacy  as  that  is.  For  we  must  remember  that  even 
this  other  and  better  generalization,  the  progressive  change  in  the  condition 
of  the  human  species,  is,  after  all,  but  an  empirical  law;  to  which,  too,  it  is 
not  difficult  to  point  out  exceedingly  large  exceptions  ; and  even  if  these 
could  be  got  rid  of,  either  by  disputing  the  facts  or  by  explaining  and  lim- 
iting the  theory,  the  general  objection  remains  valid  against  the  supposed 
law,  as  applicable  to  any  other  than  what,  in  our  third  book,  were  termed 
Adjacent  Cases.  For  not  only  is  it  no  ultimate,  but  not  even  a causal  law. 
Changes  do  indeed  take  place  in  human  affairs,  but  every  one  of  those 
changes  depends  on  determinate  causes;  the  “ progressiveness  of  the  spe- 
cies” is  not  a cause,  but  a summary  expression  for  the  general  result  of  all  the 
causes.  So  soon  as,  by  a quite  different  sort  of  induction,  it  shall  be  ascer- 
tained what  causes  have  produced  these  successive  changes,  from  the  begin- 
ning of  history,  in  so  far  as  they  have  really  taken  place,  and  by  what  causes 
of  a contrary  tendency  they  have  been  occasionally  checked  or  entirely 
counteracted,  we  may  then  be  prepared  to  predict  the  future  with  reason- 
able foresight;  we  may  be  in  possession  of  the  real  law  of  the  future;  and 
may  be  able  to  declare  on  what  circumstances  the  continuance  of  the  same 
onward  movement  will  eventually  depend.  But  this  it  is  the  error  of  many 
of  the  more  advanced  thinkers,  in  the  present  age,  to  overlook;  and  to  im- 
agine that  the  empirical  law  collected  from  a mere  comparison  of  the  con- 
dition of  our  species  at  different  past  times,  is  a real  law,  is  the  law  of  its 
changes,  not  only  past  but  also  to  come.  The  truth  is,  that  the  causes  on 
which  the  phenomena  of  the  moral  world  depend,  are  in  every  age,  and  al- 
most in  every  country,  combined  in  some  different  proportion;  so  that  it  is 
scarcely  to  be  expected  that  the  general  result  of  them  all  should  conform 
very  closely,  in  its  details  at  least,  to  any  uniformly  progressive  series.  And 
all  generalizations  which  affirm  that  mankind  have  a tendency  to  grow  bet- 
ter or  worse,  richer  or  poorer,  more  cultivated  or  more  barbarous,  that  pop- 
ulation increases  faster  than  subsistence,  or  subsistence  than  population, 
that  inequality  of  fortune  has  a tendency  to  increase  or  to  break  down,  and 
the  like,  propositions  of  considerable  value  as  empirical  laws  within  certain 
(but  generally  rather  narrow)  limits,  are  in  reality  true  or  false  according 
to  times  and  circumstances. 

What  we  have  said  of  empirical  generalizations  from  times  past  to  times 
still  to  come,  holds  equally  true  of  similar  generalizations  from  present 
times  to  times  past ; when  persons  whose  acquaintance  with  moral  and  so- 
cial facts  is  confined  to  their  own  age,  take  the  men  and  the  things  of  that 
age  for  the  type  of  men  and  things  in  general,  and  apply  without  scruple 
to  the  interpretation  of  the  events  of  history,  the  empirical  laws  which  rep- 
resent sufficiently  for  daily  guidance  the  common  phenomena  of  human 
nature  at  that  time  and  in  that  particular  state  of  society.  If  examples 
are  wanted,  almost  every  historical  work,  until  a very  recent  period,  abound- 
ed in  them.  The  same  may  be  said  of  those  who  generalize  empirically 
from  the  people  of  their  own  country  to  the  people  of  other  countries,  as 
if  human  beings  felt,  judged,  and  acted  everywhere  in  the  same  manner. 

§5.  In  the  foregoing  instances,  the  distinction  is  confounded  between 
empirical  laws,  which  express  merely  the  customary  order  of  the  succession 
of  effects,  and  the  laws  of  causation  on  which  the  effects  depend.  There 
may,  however,  be  incorrect  generalization  when  this  mistake  is  not  com- 


552 


FALLACIES. 


mitted ; when  the  investigation  takes  its  proper  direction,  that  of  causes, 
and  the  result  erroneously  obtained  purports  to  be  a really  causal  law. 

The  most  vulgar  form  of  this  fallacy  is  that  which  is  commonly  called 
post  hoc,  ergo  propter  hoc,  or,  cum  hoc,  ergo  propter  hoc.  As  when  it  was 
inferred  that  England  owed  her  industrial  pre-eminence  to  her  restrictions 
on  commerce ; as  when  the  old  school  of  financiers,  and  some  speculative 
writers,  maintained  that  the  national  debt  was  one  of  the  causes  of  nation- 
al prosperity ; as  when  the  excellence  of  the  Church,  of  the  Houses  of 
Lords  and  Commons,  of  the  procedure  of  the  law  courts,  etc.,  were  infer- 
red from  the  mere  fact  that  the  country  had  prospered  under  them.  In 
such  cases  as  these,  if  it  can  be  rendered  probable  by  other  evidence  that 
the  supposed  causes  have  some  tendency  to  produce  the  effect  ascribed  to 
them,  the  fact  of  its  having  been  produced,  though  only  in  one  instance,  is 
of  some  value  as  a verification  by  specific  experience;  but  in  itself  it  goes 
scarcely  any  way  at  all  toward  establishing  such  a tendency,  since,  admit- 
ting the  effect,  a hundred  other  antecedents  could  show  an  equally  strong 
title  of  that  kind  to  be  considered  as  the  cause. 

In  these  examples  we  see  bad  generalization  « posteriori,  or  empiricism 
properly  so  called;  causation  inferred  from  casual  conjunction,  without  ei- 
ther due  elimination,  or  any  presumption  arising  from  known  properties 
of  the  supposed  agent.  But  bad  generalization  a priori  is  fully  as  common  ; 
which  is  properly  called  false  theory  ; conclusions  drawn,  by  way  of  deduc- 
tion, from  properties  of  some  one  agent  which  is  known  or  supposed  to  be 
present,  all  other  co-existing  agents  being  overlooked.  As  the  former  is 
the  error  of  sheer  ignorance,  so  the  latter  is  especially  that  of  semi-instruct- 
ed minds  ; and  is  mainly  committed  in  attempting  to  explain  complicated 
phenomena  by  a simpler  theory  than  their  nature  admits  of.  As  when  one 
school  of  physicians  sought  for  the  universal  principle  of  all  disease  in 
“lentor  and  morbid  viscidity  of  the  blood,”  and  imputing  most  bodily 
derangements  to  mechanical  obstructions,  thought  to  cure  them  by  me- 
chanical remedies;*  while  another,  the  chemical  school,  “acknowledged  no 
source  of  disease  but  the  presence  of  some  hostile  acid  or  alkali,  or  some 
deranged  condition  in  the  chemical  composition  of  the  fluid  or  solid  parts,” 
and  conceived,  therefore,  that  “all  remedies  must  act  by  producing  chem- 
ical changes  in  the  body.  We  find  Tournefort  busily  engaged  in  testing 
every  vegetable  juice,  in  order  to  discover  in  it  some  traces  of  an  acid  or 
alkaline  ingredient,  which  might  confer  upon  it  medicinal  activity.  The 
fatal  errors  into  which  such  an  hypothesis  was  liable  to  betray  the  practi- 
tioner, received  an  awful  illustration  in  the  history  of  the  memorable  fever 
that  raged  at  Leyden  in  the  year  1699,  and  which  consigned  two-thirds  of 
the  population  of  that  city  to  an  untimely  grave ; an  event  which  in  a great 
measure  depended  upon  the  Professor  Sylvius  de  la  Boe,  who  having  just 
embraced  the  chemical  doctrines  of  Van  Helmont,  assigned  the  origin  of 
the  distemper  to  a prevailing  acid,  and  declared  that  its  cure  could  alone 


* “Thus  Fourcroy,”  says  Dr.  Paris,  “explained  the  operation  of  mercury  by  its  specific 
gravity,  and  the  advocates  of  this  doctrine  favored  the  general  introduction  of  the  preparations 
of  iron,  especially  in  scirrhus  of  the  spleen  or  liver,  upon  the  same  hypothetical  principle ; for, 
say  they,  whatever  is  most  forcible  in  removing  the  obstruction  must  be  the  most  proper  in- 
strument of  cure:  such  is  steel,  which,  besides  the  attenuating  power  with  which  it  is  fur- 
nished, has  still  a greater  force  in  this  case  from  the  gravity  of  its  particles,  which,  being  sev- 
en times  specifically  heavier  than  any  vegetable,  acts  in  proportion  with  a stronger  impulse, 
and  therefore  is  a more  powerful  deo'bstruent.  This  may  be  taken  as  a specimen  of  the  style 
in  which  these  mechanical  physicians  reasoned  and  practiced.” — Phartnacologia,  pp.  38,  39- 


FALLACIES  OF  GENERALIZATION. 


553 


[only]  be  effected  by  the  copious  administration  of  absorbent  and  testa- 
ceous medicines.* 

These  aberrations  in  medical  theory  have  their  exact  parallels  in  politics. 
All  the  doctrines  which  ascribe  absolute  goodness  to  particular  forms  of 
government,  particular  social  arrangements,  and  even  to  particular  modes  of 
education,  without  reference  to  the  state  of  civilization  and  the  various  dis- 
tinguishing characters  of  the  society  for  which  they  are  intended,  are  open 
to  the  same  objection — that  of  assuming  one  class  of  influencing  circum- 
stances to  be  the  paramount  rulers  of  phenomena  which  depend  in  an  equal 
or  greater  degree  on  many  others.  But  on  these  considerations  it  is  the 
less  necessary  that  we  should  now  dwell,  as  they  will  occupy  our  attention 
more  largely  in  the  concluding  Book. 

§ 6.  The  last  of  the  modes  of  erroneous  generalization  to  which  I shall 
advert,  is  that  to  which  we  may  give  the  name  of  False  Analogies.  This 
Fallacy  stands  distinguished  from  those  already  treated  of  by  the  peculiar- 
ity that  it  does  not  even  simulate  a complete  and  conclusive  induction,  but 
consists  in  the  misapplication  of  an  argument  which  is  at  best  only  admis- 
sible as  an  inconclusive  presumption,  where  real  proof  is  unattainable. 

An  argument  from  analogy,  is  an  inference  that  what  is  true  in  a certain 
case  is  true  in  a case  known  to  be  somewhat  similar,  but  not  known  to  be 
exactly  parallel,  that  is,  to  be  similar  in  all  the  material  circumstances.  An 
object  has  the  property  B:  another  object  is  not  known  to  have  that  prop- 
erty, but  resembles  the  first  in  a property  A,  not  known  to  be  connected 
with  B;  and  the  conclusion  to  which  the  analogy  points,  is  that  this  object 
has  the  property  B also.  As,  for  example,  that  the  planets  are  inhabited, 
because  the  earth  is  so.  The  planets  resemble  the  earth  in  describing- 
elliptical  orbits  round  the  sun,  in  being  attracted  by  it  and  by  one  another, 
in  being  nearly  spherical,  revolving  on  their  axes,  etc.;  and,  as  we  have 
now  reason  to  believe  from  the  revelations  of  the  spectroscope,  are  com- 
posed, in  great  part  at  least,  of  similar  materials;  but  it  is  not  known  that 
any  of  these  properties,  or  all  of  them  together,  are  the  conditions  on  which 
the  possession  of  inhabitants  is  dependent,  or  are  marks  of  those  conditions. 
Nevertheless,  so  long  as  we  do  not  know  what  the  conditions  are,  they 
may  be  connected  by  some  law  of  nature  with  those  common  properties; 
and  to  the  extent  of  that  possibility  the  planets  are  more  likely  to  be  in- 
habited than  if  they  did  not  resemble  the  earth  at  all.  This  non-assignable 
and  generally  small  increase  of  probability,  beyond  what  would  otherwise 
exist,  is  all  the  evidence  which  a conclusion  can  derive  from  analogy.  For 
if  we  have  the  slightest  reason  to  suppose  any  real  connection  between 
the  two  properties  A and  B,  the  argument  is  no  longer  one  of  analogy.  If 
it  had  been  ascertained  (I  purposely  put  an  absurd  supposition)  that  there 
was  a connection  by  causation  between  the  fact  of  revolving  on  an  axis 
and  the  existence  of  animated  beings,  or  if  there  were  any  reasonable 
ground  for  even  suspecting  such  a connection,  a probability  would  arise 
of  the  existence  of  inhabitants  in  the  planets,  which  might  be  of  any  de- 
gree of  strength,  up  to  a complete  induction ; but  we  should  then  infer  the 
fact  from  the  ascertained  or  presumed  law  of  causation,  and  not  from  the 
analogy  of  the  earth. 

The  name  analogy,  however,  is  sometimes  employed  by  extension  to 
denote  those  arguments  of  an  inductive  character  but  not  amounting  to 


Pharmacologia,  pp.  39,  40. 


554 


FALLACIES. 


a real  induction,  which  are  employed  to  strengthen  the  argument  drawn 
from  a simple  resemblance.  Though  A,  the  property  common  to  the  two 
cases,  can  not  be  shown  to  be  the  cause  or  effect  of  B,  the  analogical  rea- 
soner  will  endeavor  to  show  that  there  is  some  less  close  degree  of  connec- 
tion between  them ; that  A is  one  of  a set  of  conditions  from  which,  when 
all  united,  B would  result;  or  is  an  occasional  effect  of  some  cause  which 
has  been  known  also  to  produce  B;  and  the  like.  Any  of  which  things, 
if  shown,  rvould  render  the  existence  of  B by  so  much  more  probable, 
than  if  there  had  not  been  even  that  amount  of  known  connection  be- 
tu'een  B and  A. 

Nour  an  error  or  fallacy  of  analogy  may  occur  in  two  ways.  Sometimes 
it  consists  in  employing  an  argument  of  either  of  the  above  kinds  M’ith 
correctness  indeed,  but  overrating  its  probative  force.  This  very  common 
aberration  is  sometimes  supposed  to  be  particularly  incident  to  persons 
distinguished  for  their  imagination;  but  in  reality  it  is  the  characteristic 
intellectual  vice  of  those  whose  imaginations  are  barren,  either  from  want 
of  exercise,  natural  defect,  or  the  narrowness  of  their  range  of  ideas.  To 
such  minds  objects  present  themselves  clothed  in  but  few  properties;  and 
as,  therefore,  few  analogies  between  one  object  and  another  occur  to  them, 
they  almost  invariably  overrate  the  degree  of  importance  of  those  few: 
while  one  udiose  fancy  takes  a wider  range,  perceives  and  remembers  so 
many  analogies  tending  to  conflicting  conclusions,  that  he  is  much  less 
likely  to  lay  undue  stress  on  any  of  them.  We  always  find  that  those 
are  the  greatest  slaves  to  metaphorical  language  who  have  but  one  set 
of  metaphors. 

But  this  is  oidy  one  of  the  modes  of  error  in  the  employment  of  argu- 
ments of  analogy.  There  is  another,  more  properly  deserving  the  name 
of  fallacy;  namely,  udien  resemblance  in  one  point  is  inferred  from  resem- 
blance in  another  point,  though  there  is  not  only  no  evidence  to  connect 
the  two  circumstances  by  way  of  causation,  but  the  evidence  tends  posi- 
tively to  disconnect  them.  This  is  properly  the  Fallacy  of  False  Analogies. 

As  a first  instance,  we  may  cite  that  favorite  argument  in  defense  of 
absolute  power,  drawn  from  the  analogy  of  paternal  government  in  a fam- 
ily, which  government,  however  much  in  need  of  control,  is  not  and  can 
not  be  controlled  by  the  children  themselves,  while  they  remain  children. 
Paternal  government,  says  the  argument,  works  u'ell ; therefore,  despotic 
government  in  a state  will  work  well.  I waive,  as  not  pertinent  in  this 
place,  all  that  could  be  said  in  qualification  of  the  alleged  excellence  of 
paternal  government.  However  this  might  be,  the  argument  from  the 
family  to  the  state  would  not  the  less  proceed  on  a false  analogy;  imply- 
ing that  the  beneficial  working  of  parental  government  depends,  in  the 
family,  on  the  only  point  which  it  has  in  common  with  political  despotism, 
namely,  irresponsibility.  Whereas  it  depends,  udien  real,  not  on  that  but 
on  two  other  circumstances  of  the  case,  the  affection  of  the  parent  for  the 
children,  and  the  superiority  of  the  parent  in  wisdom  and  experience; 
neither  of  which  properties  can  be  reckoned  on,  or  are  at  all  likely  to  exist, 
between  a political  despot  and  his  subjects;  and  when  either  of  these  cir- 
cumstances fails  even  in  the  family,  and  the  influence  of  the  irresponsibil- 
ity is  allowed  to  work  uncorrected,  the  result  is  any  thing  but  good  govern- 
ment. This,  therefore,  is  a false  analogy. 

Another  example  is  the  not  uncommon  dictum  that  bodies  politic  have 
youth,  maturity,  old  age,  and  death,  like  bodies  natural;  that  after  a cer- 
tain duration  of  prosperity,  they  tend  spontaneously  to  decay.  This  also 


FALLACIES  OF  GENERALIZATION. 


555 


is  a false  analogy,  because  the  decay  of  the  vital  powers  in  an  animated 
body  can  be  distinctly  traced  to  the  natural  progress  of  those  very  changes 
of  structure  which,  in  their  earlier  stages,  constitutes  its  growth  to  maturi- 
ty; while  in  the  body  politic  the  progress  of  those  changes  can  not,  gener- 
ally speaking,  have  any  effect  but  the  still  further  continuance  of  growth : 
it  is  the  stoppage  of  that  progress,  and  the  commencement  of  retrogression, 
that  alone  would  constitute  decay.  Bodies  politic  die,  but  it  is  of  disease, 
or  violent  death ; they  have  no  old  age. 

The  following  sentence  from  Hooker’s  Ecclesiastical  Polity  is  an  in- 
stance of  a false  analogy  from  physical  bodies  to  what  are  called  bodies 
politic.  “As  there  could  be  in  natural  bodies  no  motion  of  any  thing  un- 
less there  were  some  which  moveth  all  things,  and  continueth  immovable; 
even  so  in  politic  societies  there  must  be  some  unpunishable,  or  else  no 
man  shall  suffer  punishment.”  There  is  a double  fallacy  here,  for  not  only 
the  analogy,  but  the  premise  from  which  it  is  drawn,  is  untenable.  The 
notion  that  there  must  be  something  immovable  which  moves  all  other 
things,  is  the  old  scholastic  error  of  a primum  mobile. 

The  following  instance  I quote  from  Archbishop  Whately’s  Rhetoric: 
“It  would  be  admitted  that  a great  and  permanent  diminution  in  the  quan- 
tity of  some  useful  commodity,  such  as  corn,  or  coal,  or  iron,  throughout 
the  world,  would  be  a serious  and  lasting  loss ; and  again,  that  if  the  fields 
and  coal-mines  yielded  regularly  double  quantities,  with  the  same  labor, 
We  should  be  so  much  the  richer;  hence  it  might  be  inferred,  that  if  the 
quantity  of  gold  and  silver  in  the  world  were  diminished  one-half,  or  were 
doubled,  like  results  would  follow ; the  utility  of  these  metals,  for  the  pur- 
poses of  coin,  being  very  great.  Now  there  are  many  points  of  resem- 
blance and  finally  of  difference,  between  the  precious  metals  on  the  one 
hand,  and  corn,  coal,  etc.,  on  the  other;  but  the  important  circumstance  to 
the  supposed  argument  is,  that  the  utility  of  gold  and  silver  (as  coin, 
which  is  far  the  chief)  depends  on  their  value , which  is  regulated  by  their 
scarcity ; or  rather,  to  speak  strictly,  by  the  difficulty  of  obtaining  them ; 
whereas,  if  corn  and  coal  were  ten  times  as  abundant  (i.  e.,  more  easily  ob- 
tained), a bushel  of  either  would  still  be  as  useful  as  now.  But  if  it  were 
twice  as  easy  to  procure  gold  as  it  is,  a sovereign  would  be  twice  as  large ; 
if  only  half  as  easy,  it  would  be  of  the  size  of  a half-sovereign,  and  this  (be- 
sides the  trifling  circumstance  of  the  cheapness  or  dearness  of  gold  orna- 
ments) would  be  all  the  difference.  The  analogy,  therefore,  fails  in  the 
point  essential  to  the  argument.” 

The  same  author  notices,  after  Bishop  Copleston,  the  case  of  False 
Analogy  which  consists  in  inferring  from  the  similarity  in  many  respects 
between  the  metropolis  of  a country  and  the  heart  of  the  animal  body, 
that  the  increased  size  of  the  metropolis  is  a disease. 

Some  of  the  false  analogies  on  which  systems  of  physics  were  confident- 
ly grounded  in  the  time  of  the  Greek  philosophers,  are  such  as  we  now 
call  fanciful,  not  that  the  resemblances  are  not  often  real,  but  that  it  is 
long  since  any  one  has  been  inclined  to  draw  from  them  the  inferences 
which  were  then  drawn.  Such,  for  instance,  are  the  curious  speculations 
of  the  Pythagoreans  on  the  subject  of  numbers.  Finding  that  the  dis- 
tances of  the  planets  bore,  or  seemed  to  bear,  to  one  another  a proportion 
not  varying  much  from  that  of  the  divisions  of  the  monochord,  they  in- 
ferred from  it  the  existence  of  an  inaudible  music,  that  of  the  spheres ; as 
if  the  music  of  a harp  had  depended  solely  on  the  numerical  proportions, 
and  not  on  the  material,  nor  even  on  the  existence  of  any  material,  any 


556 


FALLACIES. 


Strings  at  all.  It  has  been  similarly  imagined  that  certain  combinations 
of  numbers,  which  were  found  to  prevail  in  some  natural  phenomena,  must 
run  through  the  whole  of  nature:  as  that  there  must  be  four  elements, 
because  there  are  four  possible  combinations  of  hot  and  cold,  wet  and  dry; 
that  there  must  be  seven  planets,  because  there  were  seven  metals,  and 
even  because  there  were  seven  days  of  the  week.  Kepler  himself  thought 
that  there  could  be  only  six  planets,  because  there  were  only  five  regular 
solids.  With  these  we  may  class  the  reasonings,  so  common  in  the  specu- 
lations of  the  ancients,  founded  on  a supposed  perfection  in  nature;  mean- 
ing by  nature  the  customary  order  of  events  as  they  take  place  of  them- 
selves without  human  interference.  This  also  is  a rude  guess  at  an  analo- 
gy supposed  to  pervade  all  phenomena,  however  dissimilar.  Since  what 
was  thought  to  be  perfection  appeared  to  obtain  in  some  phenomena,  it 
was  inferred  (in  opposition  to  the  plainest  evidence)  to  obtain  in  all. 
“We  always  suppose  that  which  is  better  to  take  place  in  nature,  if  it  be 
possible,”  says  Aristotle ; and  the  vaguest  and  most  heterogeneous  quali- 
ties being  confounded  together  under  the  notion  of  being  better , there  was 
no  limit  to  the  wildness  of  the  inferences.  Thus,  because  the  heavenly 
bodies  were  “perfect,”  they  must  move  in  circles  and  uniformly.  For 
“ they  ” (the  Pythagoreans)  “ would  not  allow,”  says  Geminus,*  “ of  any 
such  disorder  among  divine  and  eternal  things,  as  that  they  should  some- 
times move  quicker  and  sometimes  slower,  and  sometimes  stand  still;  for 
no  one  would  tolerate  such  anomaly  in  the  movements  even  of  a man,  who 
was  decent  and  orderly.  The  occasions  of  life,  however,  are  often  reasons 
for  men  going  quicker  or  slower;  but  in  the  incorruptible  nature  of  the 
stars,  it  is  not  possible  that  any  cause  can  be  alleged  of  quickness  or  slow- 
ness.” It  is  seeking  an  argument  of  analogy  very  far,  to  suppose  that  the 
stars  must  observe  the  rules  of  decorum  in  gait  and  carriage  prescribed 
for  themselves  by  the  long-bearded  philosophers  satirized  by  Lucian. 

As  late  as  the  Copernican  controversy  it  was  urged  as  an  argument  in 
favor  of  the  true  theory  of  the  solar  system,  that  it  placed  the  fire,  the  no- 
blest element,  in  the  centre  of  the  universe.  This  was  a remnant  of  the  no- 
tion that  the  order  of  nature  must  be  perfect,  and  that  perfection  consisted 
in  conformity  to  rules  of  precedency  in  dignity,  either  real  or  conventional. 
Again,  reverting  to  numbers:  certain  numbers  were  perfect,  therefore  those 
numbers  must  obtain  in  the  great  phenomena  of  nature.  Six  was  a per- 
fect number,  that  is,  equal  to  the  sum  of  all  its  factors ; an  additional  rea- 
son why  there  must  be  exactly  six  planets.  The  Pythagoreans,  on  the  oth- 
er hand,  attributed  perfection  to  the  number  ten;  but  agreed  in  thinking 
that  the  perfect  number  must  be  somehow"  realized  in  the  heavens ; and 
knowing  only  of  nine  heavenly  bodies,  to  make  up  the  enumeration,  they 
asserted  “that  there  was  an  antichthon,  or  counter-earth,  on  the  other  side 
of  the  sun,  invisible  to  us.”f  Even  Huygens  was  persuaded  that  when  the 
number  of  the  heavenly  bodies  had  reached  twelve,  it  could  not  admit  of 
any  further  increase.  Creative  power  could  not  go  beyond  that  sacred 
number. 

Some  curious  instances  of  false  analogy  are  to  be  found  in  the  arguments 
of  the  Stoics  to  prove  the  equality  of  all  crimes,  and  the  equal  wretchedness 
of  all  who  had  not  realized  their  idea  of  perfect  virtue.  Cicero,  toward  the 
end  of  his  Fourth  Book,  De  Finibus,  states  some  of  these  as  follows:  “Ut, 
inquit,  in  fidibus  plurimis,  si  nulla  earum  ita  contenta  numeris  sit,  ut  concen- 


I quote  from  Dr.  Whewell’s  Hist.  Ind.  Sc.,  3d  ed.,  i. , 129. 


f Hist.  Ind.  Sc.,  i.,  52. 


FALLACIES  OF  GENERALIZATION. 


551 


turn  servare  possit,  oraues  seque  incontenta3  sunt ; sic  peccata,  quia  discre- 
pant, seque  discrepant;  paria  sunt  igitur.”  To  which  Cicero  himself  aptly 
answers,  “ seque  contingit  omnibus  fidibus,  ut  incontentse  sint ; illud  non  con- 
tinuo,  ut  seque  incontentae.”  The  Stoic  resumes:  “Ut  eniin,  inquit,  guber- 
nator  seque  peccat,  si  palearum  navem  evertit,  et  si  auri : item  seque  peccat 
qui  parentem,  et  qui  servum,  injuria  verberat;”  assuming,  that  because  the 
magnitude  of  the  interest  at  stake  makes  no  difference  in  the  mere  defect 
of  skill,  it  can  make  none  in  the  moral  defect : a false  analogy.  Again, 
“Quis  ignorat,  si  plures  ex  alto  emergere  velint,  propius  fore  eos  quidem 
ad  respirandum,  qui  ad  suminam  jam  aquam  appropinquant,  sed  nihilo 
magis  respirare  posse,  quam  eos,  qui  sunt  in  profundo?  Nihil  ertro  adju- 
vat  procedere,  et  progredi  in  virtute,  quominus  miserrimus  sit,  antequam 
ad  earn  pervenerit,  quoniam  in  aqua  nihil  adjuvat:  et  quoniam  catuli,  qui 
jam  despecturi  sunt,  cseci  seque,  et  ii  qui  modo  nati ; Platonem  quoque  ne- 
cesse  est,  quoniam  nondum  videbat  sapientiam,  seque  caecum  animo,  ac 
Phalarim  fiiisse.”  Cicero,  in  his  own  person,  combats  these  false  analogies 
by  other  analogies  tending  to  an  opposite  conclusion.  “Ista  similia  non 

sunt,  Cato Ilia  sunt  similia ; hebes  acies  est  cuipiam  oculorum  : cor- 

pore  alius  languescit:  hi  curatione  adhibita  levantur  in  dies:  alter  valet 
plus  quotidie:  alter  videt.  Hi  similes  sunt  omnibus,  qui  virtuti  student; 
levantur  vitiis,  levantur  erroribus.” 

§ 1.  In  these  and  all  other  arguments  drawn  from  remote  analogies,  and 
from  metaphors,  which  are  cases  of  analogy,  it  is  apparent  (especially  when 
we  consider  the  extreme  facility  of  raising  up  contrai-y  analogies  and  con- 
flicting metaphors)  that,  so  far  from  the  metaphor  or  analogy  proving  any 
thing,  the  applicability  of  the  metaphor  is  the  very  thing  to  be  made  out. 
It  has  to  be  shown  that  in  the  two  cases  asserted  to  be  analogous,  the  same 
law  is  really  operating;  that  between  the  known  resemblance  and  the  in- 
ferred one  there  is  some  connection  by  means  of  causation.  Cicero  and 
Cato  might  have  bandied  opposite  analogies  forever ; it  rested  with  each 
of  them  to  prove  by  just  induction,  or  at  least  to  render  probable,  that  the 
case  resembled  the  one  set  of  analogous  cases  and  not  the  other,  in  the  cir- 
cumstances on  which  the  disputed  question  really  hinged.  Metaphors,  for 
the  most  part,  therefore,  assume  the  proposition  which  they  are  brought  to 
prove:  their  use  is, to  aid  the  apprehension  of  it;  to  make  clearly  and  viv- 
idly comprehended  what  it  is  that  the  person  who  employs  the  metaphor  is 
proposing  to  make  out ; and  sometimes  also,  by  what  media  he  proposes  to  do  • 
so.  For  an  apt  metaphor,  though  it  can  not  prove,  often  suggests  the  proof. 

For  instance,  when  D’Alembert  (I  believe)  remarked  that  in  certain  gov- 
ernments only  two  creatures  find  their  way  to  the  highest  places,  the  eagle 
and  the  serpent,  the  metaphor  not  only  conveys  with  great  vividness  the 
assertion  intended,  but  contributes  toward  substantiating  it,  by  suggesting, 
in  a lively  manner,  the  means  by  which  the  two  opposite  characters  thus 
typified  effect  their  rise.  When  it  is  said  that  a certain  person  misunder- 
stands another  because  the  lesser  of  two  objects  can  not  comprehend  the 
greater,  the  application  of  what  is  true  in  the  literal  sense  of  the  word  com- 
prehend, to  its  metaphorical  sense,  points  to  the  fact  which  is  the  ground 
and  justification  of  the  assertion,  viz.,  that  one  mind  can  not  thoroughly 
understand  another  unless  it  can  contain  it  in  itself,  that  is,  unless  it  pos- 
sesses all  that  is  contained  in  the  other.  When  it  is  urged  as  an  argument 
for  education,  that  if  the  soil  is  left  uncultivated,  weeds  will  spring  up,  the 
metaphor,  though  no  proof,  but  a statement  of  the  thing  to  be  proved, 


558 


FALLACIES. 


states  it  in  terms  which,  by  suggesting  a parallel  case,  put  the  mind  upon 
the  track  of  the  real  proof.  For,  the  reason  why  weeds  grow  in  an  uncul- 
tivated soil,  is  that  the  seeds  of  worthless  products  exist  everywhere,  and 
can  germinate  and  grow  in  almost  all  circumstances,  while  the  reverse  is 
the  case  with  those  which  are  valuable;  and  this  being  equally  true  of 
mental  products,  this  mode  of  conveying  an  argument,  independently  of  its 
rhetorical  advantages,  has  a logical  value ; since  it  not  only  suggests  the 
grounds  of  the  conclusion,  but  points  to  another  case  in  which  those  grounds 
have  been  found,  or  at  least  deemed  to  be,  sufficient. 

On  the  other  hand,  when  Bacon,  who  is  equally  conspicuous  in  the  use 
and  abuse  of  figurative  illustration,  says  that  the  stream  of  time  has  brought 
down  to  us  only  the  least  valuable  part  of  the  writings  of  the  ancients,  as  a 
river  carries  froth  and  straws  floating  on  its  surface,  while  more  weighty 
objects  sink  to  the  bottom ; this,  even  if  the  assertion  illustrated  by  it  were 
true,  would  be  no  good  illustration,  there  being  no  parity  of  cause.  The 
levity  by  which  substances  float  on  a stream,  and  the  levity  which  is  syn- 
onymous with  worthlessness,  have  nothing  in  common  except  the  name ; 
and  (to  show  how  little  value  there  is  in  the  metaphor)  we  need  only 
change  the  word  into  buoyancy , to  turn  the  semblance  of  argument  in- 
volved in  Bacon’s  illustration  against  himself. 

A metaphor,  then,  is  not  to  be  considered  as  an  argument,  but  as  an 
assertion  that  an  argument  exists ; that  a parity  subsists  between  the  case 
from  which  the  metaphor  is  drawn  and  that  to  which  it  is  applied.  This 
parity  may  exist  though  the  two  cases  be  apparently  very  remote  from  one 
another;  the  only  resemblance  existing  between  them  may  be  a resem- 
blance of  relations,  an  analogy  in  Ferguson’s  and  Archbishop  Whately’s 
sense:  as  in  the  preceding  instance,  in  which  an  illustration  from  agricul- 
ture was  applied  to  mental  cultivation. 

§ 8.  To  terminate  the  subject  of  Fallacies  of  Generalization,  it  remains 
to  be  said,  that  the  most  fertile  source  of  them  is  bad  classification : bring- 
ing together  in  one  group,  and  under  one  name,  things  which  have  no  com- 
mon properties,  or  none  but  such  as  are  too  unimportant  to  allow  general 
propositions  of  any  considerable  value  to  be  made  respecting  the  class. 
The  misleading  effect  is  greatest,  when  a word  which  in  common  use  ex- 
presses some  definite  fact,  is  extended  by  slight  links  of  connection  to 
cases  in  which  that  fact  does  not  exist,  but  some  other  or  others,  only 
slightly  resembling  it.  Thus  Bacon,*  in  speaking  of  the  Idola  or  Fallacies 
arising  from  notions  temere  et  incequaliter  d rebus  abstracts,  exemplifies 
them  by  the  notion  of  Humidum  or  Wet,  so  familiar  in  the  physics  of  an- 
tiquity and  of  the  Middle  Ages.  “Invenietur  verbum  istud,  Humidum, 
nihil  aliud  quam  nota  confusa  diversarum  actionum,  quae  nullam  constanti- 
ain  ant  reductionem  patiuntur.  Significat  enim,et  quod  circa  aliud  corpus 
facile  se  circumfundit ; et  quod  in  se  est  indeterminabile,  nec  consistere 
potest;  et  quod  facile  cedit  undique;  et  quod  facile  se  dividit  et  dispergit; 
et  quod  facile  se  unit  et  colligit;  et  quod  facile  fluit,  et  in  motu  ponitur; 
etquod  alteri  corpori  facile  adhseret,  idque  madefacit;  et  quod  facile  redu- 
citur  in  liquidum,  sive  colliquatur,  cum  antea  consisteret.  Itaque  quum  ad 
hujus  nominis  praedicationem  et  impositionem  ventum  sit;  si  alia  accipias, 
flamma  humida  est;  si  alia  accipias,  aer  humidus  non  est;  si  alia,  pulvis 
minutus  humidus  est;  si  alia,  vitruin  humidum  est:  ut  facile  appareat, 


Nov.  Org.,  Aph.  60. 


FALLACIES  OF  RATIOCINATION. 


559 


istam  notionem  ex  aqua  tantum,  et  communibus  et  vulgaribus  liquoribus, 
absque  ulla  debita  verificatione,  temere  abstractam  esse.” 

Bacon  himself  is  not  exempt  from  a similar  accusation  when  inquiring 
into  the  nature  of  heat:  where  he  occasionally  proceeds  like  one  who,  seek- 
ing for  the  cause  of  hardness,  after  examining  that  quality  in  iron,  flint,  and 
diamond,  should  expect  to  find  that  it  is  something  which  can  be  traced 
also  in  hard  water,  a hard  knot,  and  a hard  heart. 

The  word  in  the  Greek  philosophy,  and  the  words  Generation  and 

Corruption,  both  then  and  long  afterward,  denoted  such  a multitude  of 
heterogeneous  phenomena,  that  any  attempt  at  philosophizing  in  which 
those  words  were  used  was  almost  as  necessarily  abortive  as  if  the  word 
hard  had  been  taken  to  denote  a class  including  all  the  things  mentioned 
above.  K ivr)cnc,  for  instance,  which  properly  signified  motion,  was  taken  to 
denote  not  only  all  motion  but  even  all  change:  dXXotWte  being  recognized 
as  one  of  the  modes  of  ihyrimg.  The  effect  was,  to  connect  with  every  form 
of  aWoiojaiG  or  change,  ideas  drawn  from  motion  in  the  proper  and  literal 
sense,  and  which  had  no  real  connection  with  any  other  kind  of  tdvr\aiQ  than 
that.  Aristotle  and  Plato  labored  under  a continual  embarrassment  from 
this  misuse  of  terms.  But  if  we  proceed  further  in  this  direction  we  shall 
encroach  upon  the  Fallacy  of  Ambiguity,  which  belongs  to  a different  class, 
the  last  in  order  of  our  classification,  Fallacies  of  Confusion. 


CHAPTER  VI. 

FALLACIES  OF  RATIOCINATION. 

§ 1.  We  have  now,  in  our  progress  through  the  classes  of  Fallacies,  ar- 
rived at  those  to  which,  in  the  common  books  of  logic,  the  appellation  is 
in  general  exclusively  appropriated ; those  which  have  their  seat  in  the 
ratiocinative  or  deductive  part  of  the  investigation  of  truth.  Of  these  fal- 
lacies it  is  the  less  necessary  for  us  to  insist  at  any  length,  as  they  have 
been  most  satisfactorily  treated  in  a work  familiar  to  almost  all,  in  this 
country  at  least,  who  feel  any  interest  in  these  speculations,  Archbishop 
Whately’s  Logic.  Against  the  more  obvious  forms  of  this  class  of  falla- 
cies, the  rules  of  the  syllogism  are  a complete  protection.  Not  (as  we 
have  so  often  said)  that  ratiocination  can  not  be  good  unless  it  be  in  the 
form  of  a syllogism  ; but  that,  by  showing  it  in  that  form,  we  are  sure  to 
discover  if  it  be  bad,  or  at  least  if  it  contain  any  fallacy  of  this  class. 

§ 2.  Among  Fallacies  of  Ratiocination,  we  ought  perhaps  to  include  the 
errors  committed  in  processes  which  have  the  appearance  only,  not  the  re- 
ality, of  an  inference  from  premises;  the  fallacies  connected  with  the  con- 
version and  sequipollency  of  propositions.  I believe  errors  of  this  descrip- 
tion to  be  far  more  frequently  committed  than  is  generally  supposed,  or 
than  their  extreme  obviousness  might  seem  to  admit  of.  For  example, 
the  simple  conversion  of  a universal  affirmative  proposition,  All  A are  B, 
therefore  all  B are  A,  I take  to  be  a very  common  form  of  error : though 
committed,  like  many  other  fallacies,  oftener  in  the  silence  of  thought  than 
in  express  words,  for  it  can  scarcely  be  clearly  enunciated  without  being 
detected.  And  so  with  another  form  of  fallacy,  not  substantially  different 
from  the  preceding : the  erroneous  conversion  of  an  hypothetical  propo- 
sition. The  proper  converse  of  an  hypothetical  proposition  is  this : If  the 


560 


FALLACIES. 


consequent  be  false,  the  antecedent  is  false ; but  this,  If  the  consequent  be 
true,  the  antecedent  is  true,  by  no  means  holds  good,  but  is  an  error  corre- 
sponding to  the  simple  conversion  of  a universal  affirmative.  Yet  hardly 
any  thing  is  more  common  than  for  people,  in  their  private  thoughts,  to 
draw  this  inference.  As  when  the  conclusion  is  accepted,  which  it  so  oft- 
en is,  for  proof  of  the  premises.  That  the  premises  can  not  be  true  if 
the  conclusion  is  false,  is  the  unexceptionable  foundation  of  the  legitimate 
mode  of  reasoning  called  reductio  ad  absurdum.  But  people  continually 
think  and  express  themselves,  as  if  they  also  believed  that  the  premises 
can  not  be  false  if  the  conclusion  is  true.  The  truth,  or  supposed  truth,  of 
the  inferences  which  follow  from  a doctrine,  often  enables  it  to  find  accept- 
ance in  spite  of  gross  absurdities  in  it.  How  many  philosophical  systems 
which  had  scarcely  any  intrinsic  recommendation,  have  been  received  by 
thoughtful  men  because  they  were  supposed  to  lend  additional  support  to 
religion,  morality,  some  favorite  view  of  politics,  or  some  other  cherished 
persuasion : not  merely  because  their  wishes  were  thereby  enlisted  on  its 
side,  but  because  its  leading  to  what  they  deemed  sound  conclusions  ap- 
peared to  them  a strong  presumption  in  favor  of  its  truth : though  the 
presumption,  when  viewed  in  its  true  light,  amounted  only  to  the  absence 
of  that  particular  evidence  of  falsehood,  which  would  have  resulted  from 
its  leading  by  correct  inference  to  something  already  known  to  be  false. 

Again,  the  very  frequent  error  in  conduct,  of  mistaking  reverse  of  wrong 
for  right,  is  the  practical  form  of  a logical  error  with  respect  to  the  Oppo- 
sition of  Propositions.  It  is  committed  for  want  of  the  habit  of  distin- 
guishing the  contrary  of  a proposition  from  the  contradictory  of  it,  and 
of  attending  to  the  logical  canon,  that  contrary  propositions,  though  they 
can  not  both  be  true,  may  both  be  false.  If  the  error  were  to  express  it- 
self in  words,  it  would  run  distinctly  counter  to  this  canon.  It  generally, 
however,  does  not  so  express  itself,  and  to  compel  it  to  do  so  is  the  most 
effectual  method  of  detecting  and  exposing  it. 

§ 3.  Among  Fallacies  of  Ratiocination  are  to  be  ranked,  in  the  first 
place,  all  the  cases  of  vicious  syllogism  laid  down  in  the  books.  These 
generally  resolve  themselves  into  having  more  than  three  terms  to  the  syl- 
logism, either  avowedly,  or  in  the  covert  mode  of  an  undistributed  middle 
term,  or  an  illicit  process  of  one  of  the  two  extremes.  It  is  not,  indeed, 
very  easy  fully  to  convict  an  argument  of  falling  under  any  one  of  these 
vicious  cases  in  particular;  for  the  reason  already  more  than  once  referred 
to,  that  the  premises  are  seldom  formally  set  out : if  they  were,  the  fallacy 
would  impose  upon  nobody;  and  while  they  are  not,  it  is  almost  always  to 
a certain  degree  optional  in  what  manner  the  suppressed  link  shall  be  filled 
up.  The  rules  of  the  syllogism  are  rules  for  compelling  a person  to  be 
aware  of  the  whole  of  what  he  must  undertake  to  defend  if  he  persists  in 
maintaining  his  conclusion.  He  has  it  almost  always  in  his  power  to  make 
his  syllogism  good  by  introducing  a false  premise;  and  hence  it  is  scarcely 
ever  possible  decidedly  to  affirm  that  any  argument  involves  a bad  syllo- 
gism : but  this  detracts  nothing  from  the  value  of  the  syllogistic  rules, 
since  it  is  by  them  that  a reasoner  is  compelled  distinctly  to  make  his  elec- 
tion what  premises  he  is  prepared  to  maintain.  The  election  made,  there 
is  generally  so  little  difficulty  in  seeing  whether  the  conclusion  follows 
from  the  premises  set  out,  that  we  might  without  much  logical  improprie- 
ty have  merged  this  fourth  class  of  fallacies  in  the  fifth,  or  Fallacies  of 
Confusion. 


FALLACIES  OF  RATIOCINATION. 


561 


§ 4.  Perhaps,  however,  the  commonest,  and  certainly  the  most  danger- 
ous fallacies  of  this  class,  are  those  which  do  not  lie  in  a single  syllogism, 
but  slip  in  between  one  syllogism  and  another  in  a chain  of  argument,  and 
are  committed  by  changing  the  premises.  A proposition  is  proved,  or  an 
acknowledged  truth  laid  down,  in  the  first  part  of  an  argumentation,  and 
in  the  second  a further  argument  is  founded  not  on  the  same  proposition, 
but  on  some  other,  resembling  it  sufficiently  to  be  mistaken  for  it.  In- 
stances of  this  fallacy  will  be  found  in  almost  all  the  argumentative  dis- 
courses of  imprecise  thinkers;  and  we  need  only  here  advert  to  one  of  the 
obscurer  forms  of  it,  recognized  by  the  school-men  as  the  fallacy  d dicto 
secundum  quid  ad  dictum  simpUciter.  This  is  committed  when,  in  the 
premises,  a proposition  is  asserted  with  a qualification,  and  the  qualifica- 
tion lost  sight  of  in  the  conclusion ; or  oftener,  when  a limitation  or  con- 
dition, though  not  asserted,  is  necessary  to  the  truth  of  the  proposition, 
but  is  forgotten  when  that  proposition  comes  to  be  employed  as  a premise. 
Many  of  the  bad  arguments  in  vogue  belong  to  this  class  of  error.  The 
premise  is  some  admitted  truth,  some  common  maxim,  the  reasons  or  evi- 
dence for  which  have  been  forgotten,  or  are  not  thought  of  at  the  time, 
but  if  they  had  been  thought  of  would  have  shown  the  necessity  of  so  lim- 
iting the  premise  that  it  would  no  longer  have  supported  the  conclusion 
drawn  from  it. 

Of  this  nature  is  the  fallacy  in  what  is  called,  by  Adam  Smith  and  oth- 
ers, the  Mercantile  Theory  in  Political  Economy.  That  theory  sets  out 
from  the  common  maxim,  that  whatever  brings  in  money  enriches  ; or  that 
every  one  is  rich  in  proportion  to  the  quantity  of  money  he  obtains. 
From  this  it  is  concluded  that  the  value  of  any  branch  of  trade,  or  of  the 
trade  of  the  country  altogether,  consists  in  the  balance  of  money  it  brings 
in;  that  any  trade  which  carries  more  money  out  of  the  country  than  it 
draws  into  it  is  a losing  trade ; that  therefore  money  should  be  attracted 
into  the  country  and  kept  there,  by  prohibitions  and  bounties ; and  a train 
of  similar  corollaries.  All  for  want  of  reflecting  that  if  the  riches  of  an 
individual  are  in  proportion  to  the  quantity  of  money  he  can  command,  it 
is  because  that  is  the  measure  of  his  power  of  purchasing  money’s  worth ; 
and  is  therefore  subject  to  the  proviso  that  he  is  not  debarred  from  em- 
ploying his  money  in  such  purchases.  The  premise,  therefore,  is  only  true 
secundum  quid ; but  the  theory  assumes  it  to  be  true  absolutely,  and  in-> 
fers  that  increase  of  money  is  increase  of  riches,  even  when  produced  by 
means  subversive  of  the  condition  under  which  alone  money  can  be  riches. 

A second  instance  is,  the  argument  by  which  it  used  to  be  contended, 
before  the  commutation  of  tithe,  that  tithes  fell  on  the  landlord,  and  were 
a deduction  from  rent;  because  the  rent  of  tithe-free  land  was  always 
higher  than  that  of  land  of  the  same  quality,  and  the  same  advantages  of 
situation,  subject  to  tithe.  Whether  it  be  true  or  not  that  a tithe  falls  on 
rent,  a treatise  on  Logic  is  not  the  place  to  examine;  but  it  is  certain  that 
this  is  no  proof  of  it.  Whether  the  proposition  be  true  or  false,  tithe-free 
laud  must,  by  the  necessity  of  the  case,  pay  a higher  rent.  For  if  tithes 
do  not  fall  on  rent,  it  must  be  because  they  fall  on  the  consumer ; because 
they  raise  the  price  of  agricultural  produce.  But  if  the  produce  be  raised 
in  price,  the  farmer  of  tithe-free  as  well  as  the  farmer  of  tithed  land  gets 
the  benefit.  To  the  latter  the  rise  is  but  a compensation  for  the  tithe  he 
pays ; to  the  first,  wrho  pays  none,  it  is  clear  gain,  and  therefore  enables 
him,  and  if  there  be  freedom  of  competition,  forces  him,  to  pay  so  much 
more  rent  to  his  landlord.  The  question  remains,  to  what  class  of  fallacies 

36 


562 


FALLACIES. 


this  belongs.  The  premise  is,  that  the  owner  of  tithed  land  receives  less 
rent  than  the  owner  of  tithe-free  land  ; the  conclusion  is,  that  therefore  he 
receives  less  than  lie  himself  would  receive  if  tithe  were  abolished.  But 
the  premise  is  only  true  conditionally;  the  owner  of  tithed  land  receives 
less  than  wliat  the  owner  of  tithe-free  land  is  enabled  to  receive  token  other 
lands  are  tithed ; while  the  conclusion  is  applied  to  a state  of  circum- 
stances in  which  that  condition  fails,  and  in  which,  by  consequence,  the 
premise  will  not  be  true.  The  fallacy,  therefore,  is  a dicto  secundum  quid 
ad  dictum  simpliciter. 

A third  example  is  the  opposition  sometimes  made  to  legitimate  inter- 
ferences of  government  in  the  economical  affairs  of  society,  grounded  on  a 
misapplication  of  the  maxim,  that  an  individual  is  a better  judge  than  the 
government  of  what  is  for  his  own  pecuniary  interest.  This  objection 
was  urged  to  Mr.  Wakefield’s  principle  of  colonization;  the  concentration 
of  the  settlers,  by  fixing  such  a price  on  unoccupied  land  as  may  preserve 
the  most  desirable  proportion  between  the  quantity  of  land  in  culture  and 
the  laboring  population.  Against  this  it  was  argued,  that  if  individuals 
found  it  for  their  advantage  to  occupy  extensive  tracts  of  land,  they,  being 
better  judges  of  their  own  interest  than  the  legislature  (which  can  only 
proceed  on  general  rules),  ought  not  to  be  restrained  from  doing  so.  But 
in  this  argument  it  was  forgotten  that  the  fact  of  a person’s  taking  a large 
tract  of  land  is  evidence  only  that  it  is  his  interest  to  take  as  much  as 
other  people,  but  not  that  it  might  not  be  for  his  interest  to  content  him- 
self with  less,  if  he  could  be  assured  that  other  people  would  do  so  too  ; 
an  assurance  which  nothing  but  a government  regulation  can  give.  If  all 
other  people  took  much,  and  he  only  a little,  he  would  reap  none  of  the 
advantages  derived  from  the  concentration  of  the  population  and  the  con- 
sequent possibility  of  procuring  labor  for  hire,  but  would  have  placed  him- 
self, without  equivalent,  in  a situation  of  voluntary  inferiority.  The  prop- 
osition, therefore,  that  the  quantity  of  land  which  people  will  take  when 
left  to  themselves  is  that  which  is  most  for  their  interest  to  take,  is  true 
only  secundum  quid:  it  is  only  their  interest  while  they  have  no  guar- 
antee for  the  conduct  of  one  another.  But  the  arrangement  disregards 
the  limitation,  and  takes  the  proposition  for  true  simpliciter. 

One  of  the  conditions  oftenest  dropped,  when  what  would  otherwise  be 
a true  proposition  is  employed  as  a premise  for  proving  others,  is  the  con- 
dition of  time.  It  is  a principle  of  political  economy  that  prices,  profits, 
wages,  etc.,  “ always  find  their  level;”  but  this  is  often  interpreted  as  if  it 
meant  that  they  are  always,  or  generally,  at  their  level,  while  the  truth 
is,  as  Coleridge  epigramraatically  expresses  it,  that  they  are  always  finding 
their  level,  “ which  might  be  taken  as  a paraphrase  or  ironical  definition  of 
a storm.” 

Under  the  same  head  of  fallacy  (cl  dicto  secundum  quid  ad  dictum  sim- 
pliciter) might  be  placed  all  the  errors  which  are  vulgarly  called  misappli- 
cations of  abstract  truths ; that  is,  where  a principle,  true  (as  the  common 
expression  is)  in  the  abstract , that  is,  all  modifying  causes  being  supposed 
absent,  is  reasoned  on  as  if  it  were  true  absolutely,  and  no  modifying  cir- 
cumstance could  ever  by  possibility  exist.  This  very  common  form  of 
error  it  is  not  requisite  that  we  should  exemplify  here,  as  it  will  be  partic- 
ularly treated  of  hereafter  in  its  application  to  the  subjects  on  which  it  is 
most  frequent  and  most  fatal,  those  of  politics  and  society.* 

* “An  advocate,”  says  Mr.  De  Morgan  ( Formal  Logic,  p.  270),  “is  sometimes  guilty  of 
the  argument  a dicto  secundum  quid  ad  dictum  simpliciter:  it  is  his  business  to  do  for  his 


FALLACIES  OF  CONFUSION. 


563 


CHAPTER  VII. 

FALLACIES  OF  CONFUSION. 

§ 1.  Under  this  fifth  and  last  class  it  is  convenient  to  arrange  all  those 
fallacies  in  which  the  source  of  error  is  not  so  much  a false  estimate  of  the 
probative  force  of  known  evidence,  as  an  indistinct,  indefinite,  and  fluctua- 
ting conception  of  what  the  evidence  is. 

At  the  head  of  these  stands  that  multitudinous  body  of  fallacious  rea- 
sonings in  which  the  source  of  error  is  the  ambiguity  of  terms:  when 
something  which  is  true  if  a word  be  used  in  a particular  sense,  is  reasoned 
on  as  if  it  were  true  in  another  sense.  In  such  a case  there  is  not  a mal- 
estimation  of  evidence,  because  there  is  not  properly  any  evidence  to  the 
point  at  all;  there  is  evidence,  but  to  a different  point,  which  from  a con- 
fused apprehension  of  the  meaning  of  the  terms  used,  is  supposed  to  be 
the  same.  This  error  will  naturally  be  oftener  committed  in  our  ratiocina- 
tions than  in  our  direct  inductions,  because  in  the  former  we  are  decipher- 
ing our  own  or  other  people’s  notes,  while  in  the  latter  we  have  the  things 
themselves  present,  either  to  the  senses  or  to  the  memory.  Except,  indeed, 
when  the  induction  is  not  from  individual  cases  to  a generality,  but  from 
generalities  to  a still  higher  generalization;  in  that  case  the  fallacy  of  am- 
biguity may  affect  the  inductive  process  as  well  as  the  ratiocinative.  It 
occurs  in  ratiocination  in  two  ways:  when  the  middle  term  is  ambiguous, 
or  when  one  of  the  terms  of  the  syllogism  is  taken  in  one  sense  in  the 
premises,  and  in  another  sense  in  the  conclusion. 

Some  good  exemplifications  of  this  fallacy  are  given  by  Archbishop 
Whately.  “ One  case,”  says  he,  “ which  may  be  regarded  as  coming  under 
the  head  of  Ambiguous  Middle,  is  (what  I believe  logical  writers  mean  by 
‘Fallacia  Figurce  Fictiotiis’’)  the  fallacy  built  on  the  grammatical  struc- 
ture of  language,  from  men’s  usually  taking  for  granted  that  paronymons 
(or  conjugate)  words,  i.  e.,  those  belonging  to  each  other,  as  the  substantive, 
adjective,  verb,  etc.,  of  the  same  root,  have  a precisely  corresponding  mean- 
ing; which  is  by  no  means  universally  the  case.  Such  a fallacy  could  not 
indeed  be  even  exhibited  in  strict  logical  form,  which  would  preclude  even 
the  attempt  at  it,  since  it  has  two  middle  terms  in  sound  as  well  as  sense. 
But  nothing  is  more  common  in  practice  than  to  vary  continually  the  terms 
employed,  with  a view  to  grammatical  convenience  ; nor  is  there  any  thing 
unfair  in  such  a practice,  as  long  as  the  meaning  is  preserved  unaltered ; 
e.  g.,  ‘ murder  should  be  punished  with  death  ; this  man  is  a murderer, 

client  all  that  his  client  might  honestly  do  for  himself.  Is  not  the  word  in  italics  frequently 
omitted?  Might  any  man  honestly  try  to  do  for  himself  all  that  counsel  frequently  try  to  do 
for  him  ? We  are  often  reminded  of  the  two  men  who  stole  the  leg  of  mutton ; one  could 
swear  he  had  not  got  it,  the  other  that  he  had  not  taken  it.  The  counsel  is  doing  his  duty 
by  his  client,  the  client  has  left  the  matter  to  his  counsel.  Between  the  unexecuted  inten- 
tion of  the  client,  and  the  unintended  execution  of  the  counsel,  there  may  be  a wrong  done, 
and,  if  we  are  to  believe  the  usual  maxims,  no  wrong-doer.'’ 

The  same  writer  justly  remarks  (p.  251)  that  there  is  a converse  fallacy,  a dicto  simpliciter 
ad  dictum  secundum  quid,  called  by  the  scholastic  logicians  fallacia  accidentis ; and  another 
which  may  be  called  a.  dicto  secundum  quid  ad  dictum  secundum  alterum  quid  (p.  265).  For 
apt  instances  of  both,  I must  refer  the  reader  to  Mr.  De  Morgan’s  able  chapter  on  Fallacies. 


564 


FALLACIES. 


therefore  he  deserves  to  die,’  etc.  Here  we  proceed  on  the  assumption  (in 
this  case  just)  that  to  commit  murder,  and  to  be  a murderer — to  deserve 
death,  and  to  be  one  who  ought  to  die,  are,  respectively,  equivalent  expres- 
sions ; and  it  would  frequently  prove  a heavy  inconvenience  to  be  debarred 
this  kind  of  liberty;  but  the  abuse  of  it  gives  rise  to  the  Fallacy  in  ques- 
tion ; e.  g\,  projectors  are  unfit  to  be  trusted  ; this  man  has  formed  v,  project, 
therefore  he  is  unfit  to  be  trusted  : here  the  sophist  proceeds  on  the  hy- 
pothesis that  he  who  forms  a project  must  be  a projector:  whereas  the  bad 
sense  that  commonly  attaches  to  the  latter  word,  is  not  at  all  implied  in  the 
former.  This  fallacy  may  often  be  considered  as  lying  not  in  the  Middle, 
but  in  one  of  the  terms  of  the  Conclusion ; so  that  the  conclusion  drawn 
shall  not  be,  in  reality,  at  all  warranted  by  the  premises,  though  it  will  ap- 
pear to  be  so,  by  means  of  the  grammatical  affinity  of  the  words  ; e.  g.,  to 
be  acquainted  with  the  guilty  is  a presumption  of  guilt;  this  man  is  so  ac- 
quainted, therefore  we  may  presume  that  he  is  guilty:  this  argument  pro- 
ceeds on  the  supposition  of  an  exact  correspondence  between  presume  and 
presumption,  which,  however,  does  not  really  exist;  for  ‘presumption’  is 
commonly  used  to  express  a kind  of  slight  suspicion ; whereas,  ‘ to  pre- 
sume ’ amounts  to  actual  belief.  There  are  innumerable  instances  of  a 
non-correspondence  in  paronymous  words,  similar  to  that  above  instanced ; 
as  between  art  and  artful,  design  and  designing , faith  and  faithful,  etc.; 
and  the  more  slight  the  variation  of  the  meaning,  the  more  likely  is  the 
fallacy  to  be  successful;  for  when  the  words  have  become  so  widely  re- 
moved in  sense  as  £ pity  ’ and  £ pitiful,’  every  one  would  perceive  such  a 
fallacy,  nor  would  it  be  employed  but  in  jest.* 

“ The  present  Fallacy  is  nearly  allied  to,  or  rather,  perhaps,  may  be  re- 
garded as  a branch  of,  that  founded  on  etymology — viz.,  when  a term  is 
used,  at  one  time  in  its  customary,  and  at  another  in  its  etymological  sense. 
Perhaps  no  example  of  this  can  be  found  that  is  more  extensively  and  mis- 
chievously employed  than  in  the  case  of  the  word  representative : assuming 
that  its  right  meaning  must  correspond  exactly  with  the  strict  and  original 
sense  of  the  verb  £ represent,’  the  sophist  persuades  the  multitude  that  a 
member  of  the  House  of  Commons  is  bound  to  be  guided  in  all  points  by 
the  opinion  of  his  constituents ; and,  in  short,  to  be  merely  their  spokes- 
man; whereas  law  and  custom,  which  in  this  case  may  be  considered  as 
fixing  the  meaning  of  the  term,  require  no  such  thing,  but  enjoin  the  rep- 
resentative to  act  according  to  the  best  of  his  own  judgment,  and  on  his 
own  responsibility.” 

The  following  are  instances  of  great  practical  importance,  in  which  argu- 
ments are  habitually  founded  on  a verbal  ambiguity. 

The  mercantile  public  are  frequently  led  into  this  fallacy  by  the  phrase 
“scarcity  of  money.”  In  the  language  of  commerce,  “ money ” has  two 
meanings : currency,  or  the  circulating  medium ; and  capital  seeking  in- 
vestment, especially  investment  on  loan.  In  this  last  sense  the  word  is  used 
when  the  “ money  market  ” is  spoken  of,  and  when  the  “ value  of  money  ” 
is  said  to  be  high  or  low,  the  rate  of  interest  being  meant.  The  conse- 

* An  example  of  this  fallacy  is  the  popular  error  that  strong  drink  must  he  a cause  of 
strength.  There  is  here  fallacy  within  fallacy;  for  granting  that  the  words  “strong”  and 
“ strength  ” were  not  (as  they  are)  applied  in  a totally  different  sense  to  fermented  liquors  and 
to  the  human  body,  there  would  still  be  involved  the  error  of  supposing  that  an  effect  must 
be  like  its  cause;  that  the  conditions  of  a phenomenon  are  likely  to  resemble  the  phenomenon 
itself ; which  we  have  already  treated  of  as  an  a priori  fallacy  of  the  first  rank.  ' As  well 
might  it  be  supposed  that  a strong  poison  will  make  the  person  who  takes  it  strong. 


FALLACIES  OF  CONFUSION. 


565 


quence  of  this  ambiguity  is,  that  as  soon  as  scarcity  of  money  in  the  latter 
of  these  senses  begins  to  be  felt — as  soon  as  there  is  difficulty  of  obtaining 
loans,  and  the  rate  of  interest  is  high — it  is  concluded  that  this  must  arise 
from  causes  acting  upon  the  quantity  of  money  in  the  other  and  more  pop* 
ular  sense;  that  the  circulating  medium  must  have  diminished  in  quantity, 
or  ought  to  be  increased.  I am  aware  that,  independently  of  the  double 
meaning  of  the  term,  there  are  in  the  facts  themselves  some  peculiarities, 
giving  an  apparent  support  to  this  error ; but  the  ambiguity  of  the  lan- 
guage stands  on  the  very  threshold  of  the  subject,  and  intercepts  all  at- 
tempts to  throw  light  upon  it. 

Another  ambiguous  expression  which  continually  meets  us  in  the  polit- 
ical controversies  of  the  present  time,  especially  in  those  which  relate  to 
organic  changes,  is  the  phrase  “ influence  of  property” — which  is  sometimes 
used  for  the  influence  of  respect  for  superior  intelligence  or  gratitude  for 
the  kind  offices  which  persons  of  large  property  have  it  so  much  in  their 
power  to  bestow;  at  other  times  for  the  influence  of  fear;  fear  of  the 
worst  sort  of  power,  which  large  property  also  gives  to  its  possessor,  the 
power  of  doing  mischief  to  dependents.  To  confound  these  tw'O,  is  the 
standing  fallacy  of  ambiguity  brought  against  those  wTho  seek  to  purify 
the  electoral  system  from  corruption  and  intimidation.  Persuasive  influ- 
ence, acting  through  the  conscience  of  the  voter,  and  carrying  his  heart 
and  mind  with  it,  is  beneficial — therefore  (it  is  pretended)  coercive  influ- 
ence, which  compels  him  to  forget  that  he  is  a moral  agent,  or  to  act  in 
opposition  to  his  moral  convictions,  ought  not  to  be  placed  under  restraint. 

Another  word  which  is  often  turned  into  an  instrument  of  the  fallacy  of 
ambiguity,  is  Theory.  In  its  most  proper  acceptation,  theory  means  the 
completed  result  of  philosophical  induction  from  experience.  In  that 
sense,  there  are  erroneous  as  well  as  true  theories,  for  induction  may  be 
incorrectly  performed,  but  theory  of  some  sort  is  the  necessary  result  of 
knowing  any  thing  of  a subject,  and  having  put  one’s  knowledge  into  the 
form  of  general  projrositions  for  the  guidance  of  practice.  In  this,  the 
proper  sense  of  the  word,  Theory  is  the  explanation  of  practice.  In  an- 
other and  a more  vulgar  sense,  theory  means  any  mere  fiction  of  the  im- 
agination, endeavoring  to  conceive  how  a thing  may  possibly  have  been 
produced,  instead  of  examining  how  it  was  produced.  In  this  sense  only 
are  theory  and  theorists  unsafe  guides ; but  because  of  this,  ridicule  or 
discredit  is  attempted  to  be  attached  to  theory  in  its  proper  sense,  that  is, 
to  legitimate  generalization,  the  end  and  aim  of  all  philosophy;  and  a con- 
clusion is  represented  as  worthless,  just  because  that  has  been  done  which, 
if  done  correctly,  constitutes  the  highest  worth  that  a principle  for  the 
guidance  of  practice  can  possess,  namely,  to  comprehend  in  a few  wTords 
the  real  law  on  wThich  a phenomenon  depends,  or  some  property  or  relation 
which  is  universally  true  of  it. 

“ The  Church”  is  sometimes  understood  to  mean  the  clergy  alone,  some- 
times the  whole  body  of  believers,  or  at  least  of  communicants.  The  dec- 
lamations respecting  the  inviolability  of  church  property  are  indebted  for 
the  greater  part  of  their  apparent  force  to  this  ambiguity.  The  clergy, 
being  called  the  church,  are  supposed  to  be  the  real  owners  of  what  is 
called  church  property ; whereas  they  are  in  truth  only  the  managing  mem- 
bers of  a much  larger  body  of  proprietors,  and  enjoy  on  their  own  part  a 
mere  usufruct,  not  extending  beyond  a life  interest. 

The  following  is  a Stoical  argument  taken  from  Cicero,  De  Finibus,  book 
the  third:  “Quod  est  bonum,  omne  laudabile  est.  Quod  autem  laudabile 


566 


FALLACIES. 


est,  omne  honestum  est.  Bonura  igitur  quod  est,  honestum  est.”  Here 
the  ambiguous  word  is  laudabile,  which  in  the  minor  premise  means  any 
thing  which  mankind  are  accustomed,  on  good  grounds,  to  admire  or 
value;  as  beauty,  for  instance,  or  good  fortune:  but  in  the  major,  it  de- 
notes exclusively  moral  qualities.  In  much  the  same  manner  the  Stoics 
endeavored  logically  to  justify  as  philosophical  truths,  their  figurative  and 
rhetorical  expressions  of  ethical  sentiment:  as  that  the  virtuous  man  is 
alone  free,  alone  beautiful,  alone  a king,  etc.  Whoever  has  virtue  has 
Good  (because  it  has  been  previously  determined  not  to  call  any  thing  else 
good) ; but,  again,  Good  necessarily  includes  freedom,  beauty,  and  even 
kingship,  all  these  being  good  things ; therefore  whoever  has  virtue  has 
all  these. 

The  following  is  an  argument  of  Descartes  to  prove,  in  his  a priori 
manner,  the  being  of  a God.  The  conception,  says  he,  of  an  infinite  Being 
proves  the  real  existence  of  such  a being.  For  if  there  is  not  really  any 
such  being,  I must  have  made  the  conception  ; but  if  I could  make  it,  I can 
also  unmake  it ; which  evidently  is  not  true  ; therefore  there  must  be,  exter- 
nally to  myself,  an  archetype,  from  which  the  conception  was  derived.  In 
this  argument  (which,  it  may  be  observed,  would  equally  prove  the  real 
existence  of  ghosts  and  of  witches)  the  ambiguity  is  in  the  pronoun  1 , by 
which,  in  one  place,  is  to  be  understood  my  will,  in  another  the  laws  of 
my  nature.  If  the  conception,  existing  as  it  does  in  my  mind,  had  no 
original  without,  the  conclusion  would  unquestionably  follow  that  I made 
it ; that  is,  the  laws  of  my  nature  must  have  somehow  evolved  it : but  that 
my  will  made  it,  would  not  follow.  Now  when  Descartes  afterward  adds 
that  I can  not  unmake  the  conception,  he  means  that  I can  not  get  rid  of 
it  by  an  act  of  my  will : which  is  true,  but  is  not  the  proposition  required. 
I can  as  much  unmake  this  conception  as  I can  any  other : no  conception 
which  I have  once  had,  can  I ever  dismiss  by  mere  volition;  but  what 
some  of  the  laws  of  my  nature  have  produced,  other  laws,  or  those  same 
laws  in  other  circumstances,  may,  and  often  do,  subsequently  efface. 

Analogous  to  this  are  some  of  the  ambiguities  in  the  free-will  controversy  ; 
which,  as  they  will  come  under  special  consideration  in  the  concluding  Book, 
I only  mention  memoriae  causd.  In  that  discussion,  too,  the  word  I is  often 
shifted  from  one  meaning  to  another,  at  one  time  standing  for  my  volitions, 
at  another  time  for  the  actions  which  are  the  consequences  of  them,  or  the 
mental  dispositions  from  which  they  proceed.  The  latter  ambiguity  is  ex- 
emplified in  an  argument  of  Coleridge  (in  his  Aids  to  Reflection),  in  sup- 
port of  the  freedom  of  the  will.  It  is  not  true,  he  says,  that  a man  is  gov- 
erned by  motives ; “ the  man  makes  the  motive,  not  the  motive  the  man ;” 
the  proof  being  that  “ what  is  a strong  motive  to  one  man  is  no  motive  at 
all  to  another.”  The  premise  is  true,  but  only  amounts  to  this,  that  differ- 
ent persons  have  different  degrees  of  susceptibility  to  the  same  motive  ; as 
they  have  also  to  the  same  intoxicating  liquid,  which,  however,  does  not 
prove  that  they  are  free  to  be  drunk  or  not  drunk,  whatever  quantity  of  the 
fluid  they  may  drink.  What  is  proved  is,  that  certain  mental  conditions  in 
the  person  himself  must  co-operate,  in  the  production  of  the  act,  with  the 
external  inducement;  but  those  mental  conditions  also  are  the  effect  of 
causes;  and  there  is  nothing  in  the  argument  to  prove  that  they  can  arise 
without  a cause — that  a spontaneous  determination  of  the  will,  without  any 
cause  at  all,  ever  takes  place,  as  the  free-will  doctrine  supposes. 

The  double  use,  in  the  free-will  controversy,  of  the  word  Necessity,  which 
sometimes  stands  only  for  Certainty,  at  other  times  for  Compulsion ; some- 


FALLACIES  OF  CONFUSION. 


567 


times  for  what  can  not  be  prevented,  at  other  times  only  for  what  we  have 
reason  to  be  assured  will  not;  we  shall  have  occasion  hereafter  to  pursue 
to  some  of  its  ulterior  consequeuces. 

A most  important  ambiguity,  both  in  common  and  in  metaphysical  lan- 
guage, is  thus  pointed  out  by  Archbishop  Whately  in  the  Appendix  to  his 
Logic : “Same  (as  well  as  One , Identical , and  other  words  derived  from 
them)  is  used  frequently  in  a sense  very  different  from  its  primary  one,  as 
applicable  to  a single  object;  being  employed  to  denote  great  similarity. 
When  several  objects  are  undistinguishably  alike,  one  single  description  will 
apply  equally  to  any  of  them ; and  thence  they  are  said  to  be  all  of  one  and 
the  same  nature,  appearance,  etc.  As,  e.  g.,  when  we  say  £ this  house  is  built 
of  the  same  stone  with  such  another,’  we  only  mean  that  the  stones  are 
undistinguishable  in  their  qualities;  not  that  the  one  building  was  pulled 
down,  and  the  other  constructed  with  the  materials.  Whereas  sameness, 
in  the  primary  sense,  does  not  even  necessarily  imply  similarity;  for  if  we 
say  of  any  man  that  he  is  greatly  altered  since  such  a time,  we  understand, 
and  indeed  imply  by  the  very  expression,  that  he  is  one  person,  though 
different  in  several  qualities.  It  is  worth  observing  also,  that  Same,  in 
the  secondary  sense,  admits,  according  to  popular  usage,  of  degrees  : we 
speak  of  two  things  being  nearly  the  same,  but  not  entirely  : personal  identi- 
ty does  not  admit  of  degrees.  Nothing,  perhaps,  has  contributed  more  to  the 
error  of  Realism  than  inattention  to  this  ambiguity.  When  several  persons 
are  said  to  have  one  and  the  same  opinion,  thought,  or  idea,  many  men,  over- 
looking the  true  simple  statement  of  the  case,  which  is,  that  they  are  all 
thinking  alike,  look  for  something  more  abstruse  and  mystical,  and  imag- 
ine there  must  be  some  One  Thing,  in  the  primary  sense,  though  not  an 
individual  which  is  present  at  once  in  the  mind  of  each  of  these  persons  ; 
and  thence  readily  sprung  Plato’s  theory  of  Ideas,  each  of  which  was,  ac- 
cording to  him,  one  real,  eternal  object,  existing  entire  and  complete  in 
each  of  the  individual  objects  that  are  known  by  one  name.” 

It  is,  indeed,  not  a matter  of  inference,  but  of  authentic  history,  that 
Plato’s  doctrine  of  Ideas,  and  the  Aristotelian  doctrine  (in  this  respect  sim- 
ilar to  the  Platonic)  of  substantial  forms  and  second  substances,  grew  up 
in  the  precise  way  here  pointed  out;  from  the  supposed  necessity  of  find- 
ing, in  things  which  were  said  to  have  the  same  nature,  or  the  same  quali- 
ties, something  which  was  the  same  in  the  very  sense  in  which  a man  is  the 
same  as  himself.  All  the  idle  speculations  respecting  -o  or,  -o  tv,  -o  byuior, 
and  similar  abstractions,  so  common  in  the  ancient  and  in  some  modern 
schools  of  thought,  sprang  from  the  same  source.  The  Aristotelian  logi- 
cians saw,  however,  one  case  of  the  ambiguity,  and  provided  against  it  with 
their  peculiar  felicity  in  the  invention  of  technical  language,  when  they 
distinguished  things  which  differed  both  specie  and  numero,  from  those 
which  differed  numero  tantum , that  is,  which  were  exactly  alike  (in  some 
particular  respect  at  least)  but  were  distinct  individuals.  An  extension  of 
this  distinction  to  the  two  meanings  of  the  word  Same,  namely,  things  which 
are  the  same  specie  tantum,  and  a thing  which  is  the  same  numero  as  well 
as  specie,  would  have  prevented  the  confusion  which  has  been  a source  of 
so  much  darkness  and  such  an  abundance  of  positive  error  in  metaphysical 
philosophy. 

One  of  the  most  singular  examples  of  the  length  to  which  a thinker  of 
eminence  may  be  led  away  by  an  ambiguity  of  language,  is  afforded  by  this 
very  case.  I refer  to  the  famous  argument  by  which  Bishop  Berkeley  flat- 
tered himself  that  he  had  forever  put  an  end  to  “ skepticism,  atheism,  and 


568 


FALLACIES. 


irreligion.”  It  is  briefly  as  follows:  I thought  of  a thing  yesterday;  I 
ceased  to  think  of  it;  I think  of  it  again  to-day.  I had,  therefore,  in  my 
mind  yesterday  an  idea  of  the  object ; I have  also  an  idea  of  it  to-day ; 
this  idea  is  evidently  not  another,  but  the  very  same  idea.  Yet  an  inter- 
vening time  elapsed  in  which  I had  it  not.  Where  was  the  idea  during 
this  interval?  It  must  have  been  somewhere;  it  did  not  cease  to  exist; 
otherwise  the  idea  I had  yesterday  could  not  be  the  same  idea ; no  more 
than  the  man  I see  alive  to-day  can  be  the  same  whom  I saw  yesterday  if 
the  man  has  died  in  the  mean  while.  Now  an  idea  can  not  be  conceived  to 
exist  anywhere  except  in  a mind;  and  hence  there  must  exist  a Universal 
Mind,  in  which  all  ideas  have  their  permanent  residence  during  the  inter- 
vals of  their  conscious  presence  in  our  own  minds. 

It  is  evident  that  Berkeley  here  confounded  sameness  numero  with 
sameness  specie,  that  is,  with  exact  resemblance,  and  assumed  the  former 
where  there  was  only  the  latter ; not  perceiving  that  when  we  say  we  have 
the  same  thought  to-day  which  we  had  yesterday,  we  do  not  mean  the  same 
individual  thought,  but  a thought  exactly  similar : as  we  say  that  we  have 
the  same  illness  which  we  had  last  year,  meaning  only  the  same  sort  of  illness. 

In  one  remarkable  instance  the  scientific  world  was  divided  into  two 
furiously  hostile  parties  by  an  ambiguity  of  language  affecting  a branch  of 
science  which,  more  completely  than  most  others,  enjoys  the  advantage  of 
a precise  and  well-defined  terminology.  I refer  to  the  famous  dispute  re- 
specting the  vis  viva,  the  history  of  which  is  given  at  large  in  Professor 
Playfair’s  Dissertation.  The  question  was,  whether  the  force  of  a mov- 
ing body  was  proportional  (its  mass  being  given)  to  its  velocity  simply,  or 
to  the  square  of  its  velocity:  and  the  ambiguity  was  in  the  word  Force. 
“ One  of  the  effects,”  says  Playfair,  “ produced  by  a moving  body  is  pro- 
portional to  the  square  of  the  velocity,  while  another  is  proportional  to  the 
velocity  simply :”  from  whence  clearer  thinkers  were  subsequently  led  to 
establish  a double  measure  of  the  efficiency  of  a moving  power,  one  being 
called  vis  viva.,  and  the  other  momentum.  About  the  facts,  both  parties 
were  from  the  first  agreed : the  only  question  was,  with  which  of  the  two 
effects  the  term  force  should  be,  or  could  most  conveniently  be,  associa- 
ted. But  the  disputants  were  by  no  means  aware  that  this  was  all;  they 
thought  that  force  was  one  thing,  the  production  of  effects  another;  and 
the  question,  by  which  set  of  effects  the  force  which  produced  both  the 
one  and  the  other  should  be  measured,  was  supposed  to  be  a question  not 
of  terminology,  but  of  fact. 

The  ambiguity  of  the  word  Infinite  is  the  real  fallacy  in  the  amusing 
logical  puzzle  of  Achilles  and  the  Tortoise,  a puzzle  which  has  been  too 
hard  for  the  ingenuity  or  patience  of  many  philosophers,  and  which  no  less 
a thinker  than  Sir  William  Hamilton  considered  as  insoluble ; as  a sound 
argument,  though  leading  to  a palpable  falsehood.  The  fallacy,  as  Hobbes 
hinted,  lies  in  the  tacit  assumption  that  whatever  is  infinitely  divisible  is 
infinite;  but  the  following  solution  (to  the  invention  of  which  I have  no 
claim)  is  more  precise  and  satisfactory. 

The  argument  is,  let  Achilles  run  ten  times  as  fast  as  the  tortoise,  yet 
if  the  tortoise  has  the  start,  Achilles  will  never  overtake  him.  For  sup- 
pose them  to  be  at  first  separated  by  an  interval  of  a thousand  feet : when 
Achilles  has  run  these  thousand  feet,  the  tortoise  will  have  got  on  a hun- 
dred ; when  Achilles  has  run  those  hundred,  the  tortoise  will  have  run  ten, 
and  so  on  forever : therefore  Achilles  may  run  forever  without  overtaking 
the  tortoise. 


FALLACIES  OF  CONFUSION. 


5C9 


Now  the  “ forever,”  in  the  conclusion,  means,  for  any  length  of  time 
that  can  be  supposed;  but  in  the  premises,  “ever ’’does  not  mean  any 
length  of  time ; it  means  any  number  of  subdivisions  of  time.  It  means 
that  we  may  divide  a thousand  feet  by  ten,  and  that  quotient  again  by  ten, 
and  so  on  as  often  as  we  please ; that  there  never  needs  be  an  end  to  the 
subdivisions  of  the  distance,  nor  consequently  to  those  of  the  time  in  which 
it  is  performed.  But  an  unlimited  number  of  subdivisions  may  be  made 
of  that  which  is  itself  limited.  The  argument  proves  no  other  infinity  of 
duration  than  may  be  embraced  within  five  minutes.  As  long  as  the  five 
minutes  are  not  expired,  what  remains  of  them  may  be  divided  by  ten, 
and  again  by  ten,  as  often  as  we  like,  which  is  perfectly  compatible  with 
their  being  only  five  minutes  altogether.  It  proves,  in  short,  that  to  pass 
through  this  finite  space  requires  a time  which  is  infinitely  divisible,  bu-t 
not  an  infinite  time;  the  confounding  of  which  distinction  Hobbes  had 
already  seen  to  be  the  gist  of  the  fallacy. 

The  following  ambiguities  of  the  word  right  (in  addition  to  the  obvious 
and  familiar  one  of  a right  and  the  adjective  right)  are  extracted  from  a 
forgotten  paper  of  my  own,  in  a periodical : 

“ Speaking  morally,  you  are  said  to  have  a right  to  do  a thing,  if  all 
persons  are  morally  bound  not  to  hinder  you  from  doing  it.  But,  in  an- 
other sense,  to  have  a right  to  do  a thing  is  the  opposite  of  having  no 
right  to  do  it,  i.  e.,  of  being  under  a moral  obligation  to  forbear  doing  it. 
In  this  sense,  to  say  that  you  have  a right  to  do  a thing,  means  that  you 
may  do  it  without  any  breach  of  duty  on  your  part;  that  other  persons 
not  only  ought  not  to  hinder  you,  but  have  no  cause  to  think  worse  of  you 
for  doing  it.  This  is  a perfectly  distinct  proposition  from  the  preceding. 
The  right  which  you  have  by  virtue  of  a duty  incumbent  upon  other  per- 
sons, is  obviously  quite  a different  thing  from  a right  consisting  in  the 
absence  of  any  duty  incumbent  upon  yourself.  Yet  the  two  things  are 
perpetually  confounded.  Thus,  a man  will  say  he  has  a right  to  publish 
his  opinions ; which  may  be  true  in  this  sense,  that  it  would  be  a breach 
of  duty  in  any  other  person  to  interfere  and  prevent  the  publication : but 
he  assumes  thereupon  that,  in  publishing  his  opinions,  he  himself  violates 
no  duty ; which  may  either  be  true  or  false,  depending,  as  it  does,  on  his 
having  taken  due  pains  to  satisfy  himself,  first,  that  the  opinions  are  true, 
and  next,  that  their  publication  in  this  manner,  and  at  this  particular  junc- 
ture, will  probably  be  beneficial  to  the  interests  of  truth  on  the  whole. 

“ The  second  ambiguity  is  that  of  confounding  a right  of  any  kind,  with 
a right  to  enforce  that  right  by  resisting  or  punishing  a violation  of  it. 
People  will  say,  for  example,  that  they  have  a right  to  good  government, 
which  is  undeniably  true,  it  being  the  moral  duty  of  their  governors  to 
govern  them  well.  But  in  granting  this,  you  are  supposed  to  have  admit- 
ted their  right  or  liberty  to  turn  out  their  governors,  and  perhaps  to  pun- 
ish them,  for  having  failed  in  the  performance  of  this  duty;  which,  far 
from  being  the  same  thing,  is  by  no  means  universally  true,  but  depends 
on  an  immense  number  of  varying  circumstances,”  requiring  to  be  con- 
scientiously weighed  before  adopting  or  acting  on  such  a resolution.  This 
last  example  is  (like  others  which  have  been  cited)  a case  of  fallacy  within 
fallacy ; it  involves  not  only  the  second  of  the  two  ambiguities  pointed 
out,  but  the  first  likewise. 

One  not  unusual  form  of  the  Fallacy  of  Ambiguous  Terms  is  known 
technically  as  the  Fallacy  of  Composition  and  Division ; when  the  same 
term  is  collective  in  the  premises,  distributive  in  the  conclusion,  or  vied 


570 


FALLACIES. 


versa;  or  when  the  middle  term  is  collective  in  one  premise,  distributive 
in  the  other.  As  if  one  were  to  say  (I  quote  from  Archbishop  Whately), 
“All  the  angles  of  a triangle  are  equal  to  two  right  angles:  ABC  is 

an  angle  of  a triangle ; therefore  ABC  is  equal  to  two  right  angles 

There  is  no  fallacy  more  common,  or  more  likely  to  deceive,  than  the  one 
now  before  us.  The  form  in  which  it  is  most  usually  employed  is  to  es- 
tablish some  truth,  separately,  concerning  each  single  member  of  a certain 
class,  and  thence  to  infer  the  same  of  the  whole  collectively .”  As  in  the 
argument  one  sometimes  hears,  to  prove  that  the  world  could  do  without 
great  men.  If  Columbus  (it  is  said)  had  never  lived,  America  would  still 
have  been  discovered,  at  most  only  a few  years  later;  if  Newton  had  never 
lived,  some  other  person  would  have  discovered  the  law  of  gravitation; 
and  so  forth.  Most  true : these  things  would  have  been  done,  but  in  all 
probability  not  till  some  one  had  again  been  found  with  the  qualities  of 
Columbus  or  Newton.  Because  any  one  great  man  might  have  had  his 
place  supplied  by  other  great  men,  the  argument  concludes  that  all  great 
men  could  have  been  dispensed  with.  The  term  “great  men”  is  distribu- 
tive in  the  premises  and  collective  in  the  conclusion. 

“ Such  also  is  the  fallacy  which  probably  operates  on  most  adventurers 
in  lotteries  ; e.  g.,  ‘ the  gaining  of  a high  prize  is  no  uncommon  occurrence; 
and  what  is  no  uncommon  occurrence  may  reasonably  be  expected  ; there- 
fore the  gaining  of  a high  prize  may  reasonably  be  expected ;’  the  conclu- 
sion, when  applied  to  the  individual  (as  in  practice  it  is),  must  be  under- 
stood in  the  sense  of  ‘ reasonably  expected  by  a certain  individual f there- 
fore for  the  major  premise  to  be  true,  the  middle  term  must  be  under- 
stood to  mean,  ‘ no  uncommon  occurrence  to  some  one  particular  person  ;’ 
whereas  for  the  minor  (which  has  been  placed  first)  to  be  true,  you  must 
understand  it  of  ‘no  uncommon  occurrence  to  some  one  or  other;’’  and  thus 
you  will  have  the  Fallacy  of  Composition. 

“ This  is  a Fallacy  with  which  men  are  extremely  apt  to  deceive  them- 
selves; for  when  a multitude  of  particulars  are  presented  to  the  mind, 
many  are  too  weak  or  too  indolent  to  take  a comprehensive  view  of  them, 
but  confine  their  attention  to  each  single  point,  by  turns;  and  then  decide, 
infer,  and  act  accordingly;  e.  g.,  the  imprudent  spendthrift,  finding  that  he 
is  able  to  afford  this,  or  that,  or  the  other  expense,  forgets  that  cdl  of  them 
together  will  ruin  him.”  The  debauchee  destroys  his  health  by  successive 
acts  of  intemperance,  because  no  one  of  those  acts  would  be  of  itself  suffi- 
cient to  do  him  any  serious  harm.  A sick  person  reasons  with  himself, 
“ one,  and  another,  and  another,  of  my  symptoms  do  not  prove  that  I have 
a fatal  disease ;”  and  practically  concludes  that  all  taken  together  do  not 
prove  it. 

§ 2.  We  have  now  sufficiently  exemplified  one  of  the  principal  Genera 
in  this  Order  of  Fallacies ; where,  the  source  of  error  being  the  ambiguity 
of  terms,  the  premises  are  verbally  what  is  required  to  support  the  conclu- 
sion, but  not  really  so.  In  the  second  great  Fallacy  of  Confusion  they  are 
neither  verbally  nor  really  sufficient,  though,  from  their  multiplicity  and 
confused  arrangement,  and  still  oftener  from  defect  of  memory,  they  are 
not  seen  to  be  what  they  are.  The  fallacy  I mean  is  that  of  Petitio  Prin- 
cipii,  or  begging  the  question ; including  the  more  complex  and  not  un- 
common variety  of  it,  which  is  termed  Reasoning  in  a Circle. 

Petitio  Principii,  as  defined  by  Archbishop  Whately,  is  the  fallacy  “in 
which  the  premise  either  appears  manifestly  to  be  the  same  as  the  conclu- 


FALLACIES  OF  CONFUSION. 


571 


sion,  or  is  actually  proved  from  the  conclusion,  or  is  such  as  would  natu- 
rally and  properly  so  be  proved.”  By  the  last  clause  I presume  is  meant, 
that  it  is  not  susceptible  of  any  other  proof;  for  otherwise,  there  would  be 
no  fallacy.  To  deduce  from  a proposition  propositions  from  which  it 
would  itself  more  naturally  be  deduced,  is  often  an  allowable  deviation 
from  the  usual  didactic  order;  or  at  most,  what,  by  an  adaptation  of  a 
phrase  familiar  to  mathematicians,  may  be  called  a logical  inelegance .* 

The  employment  of  a proposition  to  prove  that  on  which  it  is  itself  de- 
pendent for  proof,  by  no  means  implies  the  degree  of  mental  imbecility 
which  might  at  first  be  supposed.  The  difficulty  of  comprehending  how 
this  fallacy  could  possibly  be  committed,  disappears  when  we  reflect  that 
all  persons,  even  the  instructed,  hold  a great  number  of  opinions  without 
exactly  recollecting  how  they  came  by  them.  Believing  that  they  have  at 
some  former  time  verified  them  by  sufficient  evidence,  but  having  forgotten 
what  the  evidence  was,  they  may  easily  be  betrayed  into  deducing  from 
them  the  very  propositions  which  are  alone  capable  of  serving  as  premises 
for  their  establishment.  “As  if,”  says  Archbishop  Whately,  “one  should 
attempt  to  prove  the  being  of  a God  from  the  authority  of  Holy  Writ;” 
which  might  easily  happen  to  one  with  whom  both  doctrines,  as  funda- 
mental tenets  of  his  religious  creed,  stand  on  the  same  ground  of  familiar 
and  traditional  belief. 

Arguing  in  a circle,  however,  is  a stronger  case  of  the  fallacy,  and  im- 
plies more  than  the  mere  passive  reception  of  a premise  by  one  who  does 
not  remember  how  it  is  to  be  proved.  It  implies  an  actual  attempt  to 
prove  two  propositions  reciprocally  from  one  another ; and  is  seldom  re- 
sorted to,  at  least  in  express  terms,  by  any  person  in  his  own  speculations, 
but  is  committed  by  those  who,  being  hard  pressed  by  an  adversary,  are 
forced  into  giving  reasons  for  an  opinion  of  which,  when  they  began  to  ar- 
gue, they  had  not  sufficiently  considered  the  grounds.  As  in  the  following- 
example  from  Archbishop  Whately:  “ Some  mechanicians  attempt  to  prove 
(what  they  ought  to  lay  down  as  a probable  but  doubtful  hypothesis))  that 
every  particle  of  matter  gravitates  equally:  ‘why?’  ‘because  those  bodies 
which  contain  more  particles  ever  gravitate  more  strongly,  i.  e.,  are  heav- 
ier:’ ‘but  (it  may  be  urged)  those  which  are  heaviest  are  not  always  more 
bulky ;’  ‘ no,  but  they  contain  more  particles,  though  more  closely  con- 
densed:’ ‘how  do  you  know  that?’  ‘because  they  are  heavier:’  ‘how  does 
that  prove  it  ?’  ‘ because  all  particles  of  matter  gravitating  equally,  that  mass 
which  is  specifically  the  heavier  must  needs  have  the  more  of  them  in  the 
same  space.’  ” It  appears  to  me  that  the  fallacious  reasoner,  in  his  private 
thoughts,  would  not  be  likely  to  proceed  beyond  the  first  step.  He  would 
acquiesce  in  the  sufficiency  of  the  reason  first  given,  “bodies  which  contain 
more  particles  are  heavier.”  It  is  when  he  finds  this  questioned,  and  is 
called  upon  to  prove  it,  without  knowing  how,  that  he  tries  to  establish  his 

* In  his  later  editions,  Archbishop  Whately  confines  the  name  of  Petitio  Principii  “to 
those  eases  in  which  one  of  the  premises  either  is  manifestly  the  same  in  sense  with  the  con- 
clusion, or  is  actually  proved  from  it,  or  is  such  as  the  persons  you  are  addressing  are  not 
likely  to  know,  or  to  admit,  except  as  an  inference  from  the  conclusion ; as,  e.g.,  it  any  one 
should  infer  the  authenticity  of  a certain  history,  from  its  recording  such  and  such  facts,  the 
reality  of  which  rests  on  the  evidence  of  that  history.” 

t No  longer  even  a probable  hypothesis,  since  the  establishment  of  the  atomic  theory ; it 
being  now  certain  that  the  integral  particles  of  different  substances  gravitate  unequally.  It 
is  true  that  these  particles,  though  real  minima  for  the  purposes  of  chemical  combination,  may 
not  be  the  ultimate  particles  of  the  substance ; and  this  doubt  alone  renders  the  hypothesis 
admissible,  even  as  an  hypothesis. 


572 


FALLACIES. 


premise  by  supposing  proved  what  he  is  attempting  to  prove  by  it.  The 
most  effectual  way,  in  fact,  of  exposing  a petitio  principii,  when  circum- 
stances allow  of  it,  is  by  challenging  the  reasoner  to  prove  his  premises ; 
which  if  he  attempts  to  do,  he  is  necessarily  driven  into  arguing  in  a circle. 

It  is  not  uncommon,  however,  for  .thinkers,  and  those  not  of  the  lowest 
description,  to  be  led  even  in  their  own  thoughts,  not  indeed  into  formally 
proving  each  of  two  propositions  from  the  other,  but  into  admitting  propo- 
sitions which  can  only  be  so  proved.  In  the  preceding  example  the  two 
together  form  a complete  and  consistent,  though  hypothetical,  explanation 
of  the  facts  concerned.  And  the  tendency  to  mistake  mutual  coherency 
for  truth — to  trust  one’s  safety  to  a strong  chain  though  it  lias  no  point  of 
support — is  at  the  bottom  of  much  which,  when  reduced  to  the  strict  forms  of 
argumentation,  can  exhibit  itself  no  otherwise  than  as  reasoning  in  a circle. 
All  experience  bears  testimony  to  the  enthralling  effect  of  neat  concatena- 
tion in  a system  of  doctrines,  and  the  difficulty  with  which  people  admit  the 
persuasion  that  any  thing  which  holds  so  well  together  can  possibly  fall. 

Since  every  case  where  a conclusion  which  can  only  be  proved  from  cer- 
tain premises  is  used  for  the  proof  of  those  premises,  is  a case  of  petitio 
principii,  that  fallacy  includes  a very  great  proportion  of  all  incorrect  rea- 
soning. It  is  necessary,  for  completing  our  view  of  the  fallacy,  to  exempli- 
fy some  of  the  disguises  under  which  it  is  accustomed  to  mask  itself,  and 
to  escape  exposure. 

A proposition  would  not  be  admitted  by  any  person  in  his  senses  as  a 
corollary  from  itself,  unless  it  were  expressed  in  language  which  made  it 
seem  different.  One  of  the  commonest  modes  of  so  expressing  it,  is  to 
present  the  proposition  itself  in  abstract  terms,  as  a proof  of  the  same 
proposition  expressed  in  concrete  language.  This  is  a very  frequent  mode, 
not  only  of  pretended  proof,  but  of  pretended  explanation ; and  is  parodied 
when  Moliere  {Le  Malade  hnaginaire ) makes  one  of  his  absurd  physi- 
cians say, 

Mihi  a docto  doctore, 

Demandatur  causam  et  rationem  quare 
Opium  facit  dormire. 

A quoi  respondeo, 

Quia  est  in  eo 
Virtus  dormitiva, 

Cujus  est  natura 
Sensus  assoupire. 

The  words  Nature  and  Essence  are  grand  instruments  of  this  mode  of 
begging  the  question,  as  in  the  well-known  argument  of  the  scholastic 
theologians,  that  the  mind  thinks  always,  because  the  essence  of  the  mind 
is  to  think.  Locke  had  to  point  out,  that  if  by  essence  is  here  meant  some 
property  which  must  manifest  itself  by  actual  exercise  at  all  times,  the 
premise  is  a direct  assumption  of  the  conclusion;  while  if  it  only  means 
that  to  think  is  the  distinctive  property  of  a mind,  there  is  no  connection 
between  the  premise  and  the  conclusion,  since  it  is  not  necessary  that  a dis- 
tinctive property  should  be  perpetually  in  action. 

The  following  is  one  of  the  inodes  in  which  these  abstract  terms,  Nature 
and  Essence,  are  used  as  instruments  of  this  fallacy.  Some  particular  prop- 
erties of  a thing  are  selected,  more  or  less  arbitrarily,  to  be  termed  its  nature 
or  essence;  and  when  this  has  been  done,  these  properties  are  supposed  to 
be  invested  with  a kind  of  indefeasibleness;  to  have  become  paramount  to 
all  the  other  properties  of  the  thing,  and  incapable  of  being  prevailed  over 


FALLACIES  OF  CONFUSION. 


573 


or  counteracted  by  them.  As  when  Aristotle,  in  a passage  already  cited, 
“decides  that  there  is  no  void  on  such  arguments  as  this:  in  a void  there 
could  be  no  difference  of  up  and  down ; for  as  in  nothing  there  are  no  dif- 
ferences, so  there  are  none  in  a privation  or  negation ; but  a void  is  merely 
a privation  or  negation  of  matter;  therefore,  in  a void,  bodies  could  not 
move  up  and  down,  which  it  is  in  their  nature  to  do.”*  In  other  words, 
it  is  in  the  nature  of  bodies  to  move  up  and  down,  ergo  any  physical  fact 
which  supposes  them  not  so  to  move,  can  not  be  authentic.  This  mode  of 
reasoning,  by  which  a bad  generalization  is  made  to  overrule  all  facts  which 
contradict  it,  is  Petitio  Principii  in  one  of  its  most  palpable  forms. 

None  of  the  modes  of  assuming  what  should  be  proved  are  in  more  fre- 
quent use  than  what  are  termed  by  Bentham  “ question-begging  appella- 
tives;” names  which  beg  the  question  under  the  disguise  of  stating  it. 
The  most  potent  of  these  are  such  as  have  a laudatory  or  vituperative 
character.  For  instance,  in  politics,  the  word  Innovation.  The  dictionary 
meaning  of  this  term  being  merely  “ a change  to  something  new,”  it  is  dif- 
ficult for  the  defenders  even  of  the  most  salutary  improvement  to  deny 
that  it  is  an  innovation ; yet  the  word  having  acquired  in  common  usage  a 
vituperative  connotation  in  addition  to  its  dictionary  meaning,  the  admis- 
sion is  always  construed  as  a large  concession  to  the  disadvantage  of  the 
thing  proposed. 

The  following  passage  from  the  argument  in  refutation  of  the  Epicu- 
reans, in  the  second  book  of  Cicero,  “ De  Finibus,”  affords  a fine  example 
of  this  sort  of  fallacy : “ Et  quidem  illud  ipsum  non  nitnium  probo  (et 
tan  turn  patior)  philosophum  loqui  de  cupiditatibus  finiendis.  An  potest 
cupiditas  finiri  ? tollenda  est,  atque  extrahenda  radicitus.  Quis  est  enim, 
in  quo  sit  cupiditas,  quin  recte  cupidus  dici  possit?  Ergo  et  avarus  erit, 
sed  finite  : adulter,  verum  habebit  modum  : et  luxuriosus  eodem  modo. 
Qualis  ista  philosophia  est,  quae  non  interitum  afferat  pravitatis,  sed  sit 
contenta  mediocritate  vitiorum  ?”  The  question  was,  whether  certain  de- 
sires, when  kept  within  bounds,  are  vices  or  not ; and  the  argument  de- 
cides the  point  by  applying  to  them  a word  ( cupiditas ) which  implies  vice. 
It  is  shown,  however,  in  the  remarks  which  follow,  that  Cicero  did  not  in- 
tend this  as  a serious  argument,  but  as  a criticism  on  what  he  deemed  an 
inappropriate  expression.  “ Rem  ipsam  prorsus  probo : elegautiam  desi- 
dero.  Appellet  base  desideria  naturae;  cupiditatis  nomen  servet  alio,”  etc. 
But  many  persons,  both  ancient  and  modern,  have  employed  this,  or  some- 
thing equivalent  to  it,  as  a real  and  conclusive  argument.  We  may  re- 
mark that  the  passage  respecting  cupiditas  and  cupidus  is  also  an  example 
of  another  fallacy  already  noticed,  that  of  Paronymous  Terms. 

Many  more  of  the  arguments  of  the  ancient  moralists,  and  especially  of 
the  Stoics,  fall  within  the  definition  of  Petitio  Principii.  In  the  “ De  Fini- 
bus,” for  example,  which  I continue  to  quote  as  being  probably  the  best 
extant  exemplification  at  once  of  the  doctrines  and  the  methods  of  the 
schools  of  philosophy  existing  at  that  time;  of  what  value  as  arguments 
are  such  pleas  as  those  of  Cato  in  the  third  book  : That  if  virtue  were  not 
happiness,  it  could  not  be  a thing  to  boast  of : That  if  death  or  pain  were 
evils,  it  would  be  impossible  not  to  fear  them,  and  it  could  not,  therefoi-e, 
be  laudable  to  despise  them,  etc.  In  one  way  of  viewing  these  arguments, 
they  may  be  regarded  as  appeals  to  the  authority  of  the  general  sentiment 
of  mankind  which  had  stamped  its  approval  upon  certain  actions  and  char- 


* Hist.  Ind.  Sc.,  i.,  34. 


574 


FALLACIES. 


actors  by  the  phrases  referred  to ; but  that  such  could  have  been  the  mean- 
ing intended  is  very  unlikely,  considering  the  contempt  of  the  ancient  phi- 
losophers for  vulgar  opinion.  In  any  other  sense  they  are  clear  cases  of 
Petitio  Principii,  since  the  word  laudable,  and  the  idea  of  boasting,  im- 
ply principles  of  conduct;  and  practical  maxims  can  only  be  proved  from 
speculative  truths,  namely,  from  the  properties  of  the  subject-matter,  and 
can  not,  therefore,  be  employed  to  prove  those  properties.  As  well  might 
it  be  argued  that  a government  is  good  because  we  ought  to  support  it,  or 
that  there  is  a God  because  it  is  our  duty  to  pray  to  him. 

It  is  assumed  by  all  the  disputants  in  the  “ De  Finibus  ” as  the  founda- 
tion of  the  inquiry  into  the  summum  bonum,  that  “ sapiens  semper  beatus 
est.”  Not  simply  that  wisdom  gives  the  best  chance  of  happiness,  or  that 
wisdom  consists  in  knowing  what  happiness  is,  and  by  what  things  it  is 
promoted  ; these  propositions  would  not  have  been  enough  for  them ; but 
that  the  sage  always  is,  and  must  of  necessity  be,  happy.  The  idea  that 
wisdom  could  be  consistent  with  unhappiness,  was  always  rejected  as  inad- 
missible: the  reason  assigned  by  one  of  the  interlocutors,  near  the  begin- 
ning of  the  third  book,  being,  that  if  the  wise  could  be  unhappy,  there  was 
little  use  in  pursuing  wisdom.  But  by  unhappiness  they  did  not  mean 
pain  or  suffering;  to  that  it  was  granted  that  the  wisest  person  was  liable 
in  common  with  others : he  was  happy,  because  in  possessing  wisdom  he 
had  the  most  valuable  of  all  possessions,  the  most  to  be  sought  and  prized 
of  all  things,  and  to  possess  the  most  valuable  thing  was  to  be  the  most 
happy.  By  laying  it  down,  therefore,  at  the  commencement  of  the  inquiry, 
that  the  sage  must  be  happy,  the  disputed  question  respecting  the  sum- 
mum  bonum  was  in  fact  begged;  with  the  further  assumption,  that  pain 
and  suffering,  so  far  as  they  can  co-exist  with  wisdom,  are  not  unhappiness, 
and  are  no  evil. 

The  following  are  additional  instances  of  Petitio  Principii,  under  more 
or  less  of  disguise. 

Plato,  in  the  Soiihistes,  attempts  to  prove  that  things  may  exist  which 
are  incorporeal,  by  the  argument  that  justice  and  wisdom  are  incorporeal, 
and  justice  and  wisdom  must  be  something.  Here,  if  by  something  be 
meant,  as  Plato  did  in  fact  mean,  a thing  capable  of  existing  in  and  by 
itself,  and  not  as  a quality  of  some  other  thing,  he  begs  the  question  in 
asserting  that  justice  and  wisdom  must  be  something;  if  he  means  any 
thing  else,  his  conclusion  is  not  proved.  This  fallacy  might  also  be  class- 
ed under  ambiguous  middleterm ; something , in  the  one  premise,  meaning 
some  substance,  in  the  other  merely  some  object  of  thought,  whether  sub- 
stance or  attribute. 

It  was  formerly  an  argument  employed  in  proof  of  what  is  now  no  long- 
er a popular  doctrine,  the  infinite  divisibility  of  matter,  that  every  portion 
of  matter  however  small,  must  at  least  have  an  upper  and  an  under  sur 
face.  Those  who  used  this  argument  did  not  see  that  it  assumed  the  very 
point  in  dispute,  the  impossibility  of  arriving  at  a minimum  of  thickness; 
for  if  there  be  a minimum,  its  upper  and  under  surface  will  of  course  be 
one  ; it  will  be  itself  a surface,  and  no  more.  The  argument  owes  its  very 
considerable  plausibility  to  this,  that  the  premise  does  actually  seem  more 
obvious  than  the  conclusion,  though  really  identical  with  it.  As  expressed 
in  the  premise,  the  proposition  appeals  directly  and  in  concrete  language 
to  the  incapacity  of  the  human  imagination  for  conceiving  a minimum. 
Viewed  in  this  light,  it  becomes  a case  of  the  a priori  fallacy  or  natural 
prejudice,  that  whatever  can  not  be  conceived  can  not  exist.  Every  fal- 


FALLACIES  OF  CONFUSION. 


575 


lacy  of  Confusion  (it  is  almost  unnecessary  to  repeat)  will,  if  cleared  up, 
become  a fallacy  of  some  other  sort ; and  it  will  be  found  of  deductive  or 
ratiocinative  fallacies  generally,  that  when  they  mislead,  there  is  mostly,  as 
in  this  case,  a fallacy  of  some  other  description  lurking  under  them,  by 
virtue  of  which  chiefly  it  is  that  the  verbal  juggle,  which  is  the  outside  or 
body  of  this  kind  of  fallacy,  passes  undetected. 

Euler’s  Algebra,  a book  otherwise  of  great  merit,  but  full,  to  overflow- 
ing, of  logical  errors  in  respect  to  the  foundation  of  the  science,  contains 
the  following  argument  to  prove  that  minus  multiplied  by  minus  gives 
plus,  a doctrine  the  opprobrium  of  all  mere  mathematicians,  and  which 
Euler  had  not  a glimpse  of  the  true  method  of  proving.  Pie  says  minus 
multiplied  by  minus  can  not  give  minus ; for  minus  multiplied  by  plus 
gives  minus,  and  minus  multiplied  by  minus  can  not  give  the  same  prod- 
uct as  minus  multiplied  by  plus.  Now  one  is  obliged  to  ask,  why  minus 
multiplied  by  minus  must  give  any  product  at  all?  and  if  it  does,  why  its 
product  can  not  be  the  same  as  that  of  minus  multiplied  by  plus?  for  this 
would  seem,  at  the  first  glance,  not  more  absurd  than  that  minus  by  minus 
should  give  the  same  as  plus  by  plus,  the  proposition  which  Euler  prefers 
to  it.  The  premise  requires  proof,  as  much  as  the  conclusion ; nor  can  it 
be  proved,  except  by  that  more  comprehensive  view  of  the  nature  of  mul- 
tiplication, and  of  algebraic  processes  in  general,  which  would  also  supply 
a far  better  proof  of  the  mysterious  doctrine  which  Euler  is  here  endeavor- 
ing to  demonstrate. 

A striking  instance  of  reasoning  in  a circle  is  that  of  some  ethical  writers, 
who  first  take  for  their  standard  of  moral  truth  what,  being  the  general, 
they  deem  to  be  the  natural  or  instinctive  sentiments  and  perceptions  of 
mankind,  and  then  explain  away  the  numerous  instances  of  divergence 
from  their  assumed  standard,  by  representing  them  as  cases  in  which  the 
perceptions  are  unhealthy.  Some  particular  mode  of  conduct  or  feeling  is 
affirmed  to  be  unnatural ; why  ? because  it  is  abhorrent  to  the  universal 
and  natural  sentiments  of  mankind.  Finding  no  such  sentiment  in  your- 
self, you  question  the  fact;  and  the  answer  is  (if  your  antagonist  is  polite), 
that  you  are  an  exception,  a peculiar  case.  But  neither  (say  you)  do  I 
find  in  the  people  of  some  other  country,  or  of  some  former  age,  any  such 
feeling  of  abhorrence;  “ay,  biu  their  feelings  were  sophisticated  and  un- 
healthy.” 

One  of  the  most  notable  specimens  of  reasoning  in  a circle  is  the  doc- 
trine of  Hobbes,  Rousseau,  and  others,  which  rests  the  obligations  by 
which  human  beings  are  bound  as  members  of  society,  on  a supposed  so- 
cial compact.  I waive  the  consideration  of  the  fictitious  nature  of  the  com- 
pact itself;  but  when  Hobbes,  through  the  whole  Leviathan,  elaborately 
deduces  the  obligation  of  obeying  the  sovereign,  not  from  the  necessity  or 
utility  of  doing  so,  but  from  a promise  supposed  to  have  been  made  by 
our  ancestors,  on  renouncing  savage  life  and  agreeing  to  establish  political 
society,  it  is  impossible  not  to  retort  by  the  question,  Why  are  we  bound 
to  keep  a promise  made  for  us  by  others?  or  why  bound  to  keep  a promise 
at  all?  No  satisfactory  ground  can  be  assigned  for  the  obligation, except 
the  mischievous  consequences  of  the  absence  of  faith  and  mutual  confidence 
among  mankind.  We  are,  therefore,  brought  round  to  the  interests  of  so- 
ciety, as  the  ultimate  ground  of  the  obligation  of  a promise;  and  yet  those 
interests  are  not  admitted  to  be  a sufficient  justification  for  the  existence 
of  government  and  law.  Without  a promise  it  is  thought  that  we  should 
not  be  bound  to  that  which  is  implied  in  all  modes  of  living  in  society, 


5'76 


FALLACIES. 


namely,  to  yield  a general  obedience  to  the  laws  therein  established ; and 
so  necessary  is  the  promise  deemed,  that  if  none  has  actually  been  made, 
some  additional  safety  is  supposed  to  be  given  to  the  foundations  of  so- 
ciety by  feigning  one. 

§ 3.  Two  principal  subdivisions  of  the  class  of  Fallacies  of  Confusion 
having  been  disposed  of;  there  remains  a third,  in  which  the  confusion  is 
not,  as  in  the  Fallacy  of  Ambiguity,  in  misconceiving  the  import  of  the 
premises,  nor,  as  in  Petitio  Principii,  in  forgetting  what  the  premises  are, 
but  in  mistaking  the  conclusion  which  is  to  be  proved.  This  is  the  fallacy 
of  Ignoratio  Elen  chi,  in  the  widest  sense  of  the  phrase;  also  called  by 
Archbishop  Whately  the  Fallacy  of  Irrelevant  Conclusion.  His  examples 
and  remarks  are  highly  worthy  of  citation. 

“ Various  kinds  of  propositions  are,  according  to  the  occasion,  substi- 
tuted for  the  one  of  which  proof  is  required ; sometimes  the  particular  for 
the  universal;  sometimes  a proposition  with  different  terms;  and  various 
are  the  contrivances  employed  to  effect  and  to  conceal  this  substitution, 
and  to  make  the  conclusion  which  the  sophist  has  drawn,  answer  practical- 
ly the  same  purpose  as  the  one  he  ought  to  have  established.  We  say, 
‘ practically  the  same  purpose,’  because  it  will  very  often  happen  that  some 
emotion  will  be  excited,  some  sentiment  impressed  on  the  mind  (by  a dex- 
terous employment  of  this  fallacy),  such  as  shall  bring  men  into  the  dispo- 
sition requisite  for  your  purpose;  though  they  may  not  have  assented  to, 
or  even  stated  distinctly  in  their  own  minds,  the  proposition  which  it  was 
your  business  to  establish.  Thus  if  a sophist  has  to  defend  one  who  has 
been  guilty  of  some  serious  offense,  which  he  wishes  to  extenuate,  though 
he  is  unable  distinctly  to  prove  that  it  is  not  such,  yet  if  he  can  succeed  in 
making  the  audience  laugh  at  some  casual  matter,  lie  has  gained  practical- 
ly the  same  point.  So  also  if  any  one  has  pointed  out  the  extenuating  cir- 
cumstances in  some  particular  case  of  offense,  so  as  to  show  that  it  differs 
widely  from  the  generality  of  the  same  class,  the  sophist,  if  he  finds  him- 
self unable  to  disprove  these  circumstances,  may  do  away  the  force  of 
them,  by  simply  referring  the  action  to  that  very  class,  which  no  one  can 
deny  that  it  belongs  to,  and  the  very  name  of  which  will  excite  a feeling 
of  disgust  sufficient  to  counteract  the  extenuation ; e.  g.,  let  it  be  a case  of 
peculation,  and  that  many  mitigating  circumstances  have  been  brought 
forward  which  can  not  be  denied;  the  sophistical  opponent  will  reply, 
‘ Well,  but  after  all,  the  man  is  a rogue,  and  there  is  an  end  of  it;’  now  in 
reality  this  was  (by  hypothesis)  never  the  question;  and  the  mere  asser- 
tion of  what  was  never  denied  ought  not,  in  fairness,  to  be  regarded  as 
decisive ; but,  practically,  the  odiousness  of  the  word,  arising  in  great 
measure  from  the  association  of  those  very  circumstances  which  belong  to 
most  of  the  class,  but  which  we  have  supposed  to  be  absent  in  this  par- 
ticular instance,  excites  precisely  that  feeling  of  disgust  which,  in  effect, 
destroys  the  force  of  the  defense.  In  like  manner  we  may  refer  to  this 
head  all  cases  of  improper  appeal  to  the  passions,  and  every  thing  else 
which  is  mentioned  by  Aristotle  as  extraneous  to  the  matter  in  hand  (t£<i> 
roil  TTpuygarog).” 

Again,  “instead  of  proving  that  ‘this  prisoner  has  committed  an  atro- 
cious fraud,’  you  prove  that  the  fraud  he  is  accused  of  is  atrocious  ; instead 
of  proving  (as  in  the  well-known  tale  of  Cyrus  and  the  two  coats)  that  the 
taller  boy  had  a right  to  force  the  other  boy  to  exchange  coats  with  him, 
you  prove  that  the  exchange  would  have  been  advantageous  to  both;  in- 


FALLACIES  OF  CONFUSION. 


577 

stead  of  proving  that  the  poor  ought  to  be  relieved  in  this  way  rather  than 
in  that,  you  prove  that  the  poor  ought  to  be  relieved ; instead  of  proving 
that  the  irrational  agent — whether  a brute  or  a madman — can  never  be  de- 
terred from  any  act  by  apprehension  of  punishment  (as,  for  instance,  a dog 
from  sheep-biting,  by  fear  of  being  beaten),  you  prove  that  the  beating  of 
one  dog  does  not  operate  as  an  example  to  other  dogs,  etc. 

“It  is  evident  that  Ignoratio  Elenchi  may  be  employed  as  well  for  the 
apparent  refutation  of  your  opponent’s  proposition,  as  for  the  apparent  es- 
tablishment of  your  own  ; for  it  is  substantially  the  same  thing,  to  prove 
what  was  not  denied  or  to  disprove  what  was  not  asserted.  The  latter 
practice  is  not  less  common,  and  it  is  more  offensive,  because  it  frequent- 
ly amounts  to  a personal  affront,  in  attributing  to  a person  opinions,  etc., 
which  he  perhaps  holds  in  abhorrence.  Thus,  when  in  a discussion  one 
party  vindicates,  on  the  ground  of  general  expediency,  a particular  in- 
stance of  resistance  to  government  in  a case  of  intolerable  oppression,  the 
opponent  may  gravely  maintain,  ‘that  we  ought  not  to  do  evil  that  good 
may  come  a proposition  which  of  course  had  never  been  denied,  the  point 
in  dispute  being,  ‘ whether  resistance  in  this  particular  case  were  doing  evil 
or  not.’  Or  again,  by  way  of  disproving  the  assertion  of  the  right  of  pri- 
vate judgment  in  religion,  one  may  hear  a grave  argument  to  prove  that ‘it 
is  impossible  every  one  can  be  right  in  his  judgment?  ” 

The  works  of  controversial  writers  are  seldom  free  from  this  fallacy.  The 
attempts,  for  instance,  to  disprove  the  population  doctrines  of  Malthus,  have 
been  mostly  cases  of  ignoratio  elenchi.  Malthus  has  been  supposed  to  be 
refuted  if  it  could  be  shown  that  in  some  countries  or  ages  population  has 
been  nearly  stationary;  as  if  he  had  asserted  that  population  always  in- 
creases in  a given  ratio,  or  had  not  expressly  declared  that  it  increases  only 
in  so  far  as  it  is  not  restrained  by  prudence,  or  kept  down  by  poverty  and 
disease.  Or,  perhaps,  a collection  of  facts  is  produced  to  prove  that  in  some 
one  country  the  people  are  better  off  with  a dense  population  than  they 
are  in  another  country  with  a thin  one  ; or  that  the  people  have  become 
more  numerous  and  better  off  at  the  same  time.  As  if  the  assertion  were 
that  a dense  population  could  not  possibly  be  well  off;  as  if  it  were  not 
part  of  the  very  doctrine,  and  essential  to  it,  that  where  there  is  a more 
abundant  production  there  may  be  a greater  population  without  any  increase 
of  poverty,  or  even  with  a diminution  of  it. 

The  favorite  argument  against  Berkeley’s  theory  of  the  non-existence  of 
matter,  and  the  most  popularly  effective,  next  to  a “ grin  ”* — an  argument, 
moreover,  which  is  not  confined  to  “ coxcombs,”  nor  to  men  like  Samuel 
Johnson,  whose  greatly  overrated  ability  certainly  did  not  lie  in  the  direc- 
tion of  metaphysical  speculation,  but  is  the  stock  argument  of  the  Scotch 
school  of  metaphysicians — is  a palpable  Ignoratio  Elenchi.  The  argument 
is  perhaps  as  frequently  expressed  by  gesture  as  by  words,  aud  one  of  its 
commonest  forms  consists  in  knocking  a stick  against  the  ground.  This 
short  and  easy  confutation  overlooks  the  fact,  that  in  denying  matter,  Berke- 
ley did  not  deny  any  thing  to  which  our  senses  bear  witness,  and  therefore 
can  not  be  answered  by  any  appeal  to  them.  His  skepticism  related  to  the 
supposed  substratum,  or  hidden  cause  of  the  appearances  perceived  by  our 
senses ; the  evidence  of  which,  whatever  may  be  thought  of  its  conclusive- 
ness, is  certainly  not  the  evidence  of  sense.  And  it  will  always  remain  a 
signal  proof  of  the  want  of  metaphysical  profundity  of  Reid,  Stewart,  and, 


* “And  coxcombs  vanquish  Berkeley  with  a grin. 

37 


57S 


FALLACIES. 


I am  sorry  to  add,  of  Brown,  that  they  should  have  persisted  in  asserting 
that  Berkeley,  if  he  believed  his  own  doctrine,  was  bound  to  walk  into  the 
kennel,  or  run  his  head  against  a post.  As  if  persons  who  do  not  recognize 
an  occult  cause  of  their  sensations  could  not  possibly  believe  that  a fixed 
order  subsists  among  the  sensations  themselves.  Such  a want  of  compre- 
hension of  the  distinction  between  a thing  and  its  sensible  manifestation, 
or,  in  metaphysical  language,  between  the  noumenon  and  the  phenomenon, 
would  be  impossible  to  even  the  dullest  disciple  of  Kant  or  Coleridge. 

It  would  be  easy  to  add  a greater  number  of  examples  of  this  fallacy,  as 
well  as  of  the  others  which  I have  attempted  to  characterize.  But  a more 
copious  exemplification  does  not  seem  to  be  necessary  ; and  the  intelligent 
reader  will  have  little  difficulty  in  adding  to  the  catalogue  from  his  own 
reading  and  experience.  We  shall,  therefore,  here  close  our  exposition  of 
the  general  principles  of  logic,  and  proceed  to  the  supplementary  inquiry 
which  is  necessary  to  complete  our  design. 


BOOK  VI. 

ON  THE  LOGIC  OF  THE  MORAL  SCIENCES. 


“Si  l’homme  pent  predirc,  avec  une  assurance  presque  entiere,  les  plie'nomenes  dont  il  con- 
nait  les  lois ; si  lors  raeme  qu’elles  lui  sont  inconnues,  il  peat,  d’apies  l’expe'rience,  pievoir 
avec  une  grande  probability  les  evenemens  de  l'avenir ; pourquoi  regarderait-on  comme  une 
entreprise  chimerique,  celle  de  tracer  avec  quelque  vraisemblance  le  tableau  des  destine'es  futures 
de  l’espece  humaine,  d'apres  les  resultats  de  son  histoire?  Le  seul  fondement  de  croyance 
dans  les  sciences  naturelles.  est  cette  ide'e,  que  les  lois  generates,  connues  ou  ignorees,  qui 
reglent  les  phenomenes  de  l’linivers,  sont  necessaires  et  constantes ; et  par  quelle  raison  ce 
principe  serait-il  moins  vrai  pour  le  developpement  des  facultes  intellectuelles  et  morales  de 
i'homme,  que  pour  les  autres  operations  de  la  nature?  Enfin,  puisque  des  opinions  formees 
d’apres  l’experience sont  la  settle  regie  de  la  conduite  des  hommes  les  plus  sages,  pour- 

quoi interdirait-on  au  philosophe  d’appuver  ses  conjectures  stir  cette  meme  base,  pourvu  qu'il 
ne  leur  attribue  pas  une  certitude  superieure  a celle  qui  pent  naitre  du  nombre,  de  la  Constance, 
de  l’exactitude  des  observations?” — Condokcet,  Esquisse  d'un  Tableau  Historique  des  Pro- 
gres  de  1’ Esprit  Humain. 


CHAPTER  I. 

INTRODUCTORY  REMARKS. 

§ 1.  Principles  of  Evidence  and  Theories  of  Method  are  not  to  be  con- 
structeda priori . The  laws  of  our  rational  faculty,  like  those  of  every 
other  natural  agency,  are  only  learned  by  seeing  the  agent  at  work.  The 
earlier  achievements  of  science  were  made  without  the  conscious  observ- 
ance of  any  Scientific  Method ; and  we  should  never  have  known  by  what 
process  truth  is  to  be  ascertained,  if  we  had  not  previously  ascertained 
many  truths.  But  it  was  only  the  easier  problems  which  could  be  thus 
resolved : natural  sagacity,  when  it  tried  its  strength  against  the  more  dif- 
ficult ones,  either  failed  altogether,  or,  if  it  succeeded  here  and  there  in  ob- 
taining a solution,  had  no  sure  means  of  convincing  others  that  its  solution 
was  correct.  In  scientific  investigation,  as  in  all  other  works  of  human 
skill,  the  way  Air  obtaining  the  end  is  seen  as  it  were  instinctively  by  su- 
perior minds  in  some  comparatively  simple  case,  and  is  then,  by  judicious 
generalization,  adapted  to  the  variety  of  complex  cases.  We  learn  to  do 
a thing  in  difficult  circumstances,  by  attending  to  the  manner  in  which  we 
have  spontaneously  done  the  same  thing  in  easier  ones. 

This  truth  is  exemplified  by  the  history  of  the  various  branches  of  knowl- 
edge which  have  successively,  in  the  ascending  order  of  their  complication, 
assumed  the  character  of  sciences ; and  will  doubtless  receive  fresh  con- 
firmation from  those  of  which  the  final  scientific  constitution  is  yet  to 
come,  and  which  are  still  abandoned  to  the  uncertainties  of  vague  and 
popular  discussion.  Although  several  other  sciences  have  emerged  from 
this  state  at  a comparatively  recent  date,  none  now  remain  in  it  except 
those  which  relate  to  man  himself,  the  most  complex  and  most  difficult 
subject  of  study  on  which  the  human  mind  can  be  engaged. 


580 


LOGIC  OF  TIIE  MORAL  SCIENCES. 


Concerning  the  physical  nature  of  man,  as  an  organized  being — though 
there  is  still  much  uncertainty  and  much  controversy,  which  can  only  be 
terminated  by  the  general  acknowledgment  and  employment  of  stricter 
rules  of  induction  than  are  commonly  recognized  — there  is,  however,  a 
considerable  body  of  truths  which  all  who  have  attended  to  the  subject 
consider  to  be  fully  established ; nor  is  there  now  any  radical  imperfection 
in  the  method  observed  in  the  department  of  science  by  its  most  distin- 
guished modern  teachers.  But  tire  laws  of  Mind,  and,  in  even  a greater 
degree,  those  of  Society,  are  so  far  from  having  attained  a similar  state 
of  even  partial  recognition,  that  it  is  still  a controversy  whether  they  are 
capable  of  becoming  subjects  of  science  in  the  strict  sense  of  the  term : 
and  among  those  who  are  agreed  on  this  point,  there  reigns  the  most  ir- 
reconcilable diversity  on  almost  every  other.  Here,  therefore,  if  anywhere, 
the  principles  laid  down  in  the  preceding  Books  may  be  expected  to  be 
useful. 

sIf  on  matters  so  much  the  most  important  with  which  human  intellect 
can  occupy  itself  a more  general  agreement  is  ever  to  exist  among  think- 
ers; if  what  has  been  pronounced  “the  proper  study  of  mankind”  is  not 
destined  to  remain  the  only  subject  which  Philosophy  can  not  succeed  in 
rescuing  from  Empiricism ; the  same  process  through  which  the  laws  of 
many  simpler  phenomena  have  by  general  acknowledgment  been  placed 
beyond  dispute,  must  be  consciously  and  deliberately  applied  to  those 
more  difficult  inquiries.  If  there  are  some  subjects  on  which  the  results 
obtained  have  finally  received  the  unanimous  assent  of  all  who  have  attend- 
ed to  the  proof,  and  others  on  which  mankind  have  not  yet  been  equally 
successful;  on  which  the  most  sagacious  minds  have  occupied  themselves 
from  the  earliest  date,  and  have  never  succeeded  in  establishing  any  con- 
siderable body  of  truths,  so  as  to  be  beyond  denial  or  doubt ; it  is  by  gen- 
eralizing the  methods  successfully  followed  in  the  former  inquiries,  and 
adapting  them  to  the  latter,  that  we  may  hope  to  remove  this  blot  on  the 
face  of  science.  The  remaining  chapters  are  an  endeavor  to  facilitate  this 
most  desirable  object. 

§ 2.  In  attempting  this,  I am  not  unmindful  how  little  can  be  done  to- 
ward it  in  a mere  treatise  on  Logic,  or  how  vague  and  unsatisfactory  all 
precepts  of  Method  must  necessarily  appear  when  not  practically  exempli- 
fied in  the  establishment  of  a body  of  doctrine.  Doubtless,  the  most  effect- 
ual mode  of  showing  how  the  sciences  of  Ethics  and  Politics  may  be  con- 
structed would  be  to  construct  them : a task  which,  it  needs  scarcely  be 
said,  I am  not  about  to  undertake.  But  even  if  there  were  no  other  ex- 
amples, the  memorable  one  of  Bacon  would  be  sufficient  to  demonstrate, 
that  it  is  sometimes  both  possible  and  useful  to  point  out  the  way,  though 
without  being  one’s  self  prepared  to  adventure  far  into  it.  And  if  more 
were  to  be  attempted,  this  at  least  is  not  a proper  place  for  the  attempt. 

In  substance,  whatever  can  be  done  in  a work  like  this  for  the  Logic  of 
the  Moral  Sciences,  has  been  or  ought  to  have  been  accomplished  in  the 
five  preceding  Books ; to  which  the  present  can  be  only  a kind  of  supple- 
ment or  appendix,  since  the  methods  of  investigation  applicable  to  moral 
and  social  science  must  have  been  already  described,  if  I have  succeeded 
in  enumerating  and  characterizing  those  of  science  in  general.  It  remains, 
however,  to  examine  which  of  those  methods  are  more  especially  suited 
to  the  various  branches  of  moral  inquiry  ; under  what  peculiar  facilities 
or  difficulties  they  are  there  employed;  how  far  the  unsatisfactory  state 


LIBERTY  AND  NECESSITY. 


581 


of  those  inquiries  is  owing  to  a wrong  choice  of  methods,  how  far  to  want 
of  skill  in  the  application  of  right  ones ; and  what  degree  of  ultimate  suc- 
cess may  be  attained  or  hoped  for  by  a better  choice  or  more  careful  em- 
ployment of  logical  processes  appropriate  to  the  case.  In  other  words, 
whether  moral  sciences  exist,  or  can  exist ; to  what  degree  of  perfection 
they  are  susceptible  of  being  carried  ; and  by  what  selection  or  adaptation 
of  the  methods  brought  to  view  in  the  previous  part  of  this  work  that  de- 
gree of  perfection  is  attainable. 

At  the  threshold  of  this  inquiry  we  are  met  by  an  objection,  which,  if 
not  removed,  would  be  fatal  to  the  attempt  to  treat  human  conduct  as  a 
subject  of  science.  Are  the  actions  of  human  beings,  like  all  other  natural 
events,  subject  to  invariable  laws  ? Does  that  constancy  of  causation,  which 
is  the  foundation  of  every  scientific  theory  of  successive  phenomena,  really 
obtain  among  them?  This  is  often  denied  ; and  for  the  sake  of  systematic 
completeness,  if  not  from  any  very  urgent  practical  necessity,  the  question 
should  receive  a deliberate  answer  in  this  place.  We  shall  devote  to  the 
subject  a chapter  apart. 


CHAPTER  II. 

OF  LIBERTY  AND  NECESSITY. 

§ 1.  The  question,  whether  the  law  of  causality  applies  in  the  same  strict 
sense  to  human  actions  as  to  other  phenomena,  is  the  celebrated  contro- 
versy concerning  the  freedom  of  the  will ; which,  from  at  least  as  far  back 
as  the  time  of  Pelagius,  has  divided  both  the  philosophical  and  the  relig- 
ious world.  ;The  affirmative  opinion  is  commonly  called  the  doctrine  of 
Necessity,  as  asserting- hum  an  volitions  and  actions  to  be  necessary  and  in- 
evitable. The  negative  maintains  that  the  will  is  not  detei'mined,  like  oth- 
er phenomena,  by  antecedents,  but  determines  itself;  that  our  volitions  are 
not,  properly  speaking,  the  effects  of  causes,  or  at  least  have  no  causes 
which  they  uniformly  and  implicitly  obey. 

'I  have  already  made  it  sufficiently  apparent  that  the  former  of  these 
opinions  is  that  which  I consider  the  true  one;  but  the  misleading  terms 
in  which  it  is  often  expressed,  and  the  indistinct  manner  in  which  it  is  usu- 
ally apprehended,  have  both  obstructed  its  reception,  and  perverted  its  in- 
fluence when  received.  The  metaphysical  theory  of  free-will,  as  held  by: 
philosophers  (for  the  practical  feeling  of  it,  common  in  a greater  or  less 
degree  to  all  mankind,  is  in  no  way  inconsistent  with  the  contrary  theory), 
was  invented  because  the  supposed  alternative  of  admitting  human  actions 
to  be  necessary  was  deemed  inconsistent  with  every  one’s  instinctive  con- 
sciousness, as  well  as  humiliating  to  the  pride  and  even  degrading  to  the 
moral  nature  of  man.  Nor  do  I deny  that  the  doctrine,  as  sometimes  held, 
is  open  to  these  imputations ; for  the  misapprehension  in  which  I shall  be 
able  to  show  that  they  originate,  unfortunately  is  not  confined  to  the  oppo- 
nents of  the  doctrine,  but  is  participated  in  by  many,  perhaps  we  might 
say  by  most,  of  its  supporters. 

§ 2.  Correctly  conceived,  the  doctrine  called  Philosophical  Necessity  is 
simply  this : that,  given  the  motives  which  are  present  to  an  individual’s 
mind,  and  given  likewise  the  character  and  disposition  of  the  individual,  the 
manner  in  which  he  will  act  might  be  unerringly  inferred;  that  if  we  knew 


582 


LOGIC  OF  TIIE  MORAL  SCIENCES. 


the  person  thoroughly,  and  knew  all  the  inducements  which  are  acting  upon 
him,  we  could  foretell  his  conduct  with  as  much  certainty  as  we  can  pre- 
| diet  any  physical  event.  This  proposition  I take  to  be  a mere  interpreta- 
tion of  universal  experience,  a statement  in  words  of  what  every  one  is  in- 
ternally convinced  of.  No  one  who  believed  that  he  knew  thoroughly  the 
circumstances  of  any  case,  and  the  characters  of  the  different  persons  con- 
cerned, would  hesitate  to  foretell  how  all  of  them  would  act.  Whatever 
degree  of  doubt  he  may  in  fact  feel,  arises  from  the  uncertainty  whether  he 
really  knows  the  circumstances,  or  the  character  of  some  one  or  other  of 
the  persons,  with  the  degree  of  accuracy  required;  but  by  no  means  from 
thinking  that  if  he  did  know  these  things,  there  could  be  any  uncertainty 
what  the  conduct  would  be.  Nor  does  this  full  assurance  conflict  in  the 
smallest  degree  with  what  is  called  bur  feeling  of  freedom.  We  do  not 
feel  ourselves  the  less  free,  because  those  to  whom  we  are  intimately  known 
are  well  assured  how  we  shall  will  to  act  in  a particular  case.  We  often, 
on  the  contrary,  regard  the  doubt  what  our  conduct  will  be,  as  a mark  of 
ignorance  of  our  character,  and  sometimes  even  resent  it  as  an  imputation. 
The  religions  metaphysicians  who  have  asserted  the  freedom  of  the  will, 
have  always  maintained  it  to  be  consistent  with  divine  foreknowledge  of 
our  actions:  and  if  with  divine,  then  with  any  other  foreknowledge.  We 
may  be  free,  and  yet  another  may  have  reason  to  be  perfectly  certain  what 
use  we  shall  make  of  our  freedom.  vIt  is  not,  therefore,  the  doctrine  that 
our  volitions  and  actions  are  invariable  consequents  of  our  antecedent 
states  of  mind,  that  is  either  contradicted  by  our  consciousness,  or  felt  to 
be  degrading. 

But  the  doctrine  of  causation,  when  considered  as  obtaining  between  our 
volitions  and  their  antecedents,  is  almost  universally  conceived  as  involving 
more  than  this.  Many  do  not  believe,  and  very  few  practically  feel,  that 
there  is  nothing  in  causation  but  invariable,  certain,  and  unconditional  se- 
quence. There  are  few  to  whom  mere  constancy  of  succession  appears  a 
sufficiently  stringent  bond  of  union  for  so  peculiar  a relation  as  that  of) 
cause  and  effect.  Even  if  the  reason  repudiates,  the  imagination  retains, 
the  feeling  of  some  more  intimate  connection,  of  some  peculiar  tie,  or  mys- 
terious constraint  exercised  by  the  antecedent  over  the  consequent.  Now 
this  it  is  which,  considered  as  applying  to  the  human  will,  conflicts  with 
our  consciousness,  and  revolts  our  feelings.  We  are  certain  that,  in  the 
case  of  our  volitions,  there  is  not  this  mysterious  constraint.  We  know 
that  we  are  not  compelled,  as  by  a magical  spell,  to  obey  any  particular 
motive.  We  feel,  that  if  we  wished  to  prove  that  we  have  the  power  of 
resisting  the  motive,  we  could  do  so  (that  wish  being,  it  needs  scarcely  be 
observed,  a new  antecedent );  and  it  would  be  humiliating  to  our  pride,  and 
(what  is  of  more  importance)  paralyzing  to  our  desire  of  excellence,  if  we 
thought  otherwise.  But  neither  is  any  such  mysterious  compulsion  now 
supposed,  by  the  best  philosophical  authorities,  to  be  exercised  by  any  oth- 
er cause  over  its  effect.  Those  who  think  that  causes  draw  their  effects  af- 
ter them  by  a mystical  tie,  are  right  in  believing  that  the  relation  between 
volitions  and  their  antecedents  is  of  another  nature.  But  they  should  go 
farther,  and  admit  that  this  is  also  true  of  all  other  effects  and  their  ante- 
cedents. If  such  a tie  is  considered  to  be  involved  in  the  word  Necessity, 
the  doctrine  is  not  true  of  human  actions;  but  neither  is  it  then  true  of  in- 
animate objects.  It  would  be  more  correct  to  say  that  matter  is  not  bound 
by  necessity,  than  that  mind  is  so. 

That  the  free-will  metaphysicians,  being  mostly  of  the  school  which  re- 


LIBERTY  AND  NECESSITY. 


583 


jects  Hume’s  and  Brown’s  analysis  of  Cause  and  Effect,  should  miss  their 
way  for  want  of  the  light  which  that  analysis  affords,  can  not  surprise'  us. 
The  wonder  is,  that  the  necessitarians,  who  usually  admit  that  philosophic- 
al theory,  should  in  practice  equally  lose  sight  of  it.  The  very  same  mis- 
conception of  the  doctrine  called  Philosophical  Necessity,  which  prevents 
the  opposite  party  from  recognizing  its  truth,  I believe  to  exist  more  or 
less  obscurely  in  the  minds  of  most  necessitarians,  however  they  may  in 
words  disavow  it.  I am  much  mistaken  if  they  habitually  feel  that  the 
necessity  which  they  recognize  in  actions  is  but  uniformity  of  order,  and 
capability  of  being  predicted.  They  have  a feeling  as  if  there  were  at  bot- 
tom a stronger  tie  between  the  volitions  and  their  causes ; as  if,  when  they 
asserted  that  the  will  is  governed  by  the  balance  of  motives,  they  meant 
something  more  cogent  than  if  they  had  only  said,  that  whoever  knew  the 
motives,  and  our  habitual  susceptibilities  to  them,  could  predict  how  we 
should  will  to  act.  They  commit,  in  opposition  to  their  own  scientific 
system,  the  very  same  mistake  which  their  adversaries  commit  in  obedience 
to  theirs;  and  in  consequence  do  really  in  some  instances  suffer  those  de- 
pressing consequences  which  their  opponents  erroneously  impute  to  the 
doctrine  itself. 

§ 3.  I am  inclined  to  think  that  this  error  is  almost  wholly  an  effect  of 
the  associations  with  a word,  and  that  it  would  be  prevented;  by  forbear- 
ing to  employ,  for  the  expression  of  the  simple  fact  of  causation,  so  ex- 
tremely inappropriate  a term  as  Necessity.  That  xvord,  in  its  other  ac- 
ceptations, involves  much  more  than  mere  uniformity  of  sequence : it  im- 
plies irresistibleness.  Applied  to  the  will,  it  only  means  that  the  given 
cause  will  be  followed  by  the  effect,  subj ect  to  all  possibilities  of  counter- 
action by  other  causes ; but  in  common  use  it  stands  for  the  operation  of 
those  causes  exclusively  which  are  supposed  too  powerful  to  be  counter- 
acted at  all.  ^When  we  say  that  all  human  actions  take  place  of  necessity,  ' 
we  only  mean  that  they  will  certainly  happen  if  nothing  prevents;  when 
we  say  that  dying  of  want,  to  those  who  can  not  get  food,  is  a necessity, 
we  mean  that  it  will  certainly  happen  whatever  may  be  done  to  prevent  it. 
The  application  of  the  same  term  to  the  agencies  on  which  human  actions 
depend,  as  is  used  to  express  those  agencies  of  nature  which  are  really  un- 
controllable, can  not  fail,  when  habitual,  to  create  a feeling  of  uncontrol- 
lableness in  the  former  also.  This,  however,  is  a mere  illusion.  There  are 
physical  sequences  which  we  call  necessary,  as  death  for  want  of  food  or 
air;  there  are  others  which,  though  as  much  cases  of  causation  as  the  for- 
mer, are  not  said  to  be  necessary,  as  death  from  poison,  which  an  antidote, 
or  the  use  of  the  stomach-pump,  will  sometimes  avert.  *Tt  is  apt  to  be  for- 
gotten by  people’s  feelings,  even  if  remembered  by  their  understandings, 
that  human  actions  are  in  this  last  predicament : they  are  never  (except  in 
some  cases  of  mania)  ruled  by  any  one  motive  with  such  absolute  sway 
that  there  is  no  room  for  the  influence  of  any  other.  - The  causes,  there- 
fore, on  which  action  depends,  are  never  uncontrollable;  and  any  given  ef- 
fect is  only  necessary  provided  that  the  causes  tending  to  produce  it  are 
not  controlled.  That  whatever  happens,  could  not  have  happened  other- 
wise, unless  something  had  taken  place  which  was  capable  of  preventing  it, 
no  one  surely  needs  hesitate  to  admit.  But  to  call  this  by  the  name  Neces- 
sity is  to  use  the  term  in  a sense  so  different  from  its  primitive  and  famil- 
iar meaning,  from  that  which  it  bears  in  the  common  occasions  of  life,  as 
to  amount  almost  to  a play  upon  words.  The  associations  derived  from 


5S4 


LOGIC  OF  TIIE  MORAL  SCIENCES. 


the  ordinary  sense  of  the  term  will  adhere  to  it  in  spite  of  all  'we  can  do ; 
and  though  the  doctrine  of  Necessity,  as  stated  by  most  who  hold  it,  is  very 
remote  from  fatalism,  it  is  probable  that  most  necessitarians  are  fatalists, 
more  or  less,  in  their  feelings. 

A fatalist  believes,  or  half  believes  (for  nobody  is  a consistent  fatalist), 
not  only  that  whatever  is  about  to  happen  will  be  the  infallible  result  of 
the  causes  which  produce  it  (which  is  the  true  necessitarian  doctrine),  but 
moreover  that  there  is  no  use  in  struggling  against  it;  that  it  will  happen, 
however  we  may  strive  to  prevent  it.  Now,  a necessitarian,  believing  that 
our  actions  follow  from  our  characters,  and  that  our  characters  follow  from 
our  organization,  our  education,  and  our  circumstances,  is  apt  to  be,  with 
more  or  less  of  consciousness  on  his  part,  a fatalist  as  to  his  own  actions, 
and  to  believe  tlyit  his  nature  is  such,  or  that  his  education  and  circum- 
stances have  so  moulded  his  character,  that  nothing  can  now  prevent  him 
from  feeling  and  acting  in  a particular  way,  or  at  least  that  no  effort  of  his 
own  can  hinder  it.  In  the  words  of  the  sect  which  in  our  own  day  has 
most  perseveringly  inculcated  and  most  perversely  misunderstood  this  great 
doctrine,  his  character  is  formed  for  him,  and  not  by  him;  therefore  his 
wishing  that  it  had  been  formed  differently  is  of  no  use;  he  has  no  power 
to  alter  it.  But  this  is  a grand  error.  Pie  has,  to  a certain  extent,  a pow- 
er to  alter  his  character.  * Its  being,  in  the  ultimate  resort,  formed  for  him, 
is  not  inconsistent  with  its  being,  in  part,  formed  by  him  as  one  of  the  in- 
termediate agents.  His  character  is  formed  by  his  circumstances  (includ- 
ing among  these  his  particular  organization) ; but  his  own  desire  to  mould 
it  in  a particular  way,  is  one  of  those  circumstances,  and  by  no  means  one  of 
the  least  influential.  We  can  not,  indeed,  directly  will  to  be  different  from 
what  we  are.  But  neither  did  those  who  are  supposed  to  have  formed  our 
characters  directly  will  that  we  should  be  what  we  are.  Their  will  had  no 
direct  power  except  over  their  own  actions.  They  made  us  what  they  did 
make  us,  by  willing,  not  the  end,  but  the  requisite  means ; and  we,  when 
our  habits  are  not  too  inveterate,  can,  by  similarly  willing  the  requisite 
means,  make  ourselves  different.  If  they  could  place  us  under  the  influence 
of  certain  circumstances,  we,  in  like  manner,  can  place  ourselves  under  the 
influence  of  other  circumstances.  We  are  exactly  as  capable  of  making 
our  own  character,  if  we  will,  as  others  are  of  making  it  for  ns. 

Yes  (answers  the  Owenite),  but  these  words,  “if  we  will,”  surrender  the 
whole  point:  since  the  will  to  alter  our  own  character  is  given  us,  not  by 
any  efforts  of  ours,  but  by  circumstances  which  we  can  not  help,  it  comes 
to  us  either  from  external  causes,  or  not  at  all.  Most  true : if  the  Owenite 
stops  here,  he  is  in  a position  from  which  nothing  can  expel  him.  Our 
character  is  formed  by  us  as  well  as  for  us ; but  the  wish  which  induces 
us  to  attempt  to  form  it  is  formed  for  us;  and  how?  Not,  in  general, by 
our  organization,  nor  wholly  by  our  education,  but  by  our  experience;  ex- 
perience of  the  painful  consequences  of  the  character  we  previously  had ; 
or  by  some  strong  feeling  of  admiration  or  aspiration,  accidentally  aroused. 
But  to  think  that  we  have  no  power  of  altering  our  character,  and  to  think 
that  we  shall  not  use  our  power  unless  we  desire  to  use  it,  are  very  differ- 
ent things,  and  have  a very  different  effect  on  the  mind.  A person  who 
does  not  wish  to  alter  his  character,  can  not  be  the  person  who  is  supposed 
to  feel  discouraged  or  paralyzed  by  thinking  himself  unable  to  do  it.  The 
depressing  effect  of  the  fatalist  doctrine  can  only  be  felt  where  there  is  a 
wish  to  do  what  that  doctrine  represents  as  impossible.  It  is  of  no  conse- 
quence what  we  think  forms  our  character,  when  we  have  no  desire  of  our 


LIBERTY  AND  NECESSITY. 


585 


own  about  forming  it;  but  it  is  of  great  consequence  that  we  should  not 
be  prevented  from  forming  such  a desire  by  thinking  the  attainment  im- 
practicable, and  that  if  we  have  the  desire,  we  should  know  that  the  work 
is  not  so  irrevocably  done  as  to  be  incapable  of  being  altered. 

And  indeed,  if  we  examine  closely,  we  shall-  find  that  this  feeling,  of  our 
being  able  to  modify  our  own  character  if  ice  wish,  is  itself  the  feeling  of 
moral  freedom  which  we  are  conscious  of.  A person  feels  morally  free 
who  feels  that  his  habits  or  his  temptations  are  not  his  masters,  but  he 
theirs ; who,  even  in  yielding  to  them,  knows  that  he  could  resist ; that 
were  he  desirous  of  altogether  throwing  them  off,  there  would  not  be 
required  for  that  purpose  a stronger  desire  than  he  knows  himself  to  be 
capable  of  feeling.  It  is  of  course  necessary,  to  render  our  consciousness 
of  freedom  complete,  that  we  should  have  succeeded  in  making  our  char- 
acter all  we  have  hitherto  attempted  to  make  it ; for  if  we  have  wished 
and  not  attained,  we  have,  to  that  extent,  not  power  over  our  own  charac- 
ter; we  are  not  free.  Or  at  least,  we  must  feel  that  our  wish,  if  not  strong 
enough  to  alter  our  character,  is  strong  enough  to  conquer  our  character 
when  the  two  are  brought  into  conflict  in  any  particular  case  of  conduct. 
And  hence  it  is  said  with  truth,  that  none  but  a person  of  confirmed  virtue 
is  completely  free. 

The  application  of  so  improper  a term  as  Necessity  to  the  doctrine  of 
cause  and  effect  in  the  matter  of  human  character,  seems  to  me  one  of  the 
most  signal  instances  in  philosophy  of  the  abuse  of  terms,  and  its  practical 
consequences  one  of  the  most  striking  examples  of  the  power  of  language 
over  our  associations.  The  subject  will  never  be  generally  understood 
until  that  objectionable  term  is  dropped.  The  free-will  doctrine,  by  keep- 
ing in  view  precisely  that  portion  of  the  truth  which  the  word  Necessity 
puts  out  of  sight,  namely  the  power  of  the  mind  to  co-operate  in  the  for- 
mation of  its  own  character,  has  given  to  its  adherents  a practical  feel- 
ing much  nearer  to  the  truth  than  has  generally  (I  believe)  existed  in  the 
minds  of  necessitarians.  The  latter  may  have  had  a stronger  sense  of  the 
importance  of  what  human  beings  can  do  to  shape  the  characters  of  oue 
another;  but  the  free-will  doctrine  has,  I believe,  fostered  in  its  supporters 
a much  stronger  spirit  of  self-culture. 

§ 4.  There  is  still  one  fact  which  requires  to  be  noticed  (in  addition  to 
the  existence  of  a power  of  self-formation)  before  the  doctrine  of  the  cau- 
sation of  human  actions  can  be  freed  from  the  confusion  and  misapprehen- 
sions which  surround  it  in  many  minds.  When  the  will  is  said  to  be  de- 
termined by  motives,  a motive  does  not  mean  always,  or  solely,  the  antici- 
pation of  a pleasure  or  of  a pain.  I shall  not  here  inquire  whether  it  be 
true  that,  in  the  commencement,  all  our  voluntary  actions  are  mere  means 
consciously  employed  to  obtain  some  pleasure  or  avoid  some  pain.  It  is 
at  least  certain  that  we  gradually,  through  the  influence  of  association, 
come  to  desire  the  means  without  thinking  of  the  end  ; the  action  itself 
becomes  an  object  of  desire,  and  is  performed  without  reference  to  any 
motive  beyond  itself.  ‘ Thus  far,  it  may  still  be  objected  that,  the  action 
having  through  association  become  pleasurable,  we  are,  as  much  as  be- 
fore, moved  to  act  by  the  anticipation  of  a pleasure,  namely,  the  pleasure 
of  the  action  itself.  But  granting  this,  the  matter  does  not  end  here.  As 
we  proceed  in  the  formation  of  habits,  and  become  accustomed  to  will  a 
particular  act  or  a particular  course  of  conduct  because  it  is  pleasurable, 
we  at  last  continue  to  will  it  without  any  reference  to  its  being  pleasura- 


5SG 


LOGIC  OF  THE  MORAL  SCIENCES. 


ble.  Although,  from  some  change  in  us  or  in  our  circumstances,  we  have 
ceased  to  find  any  pleasure  in  the  action,  or  perhaps  to  anticipate  any 
pleasure  as  the  consequence  of  it,  we  still  continue  to  desire  the  action,  and 
consequently  to  do  it.  In  this  manner  it  is  that  habits  of  hurtful  excess 
continue  to  be  practiced  although  they  have  ceased  to  be  pleasurable ; and 
in  this  manner  also  it  is  that  the  habit  of  willing  to  persevere  in  the  course 
which  he  has  chosen,  does  not  desert  the  moral  hero,  even  when  the  re- 
ward, however  real,  which  he  doubtless  receives  from  the  consciousness  of 
well-doing,  is  any  thing  but  an  equivalent  for  the  sufferings  he  undergoes, 
or  the  wishes  which  he  may  have  to  renounce. 

A habit  of  willing  is  commonly  called  a purpose;  and  among  the  causes 
of  our  volitions,  and  of  the  actions  which  flow  from  them,  must  be  reckon- 
ed not  only  likings  and  aversions,  but  also  purposes.  It  is  only  when  our 
purposes  have  become  independent  of  the  feelings  of  pain  or  pleasure  from 
which  they  originally  took  their  rise,  that  we  are  said  to  have  a confirmed 
character.  “A  character,”  says  Novalis,  “ is  a completely  fashioned  will:” 
and  the  will,  once  so  fashioned,  may  be  steady  and  constant,  when  the  pas- 
sive susceptibilities  of  pleasure  and  pain  are  greatly  weakened  or  material- 
ly changed. 

With  the  corrections  and  explanations  now  given,  the  doctrine  of  the 
causation  of  our  volitions  by  motives,  and  of  motives  by  the  desirable  ob- 
jects offered  to  us,  combined  with  our  particular  susceptibilities  of  desire, 
may  be  considered,  I hope,  as  sufficiently  established  for  the  purposes  of 
this  treatise.* 


CHAPTER  III. 

THAT  THERE  IS,  OR  MAY  BE,  A SCIENCE  OF  HUMAN  NATURE. 

§ 1.  It  is  a common  notion,  or  at  least  it  is  implied  in  many  common 
modes  of  speech,  that  the  thoughts,  feelings,  and  actions  of  sentient  beings 
I are  not  a subject  of  science,  in  the  same  strict  sense  in  which  this  is  true 
of  the  objects  of  outward  nature.  This  notion  seems  to  involve  some  con- 
fusion of  ideas,  which  it  is  necessary  to  begin  by  clearing  up. 

' Any  facts  are  fitted,  in  themselves,  to  be  a subject  of  science  which  fol- 
low one  another  according  to  constant  laws,  although  those  laws  may  not 
have  been  discovered,  nor  even  be  discoverable  by  our  existing  resources. 
Take,  for  instance,  the  most  familiar  class  of  meteorological  phenomena, 
those  of  rain  and  sunshine.  Scientific  inquiry  has  not  yet  succeeded  in  as- 
certaining the  order  of  antecedence  and  consequence  among  these  phenome- 
na, so  as  to  be  able,  at  least  in  our  regions  of  the  earth,  to  predict  them  with 
certainty,  or  even  with  any  high  degree  of  probability.  Yet  no  one  doubts 
that  the  phenomena  depend  on  laws,  and  that  these  must  be  derivative 
laws  resulting  from  known  ultimate  laws,  those  of  heat,  electricity,  vapori- 
zation, and  elastic  fluids.  Nor  can  it  be  doubted  that  if  we  were  acquaint- 
ed with  all  the  antecedent  circumstances,  we  could,  even  from  those  more 
general  laws,  predict  (saving  difficulties  of  calculation)  the  state  of  the 
weather  at  any  future  time.  Meteorology,  therefore,  not  only  has  in  itself 
every  natural  requisite  for  being,  but  actually  is,  a science;  though,  from 
the  difficulty  of  observing  the  facts  on  which  the  phenomena  depend  (a  dif- 

* Some  arguments  and  explanations,  supplementary  to  those  in  the  text,  will  be  found  in 
An  Examination  of  Sir  William  Hamilton's  Philosophy,  chap.  xxvi. 


HUMAN  NATURE  A SUBJECT  OF  SCIENCE. 


587 


ficulty  inherent  in  the  peculiar  nature  of  those  phenomena),  the  science  is 
extremely  imperfect;  and  were  it  perfect,  might  probably  be  of  little  avail 
in  practice,  since  the  data  requisite  for  applying  its  principles  to  particular 
instances  would  rarely  be  procurable. 

A case  may  be  conceived,  of  an  intermediate  character,  between  the  per- 
fection of  science  and  this  its  extreme  imperfection.  It  may  happen  that 
the  greater  causes,  those  on  which  the  principal  part  of  the  phenomena 
depends,  are  within  the  reach  of  observation  and  measurement  ; so  that  if 
no  other  causes  intervened,  a complete  explanation  could  be  given  not  only 
of  the  phenomena  in  general,  but  of  all  the  variations  and  modifications 
'which  it  admits  of.  But  inasmuch  as  other,  perhaps  many  other  causes,' 
separately  insignificant  in  their  effects,  co-operate  or  conflict  in  many  or  in 
all  cases  with  those  greater  causes,  the  effect,  accordingly,  presents  more 
or  less  of  aberration  from  what  would  be  produced  by  the  greater  causes 
alone.  Now  if  these  minor  causes  are  not  so  constantly  accessible,  or  not 
accessible  at  all,  to  accurate  observation,  the  principal  mass  of  the  effect 
may  still,  as  before,  be  accounted  for,  and  even  predicted ; but  there  will 
be  variations  and  modifications  which  we  shall  not  be  competent  to  explain 
thoroughly,  and  our  predictions  will  not  be  fulfilled  accurately,  but  only  ap- 
proximately. 

It  is  thus,  for  example,  with  the  theory  of  the  tides.  No  one  doubts 
that  Tidology  (as  Dr.  Whewell  proposes  to  call  it)  is  really  a science.  As 
much  of  the  phenomena  as  depends  on  the  attraction  of  the  sun  and  moon 
is  completely  understood,  and  may,  in  any,  even  unknown,  part  of  the 
earth’s  surface,  be  foretold  with  certainty ; and  the  far  greater  part  of  the 
phenomena  depends  on  those  causes.  But  circumstances  of  a local  or  cas- 
ual nature,  such  as  the  configuration  of  the  bottom  of  the  ocean,  the  degree 
of  confinement  from  shores,  the  direction  of  the  wind,  etc.,  influence,  in 
many  or  in  all  places,  the  height  and  time  of  the  tide ; and  a portion  of 
these  circumstances  being  either  not  accurately  knowable,  not  precisely 
measurable,  or  not  capable  of  being  certainly  foreseen,  the  tide  in  known 
places  commonly  varies  from  the  calculated  result  of  general  principles 
by  some  difference  that  we  can  not  explain,  and  in  unknown  ones  may 
vary  from  it  by  a difference  that  we  are  not  able  to  foresee  or  conjecture. 
Nevertheless,  not  only  is  it  certain  that  these  variations  depend  on  causes, 
and  follow  their  causes  by  laws  of  unerring  uniformity ; not  only,  there- 
fore, is  tidology  a science,  like  meteorology,  but  it  is,  what  hitherto  at 
least  meteorology  is  not,  a science  largely  available  in  practice.  General 
laws  may  be  laid  down  respecting  the  tides,  predictions  may  be  founded 
on  those  laws,  and  the  result  will  in  the  main,  though  often  not  with  com- 
plete accuracy,  correspond  to  the  predictions. 

* And  this  is  what  is  or  ought  to  be  meant  by  those  who  speak  of  sciences 
which  are  not  exact  sciences.  Astronomy  was  once  a science,  without  be- 
ing an  exact  science.  It  could  not  become  exact  until  not  only  the  general 
course  of  the  planetary  motions,  but  the  perturbations  also,  were  account- 
ed for,  and  referred  to  their  causes.  x It  has  become  an  exact  science,  be- 
cause its  phenomena  have  been  brought  under  laws  comprehending  the 
whole  of  the  causes  by  which  the  phenomena  are  influenced,  whether  in  a 
great  or  only  in  a trifling  degree,  whether  in  all  or  only  in  some  cases,  and 
assigning  to  each  of  those  causes  the  share  of  effect  which  really  belongs 
to  it.  But  in  the  theory  of  the  tides  the  only  laws  as  yet  accurately  as- 
certained are  those  of  the  causes  which  affect  the  phenomenon  in  all  cases, 
and  in  a considerable  degree ; while  others  which  affect  it  in  some  cases 


5S8 


LOGIC  OF  THE  MORAL  SCIENCES. 


only,  or,  if  in  all,  only  in  a slight  degree,  have  not  been  sufficiently  ascer 
tained  and  studied  to  enable  us  to  lay  down  their  laws ; still  less  to  deduce 
the  completed  law  of  the  phenomenon,  by  compounding  the  effects  of  the 
greater  with  those  of  the  minor  causes.  Tidology,  therefore,  is  not  yet 
an  exact  science;  not  from  any  inherent  incapacity  of  being  so,  but  from 
the  difficulty  of  ascertaining  with  complete  precision  the  real  derivative  uni- 
formities. By  combining,  however,  the  exact  laws  of  the  greater  causes, 
and  of  such  of  the  minor  ones  as  are  sufficiently  known,  with  such  otnpir-, 
ical  laws  or  such  approximate  generalizations  respecting  the  miscellaneous* 
variations  as  can  be  obtained  by  specific  observation,  we  can  lay  down 
general  propositions  which  will  be  true  in  the  main,  and  on  which,  with'' 
allowance  for  the  degree  of  their  probable  inaccuracy,  we  may  safely 
ground  our  expectations  and  our  conduct. 

§ 2.  The  science  of  human  nature  is  of  this  description.  It  falls  far 
short  of  the  standard  of  exactness  now  realized  in  Astronomy;  but  there  is 
no  reason  that  it  should  not  be  as  much  a science  as  Tidology  is,  or  as  As- 
tronomy was  when  its  calculations  had  only  mastered  the  main  phenome- 
na, but  not  the  perturbations. 

'■'The  phenomena  with  which  this  science  is  conversant  being  the  thoughts, 
feelings,  and  actions  of  human  beings,  it  would  have  attained  the  ideal  per- 
fection of  a science  if  it  enabled  us  to  foretell  how  an  individual  would 
think,  feel,  or  act  throughout  life,  with  the  same  certainty  with  which  as- 
tronomy enables  us  to  predict  the  places  and  the  occultations  of  the  heaven- 
ly bodies.  It  needs  scarcely  be  stated  that  nothing  approaching  to  this  can 
be  done.  The  actions  of  individuals  could  not  be  predicted  with  scientific 
accuracy,  were  it  only  because  we  can  not  foresee  the  whole  of  the  circum- 
stances in  which  those  individuals  will  be  placed.  *But  further,  even  in  any 
given  combination  of  (present)  circumstances,  no  assertion,  which  is  both 
precise  and  universally  true,  can  be  made  respecting  the  manner  in  which 
human  beings  will  think,  feel,  or  act.  This  is  not,  however,  because  every 
person’s  modes  of  thinking,  feeling,  and  acting  do  not  depend  on  causes; 
nor  can  we  doubt  that  if,  in  the  case  of  any  individual,  our  data  could  be 
complete,  we  even  now  know  enough  of  the  ultimate  laws  by  which  mental 
phenomena  are  determined,  to  enable  us  in  many  cases  to  predict,  with  tol- 
erable certainty,  what,  in  the  greater  number  of  supposable  combinations  of 
circumstances,  his  conduct  or  sentiments  would  be.  But  the  impressions  and 
actions  of  human  beings  are  not  solely  the  result  of  their  present  circum- 
stances, but  the  joint  result  of  those  circumstances  and  of  the  characters  of 
the  individuals;  and  the  agencies  which  determine  human  character  are 
so  numerous  and  diversified  (nothing  which  has  happened  to  the  person 
throughout  life  being  without  its  portion  of  influence),  that  in  the  aggregate 
they  are  never  in  any  two  cases  exactly  similar.  ''Hence,  even  if  our  science 
of  human  nature  were  theoretically  perfect,  that  is,  if  we  could  calculate  any 
character  as  we  can  calculate  the  orbit  of  any  planet,  from  given  data / still, 
as  the  data  are  never  all  given,  nor  ever  precisely  alike  in  different  cases, 
we  could  neither  make  positive  predictions,  nor  lay  down  universal  propo- 
sitions. 

Inasmuch,  however,  as  many  of  those  effects  which  it  is  of  most  impor- 
tance to  render  amenable  to  human  foresight  and  control  are  determined, 
like  the  tides,  in  an  incomparably  greater  degree  by  general  causes,  than  by 
all  partial  causes  taken  together ; depending  in  the  main  on  those  circum- 
stances and  qualities  which  are  common  to  all  mankind,  or  at  least  to  large 


LAWS  OF  MIND. 


589 


bodies  of  them,  and  only  in  a small  degree  on  the  idiosyncrasies  of  organi- 
zation or  the  peculiar  history  of  individuals;  it  is  evidently  possible  with 
regard  to  all  such  effects,  to  make  predictions  which  will  almost  always 
be  verified,  and  general  propositions  which  are  almost  always  true.  And 
whenever  it  is  sufficient  to  know  how  the  great  majority  of  the  human  race, 
or  of  some  nation  or  class  of  persons,  will  think,  feel,  and  act,  these  propo- 
sitions are  equivalent  to  universal  ones.  For  the  purposes  of  political  and 
social  science  this  is  sufficient.  As  we  formerly  remarked,*  an  approximate 
generalization  is,  in  social  inquiries,  for  most  practical  purposes  equivalent 
to  an  exact  one;  that  which  is  only  probable  when  asserted  of  individual 
human  beings  indiscriminately  selected,  being  certain  when  affirmed  of  the 
character  and  collective  conduct  of  masses. 

It  is  no  disparagement,  therefore,  to  the  science  of  Human  Nature,  that 
those  of  its  general  propositions  which  descend  sufficiently  into  detail  to 
serve  as  a foundation  for  predicting  phenomena  in  the  concrete,  are  for 
the  most  part  only  approximately  true.  But  in  order  to  give  a genuinely 
scientific  character  to  the  study,  it  is  indispensable  that  these  approximate 
generalizations,  which  in  themselves  would  amount  only  to  the  lowest  kind 
of  empirical  laws,  should  be  connected  deductively  with  the  laws  of  nature 
from  which  they  result ; should  be  resolved  into  the  properties  of  the  causes  !; 
on  which  the  phenomena  depend.  In  other  words,  the  science  of  Human 
Nature  may  be  said  to  exist  in  proportion  as  the  approximate  truths,  which 
compose  a practical  knowledge  of  mankind,  can  be  exhibited  as  corollaries 
from  the  universal  laws  of  human  nature  on  which  they  rest;  whereby  the 
proper  limits  of  those  approximate  truths  would  be  shown,  and  we  should 
be  enabled  to  deduce  others  for  any  new  state  of  circumstances,  in  antici- 
pation of  specific  experience. 

The  proposition  now  stated  is  the  text  on  which  the  two  succeeding 
chapters  will  furnish  the  comment. 


CHAPTER  IV. 

OF  THE  LAWS  OF  MIND. 

§ 1.  What  the  Mind  is,  as  well  as  what  Matter  is,  or  any  other  question 
respecting  Things  in  themselves,  as  distinguished  from  their  sensible  man- 
ifestations, it  would  be  foreign  to  the  purposes  of  this  treatise  to  consider. 
Here,  as  throughout  our  inquiry,  we  shall  keep  clear  of  all  speculations  re- 
specting the  mind’s  own  nature,  and  shall  understand  by  the  laws  of  mind 
those  of  mental  Phenomena ; of  the  various  feelings  or  states  of  conscious- 
ness of  sentient  beings.  K These,  according  to  the  classification  we  have  uni- 
formly followed,  consist  of  Thoughts,  Emotions,  Volitions,  and  Sensations; 
the  last  being  as  truly  states  of  Mind  as  the  three  former.  It  is  usual,  in- 
deed, to  speak  of  sensations  as  states  of  body,  not  of  mind.  But  this  is 
the  common  confusion,  of  giving  one  and  the  same  name  to  a phenomenon 
and  to  the  approximate  cause  or  conditions  of  the  phenomenon.  ' The  im- 
mediate antecedent  of  a sensation  is  a state  of  body,  but  the  sensation  it- 
self is  a state  of  mind.  Tf  the  word  Mind  means  any  thing,  it  means  that 
which  feels.  * Whatever  opinion  we  hold  respecting  the  fundamental  iden- 
tity or  diversity  of  matter  and  mind,  in  any  case  the  distinction  between 

* Supra,  p.  424. 


590 


LOGIC  OF  THE  MORAL  SCIENCES. 


mental  and  physical  facts,  between  the  internal  and  the  external  world, 
will  always  remain,  as  a matter  of  classification ; and  in  that  classification, 
sensations,  like  all  other  feelings,  must  be  ranked  as  mental  phenomena. 
' The  mechanism  of  their  production,  both  in  the  body  itself  and  in  what  is 
called  outward  nature,  is  all  that  can  with  any  propriety  be  classed  as 
physical. 

The  phenomena  of  mind,  then,  are  the  various  feelings  of  our  nature, 
both  those  improperly  called  physical  and  those  peculiarly  designated  as 
mental;  and  by  the  laws  of  mind,  I mean  the  laws  according  to  which 
those  feelings  generate  one  another. 

§ 2/ All  states  of  mind  are  immediately  caused  either  by  other  states  of 
mind,  or  by  states  of  body.  When  a state  of  mind  is  produced  by  a state 
of  mind,  I call  the  law  concerned  in  the  case  a law  of  Mind.  When  a state 
of  mind  is  produced  directly  by  a state  of  body,  the  law  is  a law  of  Body, 
and  belongs  to  physical  science. 

With  regard  to  those  states  of  mind  which  are  called  sensations,  all  are 
agreed  that  these  have  for  their  immediate  antecedents,  states  of  body. 
Every  sensation  has  for  its  proximate  cause  some  affection  of  the  portion 
of  our  frame  called  the  nervous  system,  whether  this  affection  originates 
in  the  action  of  some  external  object,  or  in  some  pathological  condition  of 
the  nervous  organization  itself.  The  laws  of  this  portion  of  our  nature — 
the  varieties  of  our  sensations,  and  the  physical  conditions  on  which  they 
proximately  depend — manifestly  belong  to  the  province  of  Physiology. 

Whether  the  remainder  of  our  mental  states  are  similarly  dependent  on 
physical  conditions,  is  one  of  the  vexatce  questiones  in  the  science  of  hu- 
man nature.  It  is  still  disputed  whether  our  thoughts,  emotions,  and  vo- 
litions are  generated  through  the  intervention  of  material  mechanism ; 
whether  we  have  organs  of  thought  and  of  emotion,  in  the  same  sense  in 
which  we  have  organs  of  sensation.  Many  eminent  physiologists  hold  the 
affirmative.  These  contend  that  a thought  (for  example)  is  as  much  the 
result  of  nervous  agency,  as  a sensation ; that  some  particular  state  of  our 
nervous  system,  in  particular  of  that  central  portion  of  it  called  the  brain, 
invariably  precedes,  and  is  presupposed  by,  every  state  of  our  conscious- 
ness. According  to  this  theory,  one  state  of  mind  is  never  really  produced 
by  another : all  are  produced  by  states  of  body.  When  one  thought  seems 
to  call  up  another  by  association,  it  is  not  really  a thought  which  recalls  a 
thought;  the  association  did  not  exist  between  the  two  thoughts,  but  be- 
tween the  two  states  of  the  brain  or  nerves  which  preceded  the  thoughts : 
one  of  those  states  recalls  the  other,  each  being  attended  in  its  passage  by 
the  particular  state  of  consciousness  which  is  consequent  on  it.  On  this 
theory  the  uniformities  of  succession  among  states  of  mind  would  be  mere 
derivative  uniformities,  resulting  from  the  laws  of  succession  of  the  bodi- 
ly states  which  cause  them.  There  would  be  no  original  mental  laws,  no 
Laws  of  Mind  in  the  sense  in  which  I use  the  term,  at  all;  and  mental 
science  would  be  a mere  branch,  though  the  highest  and  most  recondite 
branch,  of  the  science  of  physiology.  M.  Comte,  accordingly,  claims  the 
scientific  cognizance  of  moral  and  intellectual  phenomena  exclusively  for 
physiologists;  and  not  only  denies  to  Psychology,  or  Mental  Philosophy 
properly  so  called,  the  character  of  a science,  but  places  it,  in  the  chimer- 
ical nature  of  its  objects  and  pretensions,  almost  on  a par  with  astrology. 

A But,  after  all  has  been  said  which  can  be  said,  it  remains  incontestable 
that  there  exist  uniformities  of  succession  among  states  of  mind,  and  that 


591 


LAWS  OF  MIND. 

these  can  be  ascertained  by  observation  and  experiment.  Further,  that 
every  mental  state  has  a nervous  state  for  its  immediate  antecedent  and 
proximate  cause,  though  extremely  probable,  can  not  hitherto  be  said  to 
be  proved,  in  the  conclusive  manner  in  which  this  can  be  proved  of  sensa- 
tions ; and  even  were  it  certain,  yet  every  one  must  admit  that  we  are 
wholly  ignorant  of  the  characteristics  of  these  nervous  states;  we  know 
not,  and  at  present  have  no  means  of  knowing,  in  what  respect.one  of  them 
differs  from  another;  and  our  only  mode  of  studying  their  successions  or 
co-existences  must  be  by  observing  the  successions  and  co-existences  of  the 
mental  states,  of  which  they  are  supposed  to  be  the  generators  or  causes. 
The  successions,  therefore,  which  obtain  among  mental  phenomena,  do  not 
admit  of  being  deduced  from  the  physiological  laws  of  our  nervous  organi- 
zation ; and  all  real  knowledge  of  them  must  continue,  for  a long  time  at 
least,  if  not  always,  to  be  sought  in  the  direct  study,  by  observation  and 
experiment,  of  the  mental  successions  themselves.  Since,  therefore,  the  or- 
der of  our  mental  phenomena  must  be  studied  in  those  phenomena,  and 
not  inferred  from  the  laws  of  any  phenomena  more  general,  there  is  a dis- 
tinct and  separate  Science  of  Mind. 

The  relations,  indeed,  of  that  science  to  the  science  of  physiology  must 
never  be  overlooked  or  undervalued.  It  must  by  no  means  be  forgotten 
that  the  laws  of  mind  may  be  derivative  laws  resulting  from  laws  of  ani- 
mal life,  and  that  their  truth,  therefore,  may  ultimately  depend  on  physic- 
al conditions  ; and  the  influence  of  physiological  states  or  physiological 
changes  in  altering  or  counteracting  the  mental  successions,  is  one  of  the 
most  important  departments  of  psychological  study.  But,  on  the  other 
hand,  to  reject  the  resource  of  psychological  analysis,  and  construct  the 
theory  of  the  mind  solely  on  such  data  as  physiology  at  present  affords, 
seems  to  me  as  great  an  error  in  principle,  and  an  even  more  serious  one 
in  practice.  Imperfect  as  is  the  science  of  mind,  I do  not  scruple  to  aflirm 
that  it  is  in  a considerably  more  advanced  state  than  the  portion  of  physi- 
ology which  corresponds  to  it;  and  to  discard  the  former  for  the  latter  ap- 
pears to  me  an  infringement  of  the  true  canons  of  inductive  philosophy, 
which  must  produce,  and  which  does  produce,  erroneous  conclusions  in 
some  very  important  departments  of  the  science  of  human  nature. 

§ 3.^The  subject,  then,  of  Psychology  is  the  uniformities  of  succession, 
the  laws,  whether  ultimate  or  derivative,  according  to  which  one  mental 
state  succeeds  another ; is  caused  by,  or  at  least,  is  caused  to  follow,  an- 
other. vOf  these  laws  some  are,  general,  others  more  special.  The  follow- 
ing are  examples  of  the  most  general  laws : 

First.4  Whenever  any  state  of  consciousness  has  once  been  excited  in  us, 
no  matter  by  what  cause,  an  inferior  degree  of  the  same  state  of  conscious- 
ness, a state  of  consciousness  resembling  the  former,  but  inferior  in  intensi- 
ty, is  capable  of  being  reproduced  in  us,  without  the  presence  of  any  such 
cause  as-  excited  it  at  first.  Thus,  if  we  have  once  seen  or  touched  an  ob- 
ject, we  can  afterward  think  of  the  object  though  it  be  absent  from  our 
sight  or  from  our  touch.  If  we  have  been  joyful  or  grieved  at  some  event, 
we  can  think  of  or  remember  our  past  joy  or  grief,  though  no  new  event 
of  a happy  or  painful  nature  has  taken  place.  When  a poet  has  put  to- 
gether a mental  picture  of  an  imaginary  object,  a Castle  of  Indolence,  a 
Una,  or  a Hamlet,  he  can  afterward  think  of  the  ideal  object  he  has  created, 
without  any  fresh  act  of  intellectual  combination.  This  law  is  expressed  by 
saying,  in  the  language  of  Hume,  that  every  mental  impression  has  its  idea. 


LOGIC  OF  THE  MORAL  SCIENCES. 


592 

Secondly.  These  ideas,  or  secondary  mental  states,  are  excited  by  our 
impressions,  or  by  ot^ier  ideas,  according  to  certain  laws  which  are  called 
Laws  of  Association.  Of  these  laws  the  first  is,  that  similar  ideas  tend  to 
excite  one  another.  The  second  is,  that  when  two  impressions  have  been 
frequently  experienced  (or  even  thought  of)  either  simultaneously  or  in  im- 
mediate succession,  then  whenever  one  of  these  impressions,  or  the  idea  of 
it,  recurs,  it  tends  to  excite  the  idea  of  the  other.  The  third  law  is,  that 
greater  intensity  in  either  or  both  of  the  impressions  is  equivalent,  in  ren- 
dering them  excitable  by  one  another,  to  a greater  frequency  of  conjunc- 
tion. These  are  the  laws  of  ideas,  on  which  I shall  not  enlarge  in  this 
place,  but  refer  the  reader  to  works  professedly  psychological,  in  particular 
to  Mr.  James  Mill’s  Analysis  of  the  Phenomena  of  the  Human  Mind, 
where  the  principal  laws  of  association,  along  with  many  of  their  applica- 
tions, are  copiously  exemplified,  and  with  a masterly  hand.* 

These  simple  or  elementary  Laws  of  Mind  have  been  ascertained  by  the 
ordinary  methods  of  experimental  inquiry;  nor  could  they  have  been  as- 
certained in  any  other  manner.  Mint  a certain  number  of  elementary  laws 
having  thus  been  obtained,  it  is  a fair  subject  of  scientific  inquiry  how  far 
those  laws  can  be  made  to  go  in  explaining  the  actual  phenomena.  It  is 
obvious  that  complex  laws  of  thought  and  feeling  not  only  may,  but  must, 
be  generated  from  these  simple  laws.  And  it  is  to  be  remarked,  that  the 
case  is  not  always  one  of  Composition  of  Causes:  the  effect  of  concurring 
causes  is  not  always  precisely  the  sum  of  the  effects  of  those  causes  when 
separate,  nor  even  always  an  effect  of  the  same  kind  with  them.  Revert- 
ing to  the  distinction  which  occupies  so  prominent  a place  in  the  theory  of 
induction,  the  laws  of  the  phenomena  of  mind  are  sometimes  analogous  to 
mechanical,  but  sometimes  also  to  chemical  laws.  When  many  impressions 
or  ideas  are  operating  in  the  mind  together,  there  sometimes  takes  place 
a process  of  a similar  kind  to  chemical  combination.  When  impressions 
have  been  so  often  experienced  in  conjunction,  that  each  of  them  calls  up 
readily  and  instantaneously  the  ideas  of  the  whole  group,  those  ideas  some- 
times melt  and  coalesce  into  one  another,  and  appear  not  several  ideas,  but 
one ; in  the  same  manner  as,  when  the  seven  prismatic  colors  are  present- 
ed to  the  eye  in  rapid  succession,  the  sensation  produced  is  that  of  white. 
But  as  in  this  last  case  it  is  correct  to  say  that  the  seven  colors  when  they 
rapidly  follow  one  another  generate  white,  but  not  that  they  actually  are 
white;  so  it  appears  to  me  that  the  Complex  Idea,. formed  by  the  blending 
together  of  several  simpler  ones,  should,  when  it  really  appears  simple 
(that  is,  when  the  separate  elements  are  not  consciously  distinguishable  in 
it),  be  said  to  result  from,  or  be  generated  by,  the  simple  ideas,  not  to  con- 
sist of  them.  Our  idea  of  an  orange  really  consists  of  the  simple  ideas  of 
a certain  color;  a certain  form,  a certain  taste  and  smell,  etc.,  because  we  can, 
by  interrogating  our  consciousness,  perceive  all  these  elements  in  the  idea. 

* When  this  chapter  was  written,  Professor  Bain  had  not  yet  published  even  the  first  part 
(“The  Senses  and  the  Intellect”)  of  his  profound  Treatise  on  the  Mind.  In  this  the  laws 
of  association  have  been  more  comprehensively  stated  and  more  largely  exemplified  than  bv 
any  previous  writer;  and  the  work,  having  been  completed  by  the  publication  of  “The  Emo- 
tions and  the  Will,”  may  now  be  referred  to  as  incomparably  the  most  complete  analytical  ex- 
position of  the  mental  phenomena,  on  the  basis  of  a legitimate  Induction,  which  has  yet  been 
produced.  More  recently  still,  Mr.  Bain  has  joined  with  me  in  appending  to  a new  edition 
of  the  “Analysis,”  notes  intended  to  bring  up  the  analytic  science  of  Mind  to  its  latest  im- 
provements. 

Many  striking  applications  of  the  laws  of  association  to  the  explanation  of  complex  mental 
phenomena  are  also  to  be  found  in  Mr.  Herbert  Spencer’s  “ Principles  of  Psychology.” 


LAWS  OF  MIND. 


593 


IBut  we  can  not  perceive,  in  so  apparently  simple  a feeling  as  our  percep- 
tion of  the  shape  of  an  object  by  the  eye,  all  that  multitude  of  ideas  de- 
rived from  other  senses,  without  which  it  is  well  ascertained  that  no  such 
visual  perception  would  ever  have  had  existence ; nor,  in  our  idea  of  Ex- 
tension, can  we  discover  those  elementary  ideas  of  resistance,  derived  from 
our  muscular  frame,  in  which  it  has  been  conclusively  shown  that  the  idea 
originates.  ^Ihese,  therefore,  are  cases  of  mental  chemistry  ; in  which  it  is 
proper  to  say  that  the  simple  ideas  generate,  rather  than  that  they  compose, 
the  complex  ones. 

With  respect  to  all  the  other  constituents  of  the  mind,  its  beliefs,  its  ab- 
struser  conceptions,  its  sentiments,  emotions,  and  volitions,  there  are  some 
(among  whom  are  Hartley  and  the  author  of  the  Analysis)  who  think  that 
the  whole  of  these  are  generated  from  simple  ideas  of  sensation,  by  a chem- 
istry similar  to  that  which  we  have  just  exemplified.  These  philosophers 
have  made  out  a great  part  of  their  case,  but  I am  not  satisfied  that  they 
have  established  the  whole  of  it.  They  have  shown  that  there  is  such  a 
thing  as  mental  chemistry ; that  the  heterogeneous  nature  of  a feeling  A, 
considered  in  relation  to  B and  C,  is  no  conclusive  argument  against  its 
being  generated  from  B and  C.  Having  proved  this,  they  proceed  to 
show,  that  where  A is  found,  B and  C were,  or  may  have  been  present,  and 
why,  therefore,  they  ask,  should  not  A have  been  generated  from  B and 
C?  But  even  if  this  evidence  were  carried  to  the  highest  degree  of  com- 
pleteness which  it  admits  of;  if  it  were  shown  (which  hitherto  it  has  not, 
in  all  cases,  been)  that  certain  groups  of  associated  ideas  not  only  might 
have  been,  but  actually  were,  present  whenever  the  more  recondite  mental 
feeling  was  experienced ; this  would  amount  only  to  the  Method  of  Agree- 
ment, and  could  not  prove  causation  until  confirmed  by  the  more  conclu- 
sive evidence  of  the  Method  of  Difference.  If  the  question  be  whether 
Belief  is  a mere  case  of  close  association  of  ideas,  it  would  be  necessary 
to  examine  experimentally  if  it  be  true  that  any  ideas  whatever,  provided 
they  are  associated  with  the  required  degree  of  closeness,  give  rise  to  be- 
lief. If  the  inquiry  be  into  the  origin  of  moral  feelings,  the  feeling  for  ex- 
ample of  moral  reprobation,  it  is  necessary  to  compare  all  the  varieties  of 
actions  or  states  of  mind  which  are  ever  morally  disapproved,  and  see 
whether  in  all  these  cases  it  can  be  shown,  or  reasonably  surmised,  that  the 
action  or  state  of  mind  had  become  connected  by  association,  in  the  disap- 
proving mind,  with  some  particular  class  of  hateful  or  disgusting  ideas; 
and  the  method  employed  is,  thus  far,  that  of  Agreement.  But  this  is  not 
enough.  Supposing  this  proved,  we  must  try  further  by  the  Method  of 
Difference,  whether  this  particular  kind  of  hateful  or  disgusting  ideas, 
when  it  becomes  associated  with  an  action  previously  indifferent,  will  ren- 
der that  action  a subject  of  moral  disapproval.  If  this  question  can  be 
answered  in  the  affirmative,  it  is  shown  to  be  a law  of  the  human  mind, 
that  an  association  of  that  particular  description  is  the  generating  cause  of 
moral  reprobation.  That  all  this  is  the  case  has  been  rendered  extremely 
probable,  but  the  experiments  have  not  been  tried  with  the  degi’ee  of  pre- 
cision necessary  for  a complete  and  absolutely  conclusive  induction.* 

It  is  further  to  be  remembered,  that  even  if  all  which  this  theory  of 

* In  the  case  of  the  moral  sentiments  the  place  of  direct  experiment  is  to  a considerable 
extent  supplied  by  historical  experience,  and  we  are  able  to  trace  with  a tolerable  approach  to 
certainty  the  particular  associations  by  which  those  sentiments  are  engendered.  This  has 
been  attempted,  so  far  as  respects  the  sentiment  of  justice,  in  a little  work  by  the  present  au- 
Ithor,  entitled  Utilitarianism. 


38 


594 


LOGIC  OF  THE  MORAL  SCIENCES. 


mental  phenomena  contends  for  could  be  proved,  we  should  not  be  the 
more  enabled  to  resolve  the  laws  of  the  more  complex  feelings  into  those 
of  the  simpler  ones.  The  generation  of  one  class  of  mental  phenomena 
from  another,  whenever  it  can  be  made  out,  is  a highly  interesting  fact  in 
psychological  chemistry;  but  it  no  more  supersedes  the  necessity  of  an. 
experimental  study  of  the  generated  phenomenon,  than  a knowledge  of  the 
properties  of  oxygen  and  sulphur  enables  us  to  deduce  those  of  sulphuric 
acid  without  specific  observation  and  experiment.  Whatever,  therefore, 
may  be  the  final  issue  of  the  attempt  to  account  for  the  origin  of  our  judg- 
ments, our  desires,  or  our  volitions,  from  simpler  mental  phenomena,  it  is 
not  the  less  imperative  to  ascertain  the  sequences  of  the  complex  phenom- 
ena themselves,  by  special  study  in  conformity  to  the  canons  of  Induction. 
Thus,  in  respect  to  Belief,  psychologists  will  always  have  to  inquire  what 
beliefs  we  have  by  direct  consciousness,  and  according  to  what  laws  one 
belief  produces  another;  what  are  the  laws  in  virtue  of  which  one  thing  is 
recognized  by  the  mind,  either  rightly -or  erroneously,  as  evidence  of  an- 
other thing.  In  regard  to  Desire,  they  will  have  to  examine  what  objects 
we  desire  naturally,  and  by  what  causes  we  are  made  to  desire  things 
originally  indifferent,  or  even  disagreeable  to  us;  and  so  forth.  It  may  be 
remarked  that  the  general  laws  of  association  prevail  among  these  more 
intricate  states  of  mind,  in  the  same  manner  as  among  the  simpler  ones. 
A desire,  an  emotion,  an  idea,  of  the  higher  order  of  abstraction,  even  our 
judgments  and  volitions,  when  they  have  become  habitual,  are  called  up  by 
association,  according  to  precisely  the  same  laws  as  our  simple  ideas. 

§ 4.  In  the  course  of  these  inquiries,  it  will  be  natural  and  necessary  to 
examine  how  far  the  production  of  one  state  of  mind  by  another  is  influ- 
enced by  any  assignable  state  of  body.  The  commonest  observation  shows 
that  different  minds  are  susceptible  in  very  different  degrees  to  the  action 
of  the  same  psychological  causes.  The  idea,  for  example,  of  a given  desira- 
ble object  will  excite  in  different  minds  very  different  degrees  of  intensity 
of  desire.  The  same  subject  of  meditation,  presented  to  different  minds, 
will  excite  in  them  very  unequal  degrees  of  intellectual  action.  These 
differences  of  mental  susceptibility  in  different  individuals  may  be,  first, 
original  and  ultimate  facts;  or,  secondly,  they  may  be  consequences  of  the 
previous  mental  history  of  those  individuals;  or,  thirdly  and  lastly,  they 
may  depend  on  varieties  of  physical  organization.  That  the  previous  men- 
tal history  of  the  individuals  must  have  some  share  in  producing  or  in 
modifying  the  whole  of  their  mental  character,  is  an  inevitable  conse- 
quence of  the  laws  of  mind ; but  that  differences  of  bodily  structure  also 
co-operate,  is  the  opinion  of  all  physiologists,  confirmed  by  common  experi- 
ence. It  is  to  be  regretted  that  hitherto  this  experience,  being  accepted  in 
the  gross,  without  due  analysis,  has  been  made  the  groundwork  of  empiric- 
al generalizations  most  detrimental  to  the  progress  of  real  knowledge. 

It  is  certain  that  the  natural  differences  which  really  exist  in  the  mental 
predispositions  or  susceptibilities  of  different  persons  are  often  not  uncon- 
nected with  diversities  in  their  organic  constitution.  But  it  does  not 
therefore  follow  that  these  organic  differences  must  in  all  cases  influence 
the  mental  phenomena  directly  and  immediately.  They  often  affect  them 
through  the  medium  of  their  psychological  causes.  For  example,  the  idea 
of  some  particular  pleasure  may  excite  in  different  persons,  even  independ- 
ently of  habit  or  education,  very  different  strengths  of  desire,  and  this  may 
be  the  effect  of  their  different  degrees  or  kinds  of  nervous  susceptibility ; V 

i 

) 


LAWS  OF  MIND. 


595 


but  these  organic  differences,  we  must  remember,  will  render  the  pleasura- 
ble sensation  itself  more  intense  in  one  of  these  persons  than  in  the  other; 
so  that  the  idea  of  the  pleasure  will  also  be  an  intenser  feeling,  and  will,  by 
the  operation  of  mere  mental  laws,  excite  an  intenser  desire,  without  its 
being  necessary  to  suppose  that  the  desire  itself  is  directly  influenced  by 
the  physical  peculiarity.  As  in  this,  so  in  many  cases,  such  differences  in 
the  kind  or  in  the  intensity  of  the  physical  sensations  as  must  necessarily 
result  from  differences  of  bodily  organization,  will  of  themselves  account 
for  many  differences  not  only  in  the  degree,  but  even  in  the  kind,  of  the 
other  mental  phenomena.  So  true  is  this,  that  even  different  qualities  of 
mind,  different  types  of  mental  character,  will  naturally  be  produced  by 
mere  differences  of  intensity  in  the  sensations  generally;  as  is  well  pointed 
out  in  the  able  essay  on  Dr.  Priestley,  by  Mr.  ^Jartineau,  mentioned  in  a 
former  chapter : 

“The  sensations  which  form  the  elements  of  all  knowledge  are  received 
either  simultaneously  or  successively:  when  several  are  received  simulta- 
neously, as  the  smell,  the  taste,  the  color,  the  form,  etc.,  of  a fruit,  their  as- 
sociation together  constitutes  our  idea  of  an  object;  when  received  succes- 
sively, their  association  makes  up  the  idea  of  an  event.  Any  thing,  then, 
which  favors  the  associations  of  synchronous  ideas  will  tend  to  produce  a 
knowledge  of  objects,  a perception  of  qualities;  while  any  thing  which  fa- 
vors association  in  the  successive  order,  will  tend  to  produce  a knowledge 
of  events,  of  the  order  of  occurrences,  and  of  the  connection  of  cause  and 
effect:  in  other  words,  in  the  one  case  a perceptive  mind,  with  a discrimi- 
nate feeling  of  the  pleasurable  and  painful  properties  of  things,  a sense  of 
the  grand  and  the  beautiful  will  be  the  result:  in  the  other,  a mind  atten- 
tive to  the  movements  and  phenomena,  a ratiocinative  and  philosophic  in- 
tellect. Now  it  is  an  acknowledged  principle,  that  all  sensations  experi-: 
enced  during  the  presence  of  any  vivid  impression  become  strongly  asso- 
ciated with  it,  and  with  each  other;  and  does  it  not  follow  that  the  syn- 
chronous feelings  of  a sensitive  constitution  ( i . e.,  the  one  which  has  vivid 
impressions)  will  be  more  intimately  blended  than  in  a differently  formed 
mind  ? If  this  suggestion  has  any  foundation  in  truth,  it  leads  to  an  infer- 
ence not  unimportant;  that'where  nature  has  endowed  an  individual  with 
great  original  susceptibility,  he  will  probably  be  distinguished  by  fondness 
for  natural  history,  a relish  for  the  beautiful  and  great,  and  moral  enthusi- 
asm ; where  there  is  but  a mediocrity  of  sensibility,  a love  of  science,  of  ab- 
stract. truth,  with  a deficiency  of  taste  and  of  fervor,  is  likely  to  be  the  re- 
sult.” 

' We  see  from  this  example,  that  when  the  general  laws  of  mind  are  more 
accurately  known,  and,  above  all,  more  skillfully  apjjlied  to  the  detailed  ex- 
planation of  mental  peculiarities,  they  will  account  for  many  more  of  those 
peculiarities  than  is  ordinarily  supposed.  Unfortunately  the  reaction  of 
the  last  and  present  generation  against  the  philosophy  of  the  eighteenth 
century  has  produced  a very  general  neglect  of  this  great  department  of 
analytical  inquiry;  of  which,  consequently, the  recent  progress  has  been  by 
no  means  proportional  to  its  early  promise.  The  majority  of  those  who 
speculate  on  human  nature  prefer  dogmatically  to  assume  that  the  mental 
differences  which  they  perceive,  or  think  they  perceive,  among  human  be- 
ings, are  ultimate  facts,  incapable  of  being  either  explained  or  altered,  rath- 
er than  take  the  trouble  of  fitting  themselves,  by  the  requisite  processes  of 
thought,  for  referring  those  mental  differences  to  the  outward  causes  by 
which  they  are  for  the  most  part  produced,  and  on  the  removal  of  which 


59G 


LOGIC  OF  THE  MORAL  SCIENCES. 


they  would  cease  to  exist.  The  German  school  of  metaphysical  specula- 
tion, which  has  not  yet  lost  its  temporary  predominance  in  European 
thought,  has  had  this  among  many  other  injurious  influences;  and  at  the 
opposite  extreme  of  the  psychological  scale,  no  writer,  either  of  early  or  of 
recent  date,  is  chargeable  in  a higher  degree  with  this  aberration  from  the 
true  scientific  spirit,  than  M.  Comte. 

It  is  certain  that,  in  human  beings  at  least,  differences  in  education  and  in 
outward  circumstances  are  capable  of  affording  an  adequate  explanation  of 
by  far  the  greatest  portion  of  character;  and  thau  the  remainder  may  be  in 
great  part  accounted  for  by  physical  differences  in  the  sensations  produced' 
in  different  individuals  by  the  same  external  or  internal  cause.  There  are, 
however,  some  mental  facts  which  do  not  seem  to  admit  of  these  modes  of 
explanation.  Such,  to  take  the  strongest  case,  are  the  various  instincts  of 
animals,  and  the  portion  of  human  nature  which  corresponds  to  those  in- 
stincts. No  mode  has  been  suggested,  even  by  way  of  hypothesis,  in  which 
these  can  receive  any  satisfactory,  or  even  plausible,  explanation  front  psy- 
chological causes  alone ; and  there  is  great  reason  to  think  that  they  have 
as  positive,  and  even  as  direct  and  immediate,  a connection  with  physical 
conditions  of  the  brain  and  nerves  as  any  of  our  mere  sensations  have.  A 
supposition  which  (it  is  perhaps  not  superfluous  to  add)  in  no  way  conflicts 
with  the  indisputable  fact  that  these  instincts  may  be  modified  to  any  ex- 
tent, or  entirely  conquered,  in  human  beings,  and  to  no  inconsiderable  ex- 
tent even  in  some  of  the  domesticated  animals,  by  other  mental  influences, 
and  by  education. 

Whether  organic  causes  exercise  a direct  influence  over  any  other  classes 
of  mental  phenomena,  is  hitherto  as  far  from  being  ascertained  as  is  the 
precise  nature  of  the  organic  conditions  even  in  the  case  of  instincts.  The 
physiology,  however,  of  the  brain  and  nervous  system  is  in  a state  of  such 
rapid  advance,  and  is  continually  bringing  forth  such  new  and  interesting 
results,  that  if  there  be  really  a connection  between  mental  peculiarities  and 
any  varieties  cognizable  by  our  senses  in  the  structure  of  the  cerebral  and 
nervous  apparatus,  the  nature  of  that  connection  is  now  in  a fair  way  of  be- 
ing found  out.  The  latest  discoveries  in  cerebral  physiology  appear  to  have 
proved  that  any  such  connection  which  may  exist  is  of  a radically  different 
character  from  that  contended  for  by  Gall  and  his  followers,  and  that,  what- 
ever may  hereafter  be  found  to  be  the  true  theory  of  the  subject,  phrenolo- 
gy at  least  is  untenable. 


CHAPTER  Y. 

OP  ETHOLOGY,  OR  THE  SCIENCE  OP  THE  FORMATION  OP  CHARACTER. 

§ 1.  The  laws  of  mind  as  characterized  in  the  preceding  chapter,  com- 
pose the  universal  or  abstract  portion  of  the  philosophy  of  human  nature; 
and  all  the  truths  of  common  experience,  constituting  a practical  knowledge 
of  mankind,  must,  to  the  extent  to  which  they  are  truths,  be  results  or  con- 
sequences of  these.  Such  familiar  maxims,  when  collected  a posteriori 
from  observation  of  life,  occupy  among  the  truths  of  the  science  the  place 
of  what,  in  our  analysis  of  Induction,  have  so  often  been  sjioken  of  uuder 
the  title  of  Empirical  Laws. 

An  Empirical  Law  (it  will  be  remembered)  is  a uniformity,  whether  of 


ETHOLOGY. 


59 1 


succession  or  of  co-existence,  which  holds  true  in  all  instances  within  our 
limits  of  observation,  but  is  not  of  a nature  to  afford  any  assurance  that  it 
would  hold  beyond  those  limits  ; either  because  the  consequent  is  not  really 
the  effect  of  the  antecedent,  but  forms  part  along  with  it  of  a chain  of  ef- 
fects flowing  from  prior  causes  not  yet  ascertained,  or  because  there  is 
ground  to  believe  that  the  sequence  (though  a case  of  causation)  is  resolv- 
able into  simpler  sequences,  and,  depending  therefore  on  a concurrence  of 
several  natural  agencies,  is  exposed  to  an  unknown  multitude  of  possibilities 
of  counteraction.  In  other  words,  an  empirical  law  is  a generalization,  of  " . 
which,  not  content  with  finding  it  true,  we  are  obliged  to  ask,  why  is  it  ' ' 
true?  knowing  that  its  truth  is  not  absolute,  but  dependent  on  some  more 
general  conditions,  and  that  it  can  only  be  relied  on  in  so  far  as  there  is 
ground  of  assurance  that  those  conditions  are  realized. 

Now,  the  observations  concerning  human  affairs  collected  from  common 
experience  are  precisely  of  this  nature.  Even  if  they  were  universally  and 
exactly  true  within  the  bounds  of  experience,  which  they  never  are,  still 
they  are  not  the  ultimate  laws  of  human  action  ; they  are  not  the  principles 
of  human  nature,  but  results  of  those  principles  under  the  circumstances  in 
which  mankind  have  happened  to  be  placed.  When  the  Psalmist  “said  in 
his  haste  that  all  men  are  liars,”  he  enunciated  what  in  some  ages  and  coun- 
tries is  borne  out  by  ample  experience ; but  it  is  not  a law  of  man’s  nature 
to  lie ; though  it  is  one  of  the  consequences  of  the  laws  of  human  nature, 
that  lying  is  nearly  universal  when  certain  external  circumstances  exist  uni- 
versally, especially  circumstances  productive  of  habitual  distrust  and  fear. 
jWhen  the  character  of  the  old  is  asserted  to  be  cautious,  and  of  the  young 
impetuous,  this,  again,  is  but  an  empirical  law ; for  it  is  not  because  of  their 
youth  that  the  young  are  impetuous,  nor  because  of  their  age  that  the  old 
are  cautious.  It  is  chiefly,  if  not  wholly,  because  the  old,  during  their 
many  years  of  life,  have  generally  had  much  experience  of  its  various  evils, 
and  having  suffered  or  seen  others  suffer  much  from  incautious  exposure 
to  them,  have  acquired  associations  favorable  to  circumspection;  while  the 
young,  as  well  from  the  absence  of  similar  experience  as  from  the  greater 
strength  of  the  inclinations  which  urge  them  to  enterprise,  engage  them- 
selves in  it  more  readily.  Here,  then,  is  the  explanation  of  the  empirical' 
lawj  here  are  the  conditions  which  ultimately  determine  whether  the  law 
holds  good  or  not.  If  an  old  man  has  not  been  oftener  than  most  young- 
men  in  contact  with  danger  and  difficulty,  he  will  be  equally  incautious;  if 
a youth  has  not  stronger  inclinations  than  an  old  man,  he  probably  will  be 
as  little  enterprising.  ./The  empirical  law  derives  whatever  truth  it  has 
from  the  causal  laws  of  which  it  is  a consequence.  If  we  know  those  laws, 
we  know  what  are  the  limits  to  the  derivative  law ; while,  if  we  have  not 
yet  accounted  for  the  empirical  law — if  it  rests  only  on  observation — there 
is  no  safety  in  applying  it  far  beyond  the  limits  of  time,  place,  and  circum- 
stance in  which  the  observations  were  made. 

51  The  really  scientific  truths,  then,  are  not  these  empirical  laws,  but  the- 
causal Taws  which  explain  them.-  The  empirical  laws  of  those  phenomena 
which  depend  on  known  causes,  and  of  which  a general  theory  can  there- 
fore be  constructed,  have,  whatever  may  be  their  value  in  practice,  no  other 
function  in  science  than  that  of  verifying  the  conclusions  of  theory.  Still 
more  must  this  be  the  case  when  most  of  the  empirical  laws  amount,  even 
within  the  limits  of  observation,  only  to  approximate  generalizations. 

§ 2.  This,  however,  is  not,  so  much  as  is  sometimes  supposed,  a peculiarity 


59S 


LOGIC  OF  THE  MORAL  SCIENCES. 


of  the  sciences  called  moral.  It  is  only  in  the  simplest  branches  of  science 
that  empirical  laws  are  ever  exactly  true ; and  not  always  in  those.  As- 
tronomy, for  example,  is  the  simplest  of  all  the  sciences  which  explain,  in 
the  concrete,  the  actual  course  of  natural  events.  The  causes  or  forces 
on  which  astronomical  phenomena  depend,  are  fewer  in  number  than  those 
which  determine  any  other  of  the  great  phenomena  of  nature.  According- 
ly, as  each  effect  results  from  the  conflict  of  but  few  causes,  a great  degree 
of  regularity  and  uniformity  might  be  expected  to  exist  among  the  effects; 
and  such  is  really  the  case : they  have  a fixed  order,  and  return  in  cycles. 
But  propositions  which  should  express,  with  absolute  correctness,  all  the 
successive  positions  of  a planet  until  the  cycle  is  completed,  would  be  of  al- 
most unmanageable  complexity,  and  could  be  obtained  from  theory  alone. 
The  generalizations  which  can  be  collected  on  the  subject  from  direct  ob- 
servation, even  such  as  Kepler’s  law,  are  mere  approximations  ; the  planets, 
owing  to  their  perturbations  by  one  another,  do  not  move  in  exact  ellipses. 
Thus  even  in  astronomy,  perfect  exactness  in  the  mere  empirical  laws  is 
not  to  be  lookc-d  for;  much  less,  then,  in  more  complex  subjects  of  in- 
quiry. 

The  same  example  shows  how  little  can  be  inferred  against  the  univer- 
sality or  even  the  simplicity  of  the  ultimate  laws,  from  the  impossibility  of 
establishing  any  but  approximate  empirical  laws  of  the  effects.  The  laws 
of  causation  according  to  which  a class  of  phenomena  are  produced  may 
lj)e  very  few  and  simple,  and  yet  the  effects  themselves  may  be  so  various 
and  complicated  that  it  shall  be  impossible  to  trace  any  regularity  whatev- 
er completely  through  them.  For  the  phenomena  in  question  may  be  of  an 
eminently  modifiable  character ; insomuch  that  innumerable  circumstances 
are  capable  of  influencing  the  effect,  although  they  may  all  do  it  according 
to  a very  small  number  of  laws.  Suppose  that  all  which  passes  in  the  mind 
of  man  is  determined  by  a few  simple  laws ; still,  if  those  laws  be  such  that 
there  is  not  one  of  the  facts  surrounding  a human  being,  or  of  the  events 
which  happen  to  him,  that  does  nc.„  influence  in  some  mode  or  degree  his 
subsequent  mental  history,  and  if  the  circumstances  of  different  human  be- 
ings are  extremely  different,  it  will  be  no  wonder  if  very  few  propositions 
can  be  made  respecting  the  details  of  their  conduct  or  feelings,  which  will 
be  true  of  all  mankind. 

Now,  without  deciding  whether  the  ultimate  laws  of  our  mental  nature 
are  few  or  many,  it  is  at  least  certain  that  they  are  £>f  the  above  description. 
It  is  certain  that  our  mental  states,  and  our  mental  capacities  and  suscepti- 
bilities, are  modified,  either  for  a time  or  permanently,  by  every  thing  which 
happens  to  us  in  life.  Considering,  therefore,  how  much  these  modifying 
causes  differ  in  the  case  of  any  two  individuals,  it  would  be  unreasonable 
to  expect  that  the  empirical  laws  of  the  human  mind,  the  generalizations 
which  can  be  made  respecting  the  feelings  or  actions  of  mankind  without 
reference  to  the  causes  that  determine  them,  should  be  any  thing  but  ap- 
proximate generalizations.  They  are  the  common  wisdom  of  common  life, 
and  as  such  are  invaluable;  especially  as  they  are  mostly  to  be  applied  to 
cases  not  very  dissimilar  to  those  from  which  they  were  collected.  But 
when  maxims  of  this  sort,  collected  from  Englishmen,  come  to  be  applied 
to  Frenchmen,  or  when  those  collected  from  the  present  day  are  applied 
to  past  or  future  generations,  they  are  apt  to  be  very  much  at  fault.  Un- 
less  we  have  resolved  the  empirical  law  into  the  laws  of  the  causes  on  which 
it  depends,  and  ascertained  that  those  causes  extend  to  the  case  which  we 
have  in  view,  there  can  be  no  reliance  placed  in  our  inferences.  For  every 


ETHOLOGY. 


599 


individual  is  surrounded  by  circumstances  different  from  those  of  every 
other  individual ; every  nation  or  generation  of  mankind  from  every  othei 
nation  or  generation : and  none  of  these  differences  are  without  their  influ- 
ence in  forming  a different  type  of  character.  There  is,  indeed,  also  a cer- 
tain general  resemblance;  but  peculiarities  of  circumstances  are  continually 
constituting  exceptions  even  to  the  propositions  which  are  true  in  the  great 
majority  of  cases. 

Although,  however,  there  is  scarcely  any  mode  of  feeling  or  conduct  which 
is,  in  the  absolute  sense,  common  to  all  mankind  ; and  though  the  general- 
izations which  assert  that  any  given  variety  of  conduct  or  feeling  will  be 
found  universally  (however  nearly  they  may  approximate  to  truth  within 
given  limits  of  observation),  will  be  considered  as  scientific  propositions  by 
no  one  who  is  at  all  familiar  with  scientific  investigation;  yet  all  modes  of 
feeling  and  conduct  met  with  among  mankind  have  causes  which  produce 
them;  and  in  the  propositions  which  assign  those  causes  will  be  found  the 
explanatidiTofTlie  empirical  laws,  and  the  limiting  principle  of  our  reliance 
on  them.  Human  beings  do  not  all  feel  and  act  alike  in  the  same  circum- 
stances ; but  it  is  possible  to  determine  what  makes  one  person,  in  a given 
position,  feel  or  act  in  one  way,  another  in  another;  how  any  given  mode 
of  feeling  and  conduct,  compatible  with  the  general  laws  (physical  and 
mental)  of  human  nature,  has  been,  or  may  be,  formed.  In  other  words, 
mankind  have  not  one  universal  character,  but  there  exist  universal  laws 
of  the  Formation  of  Character.  And  since  it  is  by  these  laws,  combined 
with  the  facts  of  each  particular  case,  that  the  whole  of  the  phenomena  of 
human  action  and  feeling  are  produced,  it  is  on  these  that  every  rational 
attempt  to  construct  the  science  of  human  nature  in  the  concrete,  and  for 
practical  purposes,  must  proceed. 

Ns 

§ 3.  The  laws,  then,  of  the  formation  of  character  being  the  principal  ob- 
ject of  scientific  inquiry  into  human  nature,  it  remains  to  determine  the 
method  of  investigation  best  fitted  L"-  ascertaining  them.  And  the  logical 
principles  according  to  which  this  question  is  to  be  decided,  must  be  those 
which  preside  ove^  every  other  attempt  to  investigate  the  laws  of  very  com- 
plex phenomena.  For  it  is  evident  that  both  the  character  of  any  human 
being,  and  the  aggregate  of  the  circumstances  by  which  that  character  has 
been  formed,  are  facts  of  a high  order  of  complexity.  'TSTow  to  such  cases 
we  have  seen  that  the  Deductive  Method,  setting  out  from  general  laws, 
and  verifying  their  consequences  by  specific  experience,  is  alone  applicable. 
The  grounds  of  this  great  logical  doctrine  have  formerly  been  stated;  and 
its  truth  will  derive  additional  support  from  a brief  examination  of  the 
specialties  of  the  present  case. 

There  are  only  two  modes  in  which  laws  of  nature  can  be  ascertained — 
deductively  and  experimentally  ; including  under  the  denomination  of  ex- 
perimental inquiry,  observation  as  well  as  artificial  experiment.  Are  the 
laws  of  the  formation  of  character  susceptible  of  a satisfactory  investigation 
by  the  method  of  experimentation?  Evidently  not;  because,  even  if  we 
suppose  unlimited  power  of  varying  the  expei intent  (which  is  abstractedly 
possible,  though  no  one  but  an  Oriental  despot  has  that  power,  or,  if  he  had, 
would  probably  be  disposed  to  exercise  it),  a still  more  essential  condition 
is  wanting — the  power  of  performing  any  of  the  experiments  with  scientific 
accuracy. 

The  instances  requisite  for  the  prosecution  of  a directly  experimental  in- 
quiry into  the  formation  of  character,  would  be  a number  of  human  beings 


600 


LOGIC  OF  THE  MORAL  SCIENCES. 


to  bring  up  and  educate,  from  infancy  to  mature  age.  And  to  perform  any 
one  of  these  experiments  with  scientific  propriety,  it  would  be  necessary  to 
know  and  record  every  sensation  or  impression  received  by  the  young  pu- 
pil from  a period  long  before  it  could  speak;  including  its  own  notions  re- 
specting the  sources  of  all  those  sensations  and  impressions  It  is  not  only 
impossible  to  do  this  completely,  but  even  to  do  so  much  of  it  as  should 
constitute  a tolerable  approximation.  One  apparently  trivial  circumstance 
which  eluded  our  vigilance  might  let  in  a train  of  impressions  and  associ- 
ations sufficient  to  vitiate  the  experiment  as  an  authentic  exhibition  of  the 
effects  flowing  from  given  causes.  No  one  who  has  sufficiently  reflected 
on  education  is  ignorant  of  this  truth ; and  whoever  has  not,  will  find  it 
most  instructively  illustrated  in  the  writings  of  Rousseau  and  Helvetius  on 
that  great  subject. 

Under  this  impossibility  of  studying  the  laws  of  the  formation  of  char- 
acter by  experiments  purposely  contrived  to  elucidate  them,  there  remains 
the  resource  of  simple  observation.  But  if  it  be  impossible  to  ascertain 
the  influencing  circumstances  with  any  approach  to  completeness  even 
when  we  have  the  shaping  of  them  ourselves,  much  more  impossible  is  it 
when  the  cases  are  further  removed  from  our  observation,  and  altogether 
out  of  our  control.  Consider  the  difficulty  of  the  very  first  step — of  ascer- 
taining what  actually  is  the  character  of  the  individual,  in  each  particular 
case  that  we  examine.  There  is  hardly  any  person  living  concerning  some 
essential  part  of  whose  character  there  are  not  differences  of  opinion  even 
among  his  intimate  acquaintances;  and  a single  action,  or  conduct  contin- 
ued only  for  a short  time,  goes  a very  little  way  toward  ascertaining  it. 
We  can  only  make  our  observations  in  a rough  way  and  en  masse / not  at- 
tempting to  ascertain  completely  in  any  given  instance,  what  character  has 
been  formed,  and  still  less  by  what  causes  ; but  only  observing  in  what 
state  of  previous  circumstances  it  is  found  that  certain  marked  mental 
qualities  or  deficiencies  oftenest  exist.  These  conclusions,  besides  that  they 
are  mere  approximate  generalizations,  deserve  no  reliance,  even  as  such, 
unless  the  instances  are  sufficiently  numerous  to  eliminate  not  only  chance, 
but  every  assignable  circumstance  in  which  a number  of  the  cases  ex- 
amined may  happen  to  have  resembled  one  another.  So  numerous  and 
various,  too,  are  the  circumstances  which  form  individual  character,  that 
the  consequence  of  any  particular  combination  is  hardly  ever  some  definite 
and  strongly  marked  character,  always  found  where  that  combination  ex- 
ists, and  not  otherwise.  ' What  is  obtained,  even  after  the  most  extensive 
and  accurate  observation,  is  merely  a comparative  result.;  as,  for  example, 
that  in  a given  number  of  Frenchmen,  taken  indiscriminately,  there  will  be 
found  more  persons  of  a particular  mental  tendency,  and  fewer  of  the  con- 
trary tendency,  than  among  an  equal  number  of  Italians  or  English,  simi- 
larly taken;  or  thus:  of  a hundred  Frenchmen  and  an  equal  number  of 
Englishmen,  fairly  selected,  and  arranged  according  to  the  degree  in  which 
they  possess  a particular  mental  characteristic,  each  number,  1,  2,  3,  etc., 
of  the  one  series,  will  be  found  to  possess  more  of  that  characteristic  than 
the  corresponding  number  of  the  other.  Since,  therefore,  the  comparison 
is  not  one  of  kinds,  but  of  ratios  and  degrees;  and  since,  in  proportion  as 
the  differences  are  slight,  it  requires  a greater  number  of  instances  to  elim- 
inate chance,  it  can  not  often  happen  to  any  one  to  know  a sufficient  num- 
ber of  cases  with  the  accuracy  requisite  for  making  the  sort  of  comparison 
last  mentioned ; less  than  which,  however,  would  not  constitute  a real  in- 
duction. Accordingly,  there  is  hardly  one  current  opinion  respecting  the 


ETHOLOGY. 


601 


characters  of  nations,  classes,  or  descriptions  of  persons,  which  is  univer- 
sally acknowledged  as  Indisputable.* 

And  finally,  if  we  could  even  obtain  by  way  of  experiment  a much  more 
satisfactory  assurance  of  these  generalizations  than  is  really  possible,  they 
would  still  be  only  empirical  laws.  They  would  show,  indeed,  that  there 
was  some  connection  between  the  type  of  character  formed  and  the  cir- 
cumstances existing  in  the  case ; but  not  what  the  precise  connection  was, 
nor  to  which  of  the  peculiarities  of  those  circumstances  the  effect  was  real- 
ly owing.  They  could  only,  therefore,  be  received  as  results  of  causation, 
requiring  to  be  resolved  into  the  general  laws  of  the  causes:  until  the  de- 
termination of  which,  we  could  not  judge  within  what  limits  the  derivative 
laws  might  serve  as  presumptions  in  cases  yet  unknown,  or  even  be  de- 
pended on  as  permanent  in  the  very  cases  from  which  they  were  collected. 
The  French  people  had,  or  were  supposed  to  have,  a certain  national  char- 
acter ; but  they  drive  out  their  royal  family  and  aristocracy,  alter  their  in- 
stitutions, pass  through  a series  of  extraordinary  events  for  the  greater 
part  of  a century,  and  at  the  end  of  that  time  their  character  is  found  to 
have  undergone  important  changes.  A long  list  of  mental  and  moral  dif- 
ferences are  observed,  or  supposed  to  exist  between  men  and  women ; but 
at  some  future  and,  it  may  be  hoped,  not  distant  period,  equal  freedom; 
and  an  equally  independent  social  position  come  to  be  possessed  by  both, 
and  their  differences  of  character  are  either  removed  or  totally  altered. 

But  if  the  differences  which  we  think  we  observe  between  French  and 
English,  or  between  men  and  women,  can  be  connected  with  more  general 
laws;  if  they  be  such  as  might  be  expected  to  be  produced  by  the  differ- 
ences of  government,  former  customs,  and  physical  peculiarities  in  the  two 
nations,  and  by  the  diversities  of  education,  occupations,  personal  inde- 
pendence, and  social  privileges,  and  whatever  original  differences  there 
may  be  in  bodily  strength  and  nervous  sensibility  between  the  two  sexes; 
then,  indeed,  the  coincidence  of  the  two  kinds  of  evidence  justifies  us  in 
believing  that  we  have  both  reasoned  rightly  and  observed  rightly. ' Our 
observation,  though  not  sufficient  as  proof,  is  ample  as  verification.  And 
having  ascertained  not  only  the  empirical  laws,  but  the  causes,  of  the  pe- 
culiarities, we  need  be  under  no  difficulty  in  judging  how  far  they  may  be 
expected  to  be  permanent,  or  by  what  circumstances  they  would  be  modi- 
fied or  destroyed. 

§ 4.  Since  then  it  is  impossible  to  obtain  really  accurate  propositions 

* The  most  favorable  cases  for  making  such  approximate  generalizations  are  what  may  be 
termed  collective  instances ; where  we  are  fortunately  enabled  to  see  the  whole  class  respect- 
ing which  we  are  inquiring  in  action  at  once,  and,  from  the  qualities  displayed  by  the  col- 
lective body,  are  able  to  judge  what  must  be  the  qualities  of  the  majority  of  the  individuals 
composing  it.  Thus  the  character  of  a nation  is  shown  in  its  acts  as  a nation ; not  so  much 
in  the  acts  of  its  government,  for  those  are  much  influenced  by  other  causes ; but  in  the  cur- 
rent popular  maxims,  and  other  marks  of  the  general  direction  of  public  opinion  ; in  the  char- 
acter of  the  persons  or  writings  that  are  held  in  permanent  esteem  or  admiration  ; in  laws  and 
institutions,  so  far  as  they  are  the  work  of  the  nation  itself,  or  are  acknowledged  and  support- 
ed by  it ; and  so  forth.  But  even  here  there  is  a large  margin  of  doubt  and  uncertainty. 
These  tilings  are  liable  to  be  influenced  by  many  circumstances  ; they  are  partially  determined 
by  the  distinctive  qualities  of  that  nation  or  body  of  persons,  but  partty  also  by  external  causes 
which  would  influence  any  other  body  of  persons  in  the  same  manner.  In  order,  therefore, 
to  make  the  experiment  really  complete,  we  ought  to  be  able  to  try  it  without  variation  upon 
other  nations : to  try  how  Englishmen  would  act  or  feel  if  placed  in  the  same  circumstances 
in  which  we  have  supposed  Frenchmen  to  be  placed;  to  apply,  in  short,  the  Method  of  Dif- 
ferences as  well  as  that  of  Agreement.  Now  these  experiments  we  can  not  try,  nor  even  ap- 
proximate to. 


002 


LOGIC  OF  THE  MORAL  SCIENCES. 


respecting  the  formation  of  character  from  observation  and  experiment 
alone,  we  are  driven  perforce  to  that  which,  even  if  it  had  not  been  the  in- 
dispensable, would  have  been  the  most  perfect,  mode  of  investigation,  and 
which  it  is  one  of  the  principal  aims  of  philosophy  to  extend  ; namely,  that 
which  tries  its  experiments  not  on  the  complex  facts,  but  on  the  simple 
ones  of  which  they  are  compounded;  and  after  ascertaining  the  laws  of  the 
causes,  the  composition  of  which  gives  rise  to  the  complex  phenomena, 
then  considers  whether  these  will  not  explain  and  account  for  the  approx- 
imate generalizations  which  have  been  framed  empirically  respecting  the 
sequences  of  those  complex  phenomena.  The  laws  of  the  formation  of 
character  are,  in  short,  derivative  laws,  resulting  from  the  general  laws  of 
mind,  and  are  to  be  obtained  by  deducing  them  from  those  general  laws 
by  supposing  any  given  set  of  circumstances,  and  then  considering  what, 
according  to  the  laws  of  mind,  will  be  the  influence  of  those  circumstances 
on  the  formation  of  character. 

A science  is  thus  formed,  to  which  I would  propose  to  give  the  name  of 
Ethology,  or  the  Science  of  Character,  from  } ]0oc,  a word  more  nearly  cor- 
responding to  the  term  “ character  ” as  I here  use  it,  than  any  other  word  in 
the  same  language.  Y The  name  is  perhaps  etymologically  applicable  to  the 
entire  science  of  our  mental  and  moral  nature;  but  if,  as  is  usual  and  con- 
venient, we  employ  the  name  Psychology  for  the  science  of  the  elementary 
laws  of  mind,  Ethology  will  serve  for  the  ulterior  science  which  determines 
the  kind  of  character  produced  in  conformity  to  those  general  laws  by  any 
set  of  circumstances,  physical  and  moral.  According  to  this  definition, 
Ethology  is  tfie  science  which  corresponds  to  the  art  of  education  in  the 
j widest  sense  of  the  term,  including  the  formation  of  national  or  collective 
character  as  well  as  individual.  It  would  indeed  bo  vain  to  expect  (how- 
ever completely  the  laws  of  the  formation  of  character  might  be  ascertain- 
ed) that  we  could  know  so  accurately  the  circumstances  of  any  given  case 
as  to  be  able  positively  to  predict  the  character  that  would  be  produced  in 
that  case.'-:  But  we  must  remember  that  a degree  of'knowledge  far  short  of 
the  power  of  actual  prediction  is  often  of  much  practical  value.  ''There 
may  be  great  power  of  influencing  phenomena,  with  a very  imperfect 
knowledge  of  the  causes  by  which  they  are  in  any  given  instance  deter- 
mined. ’ It  is  enough  that  we  know  that  certain  means  have  a tendency  to 
produce  a given  effect,  and  that  others  have  a tendency  to  frustrate  it. 

^When  the  circumstances  of  an  individual  or  of  a nation  are  in  any  consid- 
erable degree  under  our  control,  we  may,  by  our  knowledge  of  tendencies, 
be  enabled  to  shape  those  circumstances  in  a manner  much  more  favorable 
to  the  ends  we  desire,  than  the  shape  which  they  would  of  themselves  as- 
J same.  This  is  the  limit  of  our  power;  but  within  this  limit  the  power  is 
a most  important  one. 

This  science  of  Ethology  may  be  called  the  Exact  Science  of  Human  Na- 
ture; for  its  truths  are  not,  like  the  empirical  laws  which  depend  on  them, 
approximate  generalizations,  but  real  laws.  It  is,  however  (as  in  all  cases 
of  complex  phenomena),  necessary  to  the  exactness  of  the  propositions,  that 
they  should  be  hypothetical  only,  and  affirm  tendencies,  not  facts.  They 
must  not  assert  that  something  will  always,  or  certainly,  happen  ; but  only 
that  such  and  such  will  be  the  effect  of  a given  cause,  so  far  as  it  operates 
uncounteracted.  It  is  a scientific  proposition,  that  bodily  strength  tends  to 
make  men  courageous;  not  that  it  always  makes  them  so:  that  an  interest 
on  one  side  of  a question  tends  to  bias  the  judgment;  not  that  it  invaria- 
bly does  so : that  experience  tends  to  give  wisdom ; not  that  such  is  al- 


ETHOLOGY. 


603 


ways  its  effect.  These  propositions,  being  assertive  only  of  tendencies,  are 
not  the  less  universally  true  because  the  tendencies  may  be  frustrated. 

§ 5.  While,  on  the  one  hand,  Psychology  is  altogether,  or  principally,  a 
science  of  observation  and  experiment.  Ethology,  as  I have  conceived  it,  is, 
as  I have  already  remarked,  altogether  deductive.  The  one  ascertains  the 
simple  laws  of  Mind  in  general,  the  other  traces  their  operation  in  complex 
combinations,  of  circumstances.  Ethology  stands  to  Psychology  in  a rela- 
tion very  similar  to  that  in  which  the  various  branches  of  natural  philoso- 
phy stand  to  mechanics.  The  principles  of  Ethology  are  properly  the  mid- 
dle principles,  the  axiomata  media  (as  Bacon  would  have  said)  of  the  sci- 
ence of  mind:  as  distinguished,  on  the  one  hand,  from  the  empirical  laws 
resulting  from  simple  observation,  and,  on  the  other,  from  the  highest  gen- 
eralizations. 

And  this  seems  a suitable  place  for  a logical  remark,  which,  though  of 
general  application,  is  of  peculiar  importance  in  reference  to  the  present 
subject.  Bacon  has  judiciously  observed  that  the  axiomata  media  of  ev- 
ery science  principally  constitute  its  value.  The  lowest  generalizations,  un- 
til explained  by  and  resolved  into  the  middle  principles  of  which  they  are 
the  consequences,  have,  only  the  imperfect  accuracy  of  empirical  laws; 
while  the  most  general  laws  are  too  general,  and  include  too  few  circum- 
stances, to  give  sufficient  indication  of  what  happens  in  individual  cases, 
where  the  circumstances  are  almost  always  immensely  numerous.  In  the 
importance,  therefore,  which  Bacon  assigns,  in  every  science,  to  the  middle 
principles,  it  is  impossible  not  to  agree  with  him.  But  I conceive  him  to. 
have  been  radically  wrong  in  his  doctrine  respecting  the  mode  in  which 
these  axiomata  media  should  be  arrived  at;  though  there  is  no  one  propo- 
sition laid  down  in  his  works  for  which  he  has  been  more  extravagantly 
eulogized.  He  enunciates  as  a universal  rule  that  induction  should  pro- 
ceed from  the  lowest  to  the  middle  principles,  and  from  those  to  the  high- 
est, never  reversing  that  order,  and,  consequently,  leaving  no  room  for  the 
discovery  of  new  principles  by  way  of  deduction  at  all.  It  is  not  to  be 
conceived  that  a man  of  his  sagacity  could  have  fallen  into  this  mistake  if 
there  had  existed  in  his  time,  among  the  sciences  which  treat  of  successive 
phenomena,  one  single  instance  of  a deductive  science,  such  as  mechanics, 
astronomy,  optics,  acoustics,  etc.,  now  are.  In  those  sciences  it  is  evident 
that  the  higher  and  middle  principles  are  by  no  means  derived  from  the 
lowest,  but  the  reverse.  In  some  of  them  the  very  highest  generalizations 
were  those  earliest  ascertained  with  any  scientific  exactness ; as,  for  exam- 
ple (in  mechanics),  the  laws  of  motion.  Those  general  laws  had  not,  in- 
deed, at  first  the  acknowledged  universality  which  they  acquired  after  having 
been  successfully  employed  to  explain  many  classes  of  phenomena  to  which 
they  were  not  originally  seen  to  be  applicable ; as  when  the  laws  of  motion 
were  employed,  in  conjunction  with  other  laws,  to  explain  deductively  the 
celestial  phenomena.  Still,  the  fact  remains,  that  the  propositions  which 
were  afterward  recognized  as  the  most  general  truths  of  the  science  were, 
of  all  its  accurate  generalizations,  those  earliest  arrived  at.  Bacon’s  great- 
est merit  can  not  therefore  consist,  as  we  are  so  often  told  that  it  did,  in  ex- 
ploding the  vicious  method  pursued  by  the  ancients  of  flying  to  the  high- 
est generalizations  first,  and  deducing  the  middle  principles  from  them ; j 
since  this  is  neither  a vicious  nor  an  exploded,  but  the  universally  accredited  1 
method  of  modern  science,  and  that  to  which  it  owes  its  greatest  triumphs. 
The  error  of  ancient  speculation  did  not  consist  in  making  the  largest  gen- 


G04 


LOGIC  OF  THE  MORAL  SCIENCES. 


civilizations  first,  but  in  making  them  without  the  aid  or  warrant  of  rigor- 
ous inductive  methods,  and  applying  them  deductively  without  the  needful 
use  of  that  important  part  of  the  Deductive  Method  termed  Verification. 

The  order  in  which  truths  of  the  various  degrees  of  generality  should 
be  ascertained  can  not,  I apprehend,  be  prescribed  by  any  unbending  rule. 
I know  of  no  maxim  which  can  be  laid  down  on  the  subject,  but  to  obtain 
those  first  in  respect  to  which  the  conditions  of  a real  induction  can  be 
first  and  most  completely  realized.  /Now,  wherever  our  means  of  investi- 
gation can  reach  causes,  without  stopping  at  the  empirical  laws  of  the  ef- 
fects, the  simplest  cases,  being  those  in  which  fewest  causes  are  simulta- 
neously concerned,  will  be  most  amenable  to  the  inductive  process ; and 
, these  are  the  cases  which  elicit  laws  of  the  greatest  comprehensiveness. 
In  every  science,  therefore,  which  has  reached  the  stage  at  which  it  be- 
comes a science  of  causes,  it  will  be  usual  as  well  as  desirable  first  to  ob- 
tain the  highest  generalizations,  and  then  deduce  the  more  special  ones 
from  them.  Nor  can  I discover  any  foundation  for  the  Baconian  maxim, 
so  much  extolled  by  subsequent  writers,  except  this : That  before  we  at- 
tempt to  explain  deductively  from  more  general  laws  any  new  class  of  phe- 
nomena, it  is  desirable  to  have  gone  as  far  as  is  practicable  in  ascertaining 
the  empirical  laws  of  those  phenomena;  so  as  to  compare  the  results  of 
deduction,  not  with  one  individual  instance  after  another,  but  with  general 
propositions  expressive  of  the  points  of  agreement  which  have  been  found 
among  many  instances.  For  if  Newton  had  been  obliged  to  verify  the 
theory  of  gravitation,  not  by  deducing  from  it  Kepler’s  laws,  but  by  de- 
ducing all  the  observed  planetary  positions  which  had  served  Kepler  to 
establish  those  laws,  the  Newtonian  theory  would  probably  never  have 
emerged  from  the  state  of  an  hypothesis.* 

The  applicability  of  these  remarks  to  the  special  case  under  considera- 
tion can  not  admit  of  question.  ^The  science  of  the  formation  of  character 
is  a science  of  causes.  'The  subject  is  one  to  which  those  among  the  can- 
ons of  induction,  by  which  laws  of  causation  are  ascertained,  can  be  rigor- 
ously applied.  ' It  is,  therefore,  both  natural  and  advisable  to  ascertain  the 
simplest,  which  are  necessarily  the  most  general,  laws  of  causation  first, 
and  to  deduce  the  middle  principles  from  them.  In  other  words,  Etholo- 
gy, the  deductive  science,  is  a system  of  corollaries  from  Psychology,  the 
experimental  science. 

§ 6 Of  these,  the  earlier  alone  has  been,  as  yet,  really  conceived  or  stud- 
ied as  a science;  the  other,  Ethology,  is  still  to  be  created.*  But  its  cre- 
. ation  has  at  length  become  practicable.  ^ The  empirical  laws,  destined  to 
verify  its  deductions,  have  been  formed  in  abundance  by  every  successive 

* “To  which,”  says  Dr.  Whewell,  “we  may  add,  that  it  is  certain,  from  the  history  of  the 
subject,  that  in  that  case  the  hypothesis  would  never  have  been  framed  at  all.” 

Dr.  Whewell  ( Philosophy  of  Discovery , pp.  277-282)  defends  Bacon’s  rule  against  the  pre- 
ceding strictures.  But  his  defense  consists  only  in  asserting  and  exemplifying  a proposition 
which  I had  myself  stated,  viz.,  that  though  the  largest  generalizationsmay  be  the  earliest 
made,  they  are  not  at  first  seen  in  their  entire  generality,  but  acquire  it  by  degrees,  as  they  are 
found  to  explain  one  class  after  another  of  phenomena.  The  laws  of  motion,  for  example, 
were  not  known  to  extend  to  the  celestial  regions,  until  the  motions  of  the  celestial  bodies 
had  been  deduced  from  them.  This,  however,  does  not  in  any  way  affect  the  fact,  that  the 
middle  principles  of  astronomy,  the  central  force,  for  example,  and  the  law  of  the  inverse 
square,  could  not  have  been  discovered,  if  the  laws  of  motion,  which  are  so  much  more  uni- 
versal, had  not  been  known  first.  On  Bacon’s  system  of  step-by-step  generalization,  it  would 
be  impossible  in  any  science  to  ascend  higher  than  the  empirical  laws;  a remark  which  Dr. 
Whewell’s  own  Inductive  Tables,  referred  to  by  him  in  support  of  his  argument,  amply  bear  out. 


ETHOLOGY. 


005 


age  of  humanity ; and  the  premises  for  the  deductions  are  now  sufficient- 
ly complete.  Excepting  the  degree  of  uncertainty  which  still  exists'as  to 
the  extent  of  the  natural  differences  of  individual  minds,  and  the  physical 
circumstances  on  which  these  may  be  dependent  (considerations  which  are 
of  secondary  importance  when  we  are  considering  mankind  in  the  average, 
or  en  masse),  I believe  most  competent  judges  will  agree  tha^the  general 
laws  of  the  different  constituent  elements  of  human  nature  are  even  now 
sufficiently  understood  to  render  it  possible  for  a competent  thinker  to  de- 
duce from  those  laws,  with  a considerable  approach  to  certainty,  the  par- 
ticular type  of  character  which  would  be  formed  in  mankind  generally  by 
any  assumed  set  of  circumstances.  A science  of  Ethology,  founded  on  the 
laws  of  Psychology,  is  therefore  possible ; though  little  has  yet  been  done, 
and  that  little  not  at  all  systematically,  toward  forming  it.  The  progress 
of  this  important  but  most  imperfect  science  will  depend  on  a double  jn-oc-. 
ess:  first,  that  of  deducing  theoretically  the  ethological  consequences  of 
particular  circumstances  of  position,  and  comparing  them  with  the  recog- 
nized results  of  common  experience;  and,  secondly,  the  reverse  operation; 
increased  study  of  the  various  types  of  human  nature  that  are  to  be  found 
in  the  world ; conducted  by  persons  not  only  capable  of  analyzing  and  re- 
cording the  circumstances  in  which  these  types  severally  prevail,  but  also 
sufficiently  acquainted  with  psychological  laws  to  be  able  to  explain  and 
account  for  the  characteristics  of  the  type,  by  the  peculiarities  of  the  cir- 
cumstances : the  residuum  alone,  when  there  proves  to  be  any,  being  set 
down  to  the  account  of  congenital  predispositions. 

For  the  experimental  or  a posteriori  part  of  this  process,  the  materials 
are  continually  accumulating  by  the  observation  of  mankind.  So  far  as 
thought  is  concerned,  the  great  problem  of  Ethology  is  to  deduce  the  requi- 
site middle  principles  from  the  general  laws  of  Psychology.  The  subject 
to  be  studied  is,  the  origin  and  sources  of  all  those  qualities  in  human  be- 
ings which  are  interesting  to  us,  either  as  facts  to  be  produced,  to  be  avoid- 
ed, or  merely  to  be  understood;  and  the  object  is,  to  determine, from  the 
general  laws  of  mind,  combined  with  the  general  position  of  our  species  in 
the  universe,  what  actual  or  possible  combinations  of  circumstances  are 
capable  of  promoting  or  of  preventing  the  production  of  those  qualities. 

A science  which  possesses  middle  principles  of  this  kind,  arranged  in  the 
order,  not  of  causes,  but  of  the  effects  which  it  is  desirable  to  produce  or 
to  prevent,  is  duly  prepared  to  be  the  foundation  of  the  corresponding  , 
Art.  And  when  Ethology  shall  be  thus  prepared,  practical  education  will 
be  the  mere  transformation  of  those  principles  into  a parallel  system  of 
precepts,  and  the  adaptation  of  these  to  the  sum  total  of  the  individual  cir- 
cumstances which  exist  in  each  particular  case. 

It  is  hardly  necessary  again  to  repeat  that,  as  in  every  other  deductive 
science,  verification  a posteriori  must  proceed  pari  passu  with  deduction  V 
a priori.  *The  inference  given  by  theory  as  to  the  type  of  character  which 
would  be  formed  by  any  given  circumstances  must  be  tested  by  specific 
experience  of  those  circumstances  whenever  obtainable;  and  the  conclu- 
sions of  the  science  as  a whole  must  undergo  a perpetual  verification  and 
correction  from  the  general  remarks  afforded  by  common  experience  re- 
specting human  nature  in  our  own  age,  and  by  history  respecting  times  gone 
by.  'The  conclusions  of  theory  can  not  be  trusted,  unless  confirmed  by  ob-j 
servation ; nor  those  of  observation,  unless  they  can  be  affiliated  to  theory,! 
by  deducing  them  from  the  laws  of  human  nature,  and  from  a close  analysis 
of  the  circumstances  of  the  particular  situation.  It  is  the  accordance  of 


006 


LOGIC  OF  THE  MORAL  SCIENCES. 


those  two  kinds  of  evidence  separately  taken — the  consilience  of  a •priori 
reasoning  and  specific  experience — which  forms  the  only  sufficient  ground 
for  the  principles  of  any  science  so  “immersed  in  matter,”  dealing  with 
such  complex  and  concrete  phenomena,  as  Ethology. 


CHAPTER  YI. 

GENERAL  CONSIDERATIONS  ON  THE  SOCIAL  SCIENCE. 

§ 1.  Next  after  the  science  of  individual  man  comes  the  science  of  man 
in  society — of  the  actions  of  collective  masses  of  mankind,  and  the  various 
phenomena  which  constitute  social  life. 

If  the  formation  of  individual  character  is  already  a complex  subject  of 
study,  this  subject  must  be,  in  appearance  at  least,  still  more  complex;  be- 
cause the  number  of  concurrent  causes,  all  exercising  more  or  less  influence 
on  the  total  effect,  is  greater,  in  the  proportion  in  which  a nation,  or  the 
species  at  large,  exposes  a larger  surface  to  the  operation  of  agents,  psy- 
chological and  physical,  than  any  single  individual.  If  it  was  necessary  to 
prove,  in  opposition  to  an  existing  prejudice,  that  the  simpler  of  the  two 
is  capable  of  being  a subject  of  science,  f be  prejudice  is  likely  to  be  yet 
stronger  against  the  possibility  of  giving  a scientific  character  to  the  study 
of  Politics,  and  of  the  phenomena  of  Society.  It  is,  accordingly,  but  of 
yesterday  that  the  conception  of  a political  or  social  science  has  existed 
anywhere  but  in  the  mind  of  here  and  there  an  insulated  thinker,  generally 
very  ill  prepared  for  its  realization:  though  the  subject  itself  has  of  all 
others  engaged  the  most  general  attention,  and  been  a theme  of  interested 
and  earnest  discussions,  almost  from  the  beginning  of  recorded  time. 

The  condition,  indeed,  of  politics  as  a branch  of  knowledge  was,  until 
very  lately,  and  has  scarcely  even  yet  ceased  to  be,  that  which  Bacon  ani- 
madverted on,  as  the  natural  state  of  the  sciences  while  their  cultivation  is 
abandoned  to  practitioners ; not  being  carried  on  as  a branch  of  speculative 
inquiry,  but  only  with  a view  to  the  exigencies  of  daily  practice,  and  the 
fructifera  experimenta,  therefore,  being  aimed  at,  almost  to  the  exclusion 
of  the  lucifera.  Such  was  medical  investigation,  before  physiology  and 
natural  history  began  to  be  cultivated  as  branches  of  general  knowledge. 
The  only  questions  examined  were,  what  diet  is  wholesome,  or  what  medi- 
cine will  cure  some  given  disease;  without  any  previous  systematic  inquiry 
into  the  laws  of  nutrition,  and  of  the  healthy  and  morbid  action  of  the 
different  organs,  on  which  laws  the  effect  of  any  diet  or  medicine  must 
evidently  depend.  And  in  politics  the  questions  which  engaged  general 
attention  were  similar:  Is  such  an  enactment,  or  such  a form  of  govern- 
ment, beneficial  or  the  reverse  — either  universally,  or  to  some  particular 
community?  without  any  previous  inquiry  into  the  general  conditions  by 
which  the  operation  of  legislative  measures,  or  the  effects  produced  by 
forms  of  government,  are  determined.  Students  in  politics  thus  attempted 
to  study  the  pathology  and  therapeutics  of  the  social  body,  before  they  had 
laid  the  necessary  foundation  in  its  physiology;  to  cure  disease  without 
understanding  the  laws  of  health.  And  the  result  was  such  as  it  must  al- 
ways be  when  persons,  even  of  ability,  attempt  to  deal  with  the  complex 
questions  of  a science  before  its  simpler  and  more  elementary  truths  have 
been  established. 

No  wonder  that,  when  the  phenomena  of  society  have  so  rarely  been 


SOCIAL  SCIENCE. 


607 


contemplated  in  the  point  of  view  characteristic  of  science,  the  philosophy 
of  society  should  have  made  little  progress;  should  contain  few  general 
propositions  sufficiently  precise  and  certain  for  common  inquirers  to  recogi 
nize  in  them  a scientific  character.  The  vulgar  notion  accordingly  is,  that 
all  pretension  to  lay  down  general  truths  on  politics  and  society  is  quack- 
ery ; that  no  universality  and  no  certainty  are  attainable  in  such  matter's. 
What  partly  excuses  this  common  notion  is,  that  it  is  really  not  without 
foundation  in  one  particular  sense.  A large  proportion  of  those  who  have 
laid  claim  to  the  character  of  philosophic  politicians  have  attempted  not 
to  ascertain  universal  sequences,  but  to  frame  universal  precepts.  They 
have  imagined  some  one  form  of  government,  or  system  of  laws,  to  fit  all 
cases — a pretension  well  meriting  the  ridicule  with  which  it  is  treated  by 
practitioners,  and  wholly  unsupported  by  the  analogy  of  the  art  to  which, 
from  the  nature  of  its  subject,  that  of  politics  must  be  the  most  nearly 
allied.  No  one  now  supposes  it  possible  that  one  remedy  can  cure  all 
diseases,  or  even  the  same  disease  in  all  constitutions  and  habits  of  body. 

It  is  not  necessary  even  to  the  perfection  of  a science,  that  the  corre- 
sponding art  should  possess  universal,  or  even  general,  rules.  The  phe- 
nomena of  society  might  not  only  be  completely  dependent  on  known 
causes,  but  the  mode  of  action  of  all  those  causes  might  be  reducible  to 
laws  of  considerable  simplicity,  and  yet  no  two  cases  might  admit  of  being 
treated  in  precisely  the  same  manner.  So  great  might  be  the  variety  of 
circumstances  on  which  the  results  in  different  cases  depend,  that  the  art 
might  not  have  a single  general  precept  to  give,  except  that  of  watching 
the  circumstances  of  the  particular  case,  and  adapting  our  measures  to  the 
effects  which,  according  to  the  principles  of  the  science,  result  from  those 
circumstances.  But  although,  in  so  complicated  a class  of  subjects,  it  is  I 
impossible  to  lay  down  practical  maxims  of  universal  application,  it  does  I 
not  follow  that  the  phenomena  do  not  conform  to  universal  laws. 

§ 2/  All  phenomena  of  society  are  phenomena  of  human  nature,  gener- 
ated by  the  action  of  outward  circumstances  upon  masses  of  human  be- 
ings; and  if,  therefore,  the  phenomena  of  human  thought,  feeling,  and  ac- 
tion are  subject  to  fixed  laws,  the  phenomena  of  society  can  not  but  con- 
form to  fixed  laws,  the  consequence  of  the  preceding.  There  is,  indeed, 
no  hope  that  these  laws,  though  our  knowledge  of  them  were  as  certain 
and  as  complete  as  it  is  in  astronomy,  would  enable  us  to  predict  the  his- 
tory of  society,  like  that  of  the  celestial  appearances,  for  thousands  of 
years  to  come.  But  the  difference  of  certainty  is  not  in  the  laws  them- 
selves, it  is  in  the  data  to  which  these  laws  are  to  be  applied.  In  as- 
tronomy the  causes  influencing  the  result  are  few,  and  change  little,  and 
that  little  according  to  known  laws ; we  can  ascertain  what  they  are  now, 
and  thence  determine  what  they  will  be  at  any  epoch  of  a distant  future. 
The  data,  therefore,  in  astronomy  are  as  certain  as  the  laws  themselves. 
The  circumstances,  on  the  contrary,  which  influence  the  condition  and  prog- 
ress of  society  are  innumerable,  and  perpetually  changing;  and  though 
they  all  change  in  obedience  to  causes,  and  therefore  to  laws,  the  multitude 
of  the  causes  is  so  great  as  to  defy  our  limited  powers  of  calculation.  Not 
to  say  that  the  impossibility  of  applying  precise  numbers  to  facts  of  such 
a description  would  set  an  impassable  limit  to  the  possibility  of  calcula- 
ting them  beforehand,  even  if  the  powers  of  the  human  intellect  were  other- 
wise adequate  to  the  task. 

/(  But,  as  before  remarked,  an  amount  of  knowledge  quite  insufficient  for 


cos 


LOGIC  OF  THE  MORAL  SCIENCES. 


prediction,  may  be  most  valuable  for  guidance.  The  science  of  society 
would  have  attained  a very  high  point  of  perfection  if  it  enabled  us,  in 
any  given  condition  of  social  affairs,  in  the  condition,  for  instance,  of  Eu- 
rope or  any  European  country  at  the  present  time,  to  understand,  by  what 
causes  it  had,  in  any  and  every  particular,  been  made  what  it  was ; wheth- 
er it  was  tending  to  any,  and  to  what,  changes ; what  effects  each  feature 
of  its  existing  state  was  likely  to  produce  in  the  future;  and  by  what 
means  any  of  those  effects  might  be  prevented,  modified,  or  accelerated,  or 
a different  class  of  effects  superinduced.  There  is  nothing  chimerical  in 
the  hope  that  general  laws,  sufficient  to  enable  us  to  answer  these  various 
questions  for  any  country  or  time  with  the  individual  circumstances  of 
which  we  are  well  acquainted,  do  really  admit  of  being  ascertained  ; and 
that  the  other  branches  of  human  knowledge,  which  this  undertaking  pre- 
supposes, are  so  far  advanced  that  the  time  is  ripe  for  its  commencement. 
Such  is  the  object  of  the  Social  Science. 

That  the  nature  of  what  I consider  the  true  method  of  the  science  may 
be  made  more  palpable,  by  first  showing  what  that  method  is  not,  it  will 
be  expedient  to  characterize  briefly  two  radical  misconceptions  of  the 
proper  mode  of  philosophizing  on  society  and  government,  one  or  other  of 
which  is,  either  explicitly  or  more  often  unconsciously,  entertained  by  al- 
most all  who  have  meditated  or  argued  respecting  the  logic  of  politics, 
since  the  notion  of  treating  it  by  strict  rules,  and  on  Baconian  principles, 
lias  been  current  among  the  more  advanced  thinkers.  These  erroneous 
methods,  if  the  word  method  can  be  applied  to  erroneous  tendencies  aris- 
ing from  the  absence  of  any  sufficiently  distinct  conception  of  method,  may 
be  termed  the  Experiipental,  or  Chemical,  mode  of  investigation,  and  the 
Abstract,  or  Geometrical,  mode.  We  shall  begin  with  the  former. 


CHAPTER  VII. 

OF  THE  CHEMICAL,  OB  EXPERIMENTAL,  METHOD  IN  THE  SOCIAL  SCIENCE. 

§ l.'The  laws  of  the  phenomena  of  society  are,  and  can  be,  nothing  but 
the  laws  of  the, .actions  and  passions  of  human  beings  united  together  in 
the  social  state.  Men,  however,  in  a state  of  society  are  still  men ; their 
actions  and  passions  are  obedient  to  the  laws  of  individual  human  nature. 
Men  are  not,  when  brought  together,  converted  into  another  kind  of  sub- 
stance, with  different  properties;  as  hydrogen  and  oxygen  are  different 
from  water,  or  as  hydrogen,  oitygen,  carbon,  and  azote,  are  different  from 
nerves,  muscles,  and  tendons.  Human  beings  in  society  have  no  proper- 
ties but  those  which  are  derived  from,  and  may  be  resolved  into,  the  laws 
of  the  nature  of  individual  man.  In  social  phenomena  the  Composition  of 
Causes  is  the  universal  law. 

Now,  the  method  of  philosophizing  which  may  be  termed  chemical  over- 
looks this  fact,  and  proceeds  as  if  the  nature  of  man  as  an  individual  were 
not  concerned  at  all,  or  were  concerned  in  a very  inferior  degree,  in  the 
operations  of  human  beings  in  society.  All  reasoning  in  political  or  social 
affairs,  grounded  on  principles  of  human  nature,  is  objected  to  by  reason- 
ers  of  this  sort,  under  such  names  as  “ abstract  theory.”  For  the  direc- 
tion of  their  opinions  and  conduct,  they  profess  to  demand,  in  all  cases 
without  exception,  specific  experience. 


THE  CHEMICAL  METHOD. 


609 


This  mode  of  thinking  is  not  only  general  with  practitioners  in  poli- 
tics, and  with  that  very  numerous  class  who  (on  a subject  which  no  one, 
however  ignorant,  thinks  himself  incompetent  to  discuss)  profess  to  guide 
themselves  by  common  sense  rather  than  by  science ; but  is  often  counte- 
tenanced  by  persons  with  greater  pretensions  to  instruction — persons  who, 
having  sufficient  acquaintance  with  books  and  with  the  current  ideas  to 
have  heard  that  Bacon  taught  mankind  to  follow  experience,  and  to  ground 
their  conclusions  on  facts  instead  of  metaphysical  dogmas,  think  that,  by 
treating  political  facts  in  as  directly  experimental  a method  as  chemical 
facts,  they  are  showing  themselves  true  Baconians,  and  proving  their  ad- 
versaries to  be  mere  syllogizers  and  school-men.  As,  however,  the  notion 
of  the  applicability  of  experimental  methods  to  political  philosophy  can 
not  co-exist  with  any  just  conception  of  these  methods  themselves,  the  kind 
of  arguments  from  experience  which  the  chemical  theory  brings  forth  as 
its  fruits  (and  which  form  the  staple,  in  this  country  especially,  of  parlia- 
mentary and  hustings  oratory),  are  such  as,  at  no  time  since  Bacon,  would 
have  been  admitted  to  be  valid  in  chemistry  itself,  or  in  any  other  branch 
of  experimental  science.  They  are  such  as  these : that  the  prohibition  of 
foreign  commodities  must  conduce  to  national  wealth,  because  England 
has  flourished  under  it,  or  because  countries  in  general  which  have  adopt- 
ed it  have  flourished ; that  our  laws,  or  our  internal  administration,  or  our 
constitution,  are  excellent  for  a similar  reason;  and  the  eternal  arguments 
from  historical  examples,  from  Athens  or  Rome,  from  the  fires  in  Smith- 
field  or  the  French  Revolution. 

I will  not  waste  time  in  contending  against  modes  of  argumentation 
which  no  person  with  the  smallest  practice  in  estimating  evidence  could 
possibly  be  betrayed  into ; which  draw  conclusions  of  general  application 
from  a single  unanalyzed  instance,  or  arbitrarily  refer  an  effect  to  some 
one  among  its  antecedents,  without  any  process  of  elimination  or  compari- 
son of  instances.  It  is  a rule  both  of  justice  and  of  good  sense  to  grapple 
not  with  the  absurdest,  but  with  the  most  reasonable  form  of  a wrong 
opinion.  We  shall  suppose  our  inquirer  acquainted  with  the  true  condi- 
tions of  experimental  investigation,  and  competent  in  point  of  acquire- 
ments for  realizing  them,  so  far  as  they  can  be  realized.  He  shall  know 
as  much  of  the  facts  of  history  as  mere  erudition  can  teach — as  much  as 
can  be  proved  by  testimony,  without  the  assistance  of  any  theory;  and  if 
those  mere  facts,  properly  collated,  can  fulfill  the  conditions  of  a real  in- 
duction, he  shall  be  qualified  for  the  task. 

But  that  no  such  attempt  can  have  the  smallest  chance  of  success,  has 
been  abundantly  shown  in  the  tenth  chapter  of  the  Third  Book.*  We 
there  examined  whether  effects  which  depend  on  a complication  of  causes 
can  be  made  the  subject  of  a true  induction  by  observation  and  experi- 
ment; and  concluded,  on  the  most  convincing  grounds,  that  they  can  not. 
Since,  of  all  effects,  none  depend  on  so  great  a complication  of  causes  as 
social  phenomena,  we  might  leave  our  case  to  rest  in  safety  on  that  previ- 
ous showing.  But  a logical  principle  as  yet  so  little  familiar  to  the  ordi- 
nary run  of  thinkers,  requires  to  be  insisted  on  more  than  once,  in  order  to 
make  the  due  impression  ; and  the  present  being  the  case  which  of  all  oth- 
ers exemplifies  it  the  most  strongly,  there  will  be  advantage  in  re-, stating 
the  grounds  of  the  general  maxim,  as  applied  to  the  specialties  of  the 
class  of  inquiries  now  under  consideration. 


* Supra,  page  317  to  the  end  of  the  chapter, 
39 


G10 


LOGIC  OF  THE  MORAL  SCIENCES. 


§ 2.  The  first  difficulty  which  meets  us  in  the  attempt  to  apply  experi- 
mental methods  for  ascertaining  the  laws  of  social  phenomena,  is  that  we 
are  without  the  means  of  making  artificial  experiments.  Even  if  we  could 
contrive  experiments  at  leisure,  and  try  them  without  limit,  we  should  do 
so  under  immense  disadvantage ; both  from  the  impossibility  of  ascertain- 
ing and  taking  note  of  all  the  facts  of  each  case,  and  because  (those  facts 
being  in  a perpetual  state  of  change),  before  sufficient  time  had  elapsed  to  as- 
certain the  result  of  the  experiment,  some  material  circumstances  would  al- 
ways have  ceased  to  be  the  same.  But  it  is  unnecessary  to  consider  the  log- 
ical objections  which  would  exist  to  the  conclusiveness  of  our  experiments, 
since  we  palpably  never  have  the  power  of  trying  any.  We  can  only  watch 
those  which  nature  produces,  or  which  are  produced  for  other  reasons. 
We  can  not  adapt  our  logical  means  to  our  wants,  by  varying  the  circurn- 
stances  as  the  exigencies  of  elimination  may  require.  If  the  spontaneous 
instances,  formed  by  contemporary  events  and  by  the  successions  of  phe- 
nomena recorded  in  history,  afford  a sufficient  variation  of  circumstances, 
an  induction  from  specific  experience  is  attainable ; otherwise  not.  The 
question  to  be  resolved  is,  therefore,  whether  the  requisites  for  induction 
respecting  the  causes  of  political  effects  or  the  properties  of  political  agents, 
are  to  be  met  with  in  history  ? including  under  the  term,  contemporary  his- 
tory. And  in  order  to  give  fixity  to  our  conceptions,  it  will  be  advisable 
to  suppose  this  question  asked  in  reference  to  some  special  subject  of  po- 
litical inquiry  or  controversy;  such  as  that  frequent  topic  of  debate  in  the 
present  century,  the  operation  of  restrictive  and  prohibitory  commercial 
legislation  upon  national  wealth.  Let  this,  then,  be  the  scientific  question 
to  be  investigated  by  specific  experience. 

§ 3.  In  order  to  apply  to  the  case  the  most  perfect  of  the  methods  of  ex- 
perimental inquiry,  the  Method  of  Difference,  we  require  to  find  two  in- 
stances which  tally  in  every  particular  except  the  one  which  is  the  subject 
of  inquiry.  If  two  nations  can  be  found  which  are  alike  in  all  natural  ad- 
vantages and  disadvantages;  whose  people  resemble  each  other  in  every 
quality,  physical  and  moral,  spontaneous  and  acquired;  whose  habits, 
usages,  opinions,  laws,  and  institutions  are  the  same  in  all  respects,  except 
that  one  of  them  has  a more  protective  tariff,  or  in  other  respects  interferes 
more  with  the  freedom  of  industry ; if  one  of  these  nations  is  found  to  be 
rich  and  the  other  poor,  or  one  richer  than  the  other,  this  will  be  an  expe- 
rlmentum  crucis:  a real  proof  by  experience,  which  of  the  two  systems  is 
most  favorable  to  national  riches.  But  the  supposition  that  two  such  in- 
stances can  be  met  with  is  manifestly  absurd.  Nor  is  such  a concurrence 
even  abstractedly  possible.  Two  nations  which  agreed  in  every  thing  except 
their  commercial  policy  would  agree  also  in  that.  Differences  of  legisla- 
tion are  not  inherent  and  ultimate  diversities;  are  not  properties  of  Kinds. 
They  are  effects  of  pre-existing  causes.  If  the  two  nations  differ  in  this 
portion  of  their  institutions,  it  is  from  some  difference  in  their  position, 
and  thence  in  their  apparent  interests,  or  in  some  portion  or  other  of  their 
opinions,  habits,  and  tendencies;  which  opens  a view  of  further  differences 
without  any  assignable  limit,  capable  of  operating  on  their  industrial  pros- 
perity, as  well  as  on  every  other  feature  of  their  condition,  in  more  ways 
than  can  be  enumerated  or  imagined.  There  is  thus  a demonstrated  im- 
possibility of  obtaining,  in  the  investigations  of  the  social  science,  the  con- 
ditions required  for  the  most  conclusive  form  of  inquiry  by  specific  experi- 
ence. 


THE  CHEMICAL  METHOD. 


611 


In  the  absence  of  the  direct,  we  may  next  try,  as  in  other  cases,  the  sup- 
plementary resource,  called  in  a former  place  the  Indirect  Method  of  Dif- 
ference ; which,  instead  of  two  instances  differing  in  nothing  but  the  pres- 
ence or  absence  of  a given  circumstance,  compares  two  classes  of  instances 
respectively  agreeing  in  nothing  but  the  presence  of  a circumstance  on  the 
one  s i d e and'its  ~ab s e n c e on  the  other.  To  choose  the  most  advantageous 
case  conceivable  (a  case  far  too  advantageous  to  be  ever  obtained),  suppose 
that  we  compare  one  nation  which  has  a restrictive  policy  with  two  or 
more  nations  agreeing  in  nothing  but  in  permitting  free  trade.  We  need 
not  now  suppose  that  either  of  these  nations  agrees  with  the  first  in  all  its 
circumstances;  one  may  agree  with  it  in  some  of  its  circumstances,  and  an- 
other in  the  remainder.  And  it  may  be  argued,  that  if  these  nations  re- 
main poorer  than  the  restrictive  nation,  it  can  not  be  for  want  either  of  the 
first  or  of  the  second  set  of  circumstances,  but  it  must  be  for  want  of  the 
protective  system.  If  (we  might  say)  the  restrictive  nation  had  prospered 
front  the  one  set  of  causes,  the  first  of  the  free-trade  nations  would  have 
prospered  equally;  if  by  reason  of  the  other,  the  second  would  ; but  nei- 
ther has ; therefore  the  prosperity  was  owing  to  the  restrictions.  This 
will  be  allowed  to  be  a very  favorable  specimen  of  an  argument  from  spe- 
cific experience  in  politics,  and  if  this  be  inconclusive,  it  would  not  be  easy 
to  find  another  preferable  to  it. 

Yet,  that  it  is  inconclusive,  scarcely  requires  to  be  pointed  out.  Why 
must  the  prosperous  nation  have  prospered  from  one  cause  exclusively? 
National  prosperity  is  always  the  collective  result  of  a multitude  of  favor- 
able circumstances  ; and  of  these,  the  restrictive  nation  may  unite  a greater 
number  than  either  of  the  others,  though  it  may  have  all  of  those  circum- 
stances in  common  with  either  one  or  the  other  of  them.  Its  prosperity 
may  be  partly  owing  to  circumstances  common  to  it  with  one  of  those  na- 
tions, and  partly  with  the  other,  while  they,  having  each  of  them  only  half 
the  number  of  favorable  circumstances,  have  remained  inferior.  So  that 
the  closest  imitation  which  can  be  made,  in  the  social  science,  of  a legiti- 
mate induction  from  direct  experience,  gives  but  a specious  semblance  of 
conclusiveness,  without  any  real  value. 

§ 4.  The  Method  of  Difference  in  either  of  its  forms  being  thus  com- 
pletely out  of  the  question,  there  remains  the  Method  of  Agreement.  But 
we  are  already  aware  of  how  little  value  this  method  is,  in  cases  admitting 
Plurality  of  Causes ; and  social  phenomena  are  those  in  which  the  purality 
prevails  in  the  utmost  possible  extent. 

Suppose  that  the  observer  makes  the  luckiest  hit  which  could  be  given 
by  any  conceivable  combination  of  chances ; that  he  finds  two  nations  which 
agree  in  no  circumstance  whatever,  except  in  having  a restrictive  system, 
and  in  being  prosperous ; or  a number  of  nations,  all  prosperous,  which 
have  no  antecedent  circumstances  common  to  them  all  but  that  of  having 
a restrictive  policy.  It  is  unnecessary  to  go  into  the  consideration  of  the 
impossibility  of  ascertaining  from  history,  or  even  from  contemporary  ob- 
servation, that  such  is  really  the  fact;  that  the  nations  agree  in  no  other 
circumstance  capable  of  influencing  the  case.  Let  us  suppose  this  impossi- 
bility vanquished,  and  the  fact  ascertained  that  they  agree  only  in  a restrict- 
ive system  as  an  antecedent,  and  industrial  prosperity  as  a consequent. 
What  degree  of  presumption  does  this  raise  that  the  restrictive  system 
caused  the  prosperity  ? One  so  trifling  as  to  be  equivalent  to  none  at  all. 
That  some  one  antecedent  is  the  cause  of  a given  effect,  because  all  other  o 


G12 


LOGIC  OF  THE  MORAL  SCIENCES. 


antecedents  have  been  found  capable  of  being  eliminated,  is  a just  inference, 
only  if  the  effect  can  have  but  one  cause.  If  it  admits  of  several,  nothing 
is  more  natural  than  that  each  of  these  should  separately  admit  of  being- 
eliminated.  Now,  in  the  case  of  political  phenomena,  the  supposition  of 
unity  of  cause  is  not  only  wide  of  the  truth,  but  at  an  immeasurable  dis- 
tance from  it.  The  causes  of  every  social  phenomenon  which  we  are  par- 
ticularly interested  about;  security,  wealth,  freedom,  good  government,  pub- 
lic virtue,  general  intelligence,  or  their  opposites,  are  infinitely  numerous, 
especially  the  external  or  remote  causes,  which  alone  are,  for  the  most  part, 
accessible  to  direct  observation.  No  one  cause  suffices  of  itself  to  produce 
any  of  these  phenomena  ; while  there  are  countless  causes  which  have  some 
influence  over  them,  and  may  co-operate  either  in  their  production  or  in  their 
prevention.  From  the  mere  fact,  therefore,  of  our  having  been  able  to  elimi- 
nate some  circumstance,  we  can  by  no  means  infer  that  this  circumstance 
was  not  instrumental  to  the  effect  in  some  of  the  very  instances  from  which 
we  have  eliminated  it.  We  can  conclude  that  the  effect  is  sometimes  pro- 
duced without  it ; but  not  that,  when  present,  it  does  not  contribute  its  share. 

Similar  objections  will  be  found  to  apply  to  the  Method  of  Concomitant 
Variations.  If  the  causes  which  act  upon  the  state  of  any  society  produced 
effects  differing  from  one  another  in  kind  ; if  wealth  depended  on  one  cause, 
peace  on  another,  a third  made  people  virtuous,  a fourth  intelligent;  we 
might,  though  unable  to  sever  the  causes  from  one  another,  refer  to  each  of 
them  that  property  of  the  effect  which  waxed  as  it  waxed,  and  which  waned 
as  it  waned.  But  every  attribute  of  the  social  body  is  influenced  by  in- 
numerable causes ; and  such  is  the  mutual  action  of  the  co-existing  elements 
of  society,  that  whatever  affects  any  one  of  the  more  important  of  them, 
will  by  that  alone,  if  it  does  not  affect  the  others  directly,  affect  them  in- 
directly. The  effects,  therefore,  of  different  agents  not  being  different  in 
quality,  while  the  quantity  of  each  is  the  mixed  result  of  all  the  agents,  the 
variations  of  the  aggregate  can  not  bear  a uniform  proportion  to  those  of 
any  one  of  its  component  parts. 

§ 5.  There  remains  the  Method  of  Residues ; which  appears,  on  the  first 
view,  less  foreign  to  this  kind  of  inquiry  than  the  three  other  methods,  be- 
cause it  only  requires  that  we  should  accurately  note  the  circumstances  of 
some  one  country,  or  state  of  society.  Making  allowance,  thereupon,  for 
the  effect  of  all  causes  whose  tendencies  are  known,  the  residue  which  those 
causes  are  inadequate  to  explain  may  plausibly  be  imputed  to  the  remain- 
der of  the  circumstances  which  are  known  to  have  existed  in  the  case. 
Something  similar  to  this  is  the  method  which  Coleridge*  describes  him- 
self as  having  followed  in  his  political  essays  in  the  Morning  Post.  “ On 
every  great  occurrence  I endeavored  to  discover  in  past  history  the  event 
that  most  nearly  resembled  it.  I procured,  whenever  it  was  possible,  the 
contemporary  historians,  memorialists,  and  pamphleteers.  Then  fairly  sub- 
tracting the  points  of  difference  from  those  of  likeness,  as  the  balance  fa- 
vored the  former  or  the  latter,  I conjectured  that  the  result  would  be  the 
same  or  different.  As, for  instance,  in  the  series  of  essays  entitled  ‘A  Com- 
parison of  France  under  Napoleon  with  Rome  under  the  first  Caesars,’  and 
in  those  which  followed, £ on  the  probable  final  restoration  of  the  Bourbons.’ 
The  same  plan  I pursued  at  the  commencement  of  the  Spanish  Revolution, 
and  with  the  same  success,  taking  the  war  of  the  United  Provinces  with 


Biographia  Literaria , i. , 214. 


THE  CHEMICAL  METHOD. 


613 


Philip  II.  as  the  groundwork  of  the  comparison.”  In  this  inquiry  he  no 
doubt  employed  the  Method  of  Residues;  for,  in  “subtracting  the  points 
of  difference  from  those  of  likeness,”  he  doubtless  weighed,  and  did  not 
content  himself  with  numbering,  them : he  doubtless  took  those  points  of 
agreement  only  which  he  presumed  from  their  own  nature  to  be  capable 
of  influencing  the  effect,  and,  allowing  for  that  influence,  concluded  that  the 
remainder  of  the  result  would  be  referable  to  the  points  of  difference. 

Whatever  may  be  the  efficacy  of  this  method,  it  is,  as  we  long  ago  re- 
marked, not  a method  of  pure  observation  and  experiment ; it  concludes, 
not  from  a comparison  of  instances,  but  from  the  comparison  of  an  in- 
stance with  the  result  of  a previous  deduction.  Applied  to  social  phenom- 
ena, it  presupposes  that  the  causes  from  which  part  of  the  effect  proceeded 
are  already  known ; and  as  we  have  shown  that  these  can  not  have  been 
known  by  specific  experience,  they  must  have  been  learned  by  deduction 
from  principles  of  human  nature  ; experience  being  called  in  only  as  a sup- 
plementary resource,  to  determine  the  causes  which  produced  an  unex- 
plained residue.  But  if  the  principles  of  human  nature  may  be  had  re- 
course to  for  the  establishment  of  some  political  truths,  they  may  for  all. 
If  it  be  admissible  to  say,  England  must  have  prospered  by  reason  of 
the  prohibitory  system,  because  after  allowing  for  all  the  other  tendencies 
which  have  been  operating,  there  is  a portion  of  prosperity  still  to  be  ac- 
counted for ; it  must  be  admissible  to  go  to  the  same  source  for  the  effect 
of  the  prohibitory  system,  and  examine  what  account  the  laws  of  human 
motives  and  actions  will  enable  us  to  give  of  its  tendencies.  Nor,  in  fact, 
will  the  experimental  argument  amount  to  any  thing,  except  in  verification 
of  a conclusion  drawn  from  those  general  laws.  For  we  may  subtract 
the  effect  of  one,  two,  three,  or  four  causes,  but  we  shall  never  succeed  in 
subtracting  the  effect  of  all  causes  except  one ; while  it  would  be  a c% 
rious  instance  of  the  dangers  of  too  much  caution  if,  to  avoid  depending 
on  a •priori  reasoning  concerning  the  effect  of  a single  cause,  we  should 
oblige  ourselves  to  depend  on  as  many  separate  a priori  reasonings  as 
there  are  causes  operating  concurrently  with  that  particular  cause  in  some 
given  instance. 

We  have  now  sufficiently  characterized  the  gross  misconception  of  the 
mode  of  investigation  proper  to  political  phenomena,  which  I have  termed 
the  Chemical  Method.  So  lengthened  a discussion  would  not  have  been 
necessary,  if  the  claim  to  decide  authoritatively  on  political  doctrines  ware 
confined  to  persons  who  had  competently  studied  any  one  of  the  higher 
departments  of  physical  science.  But  since  the  generality  of  those  who 
reason  on  political  subjects,  satisfactorily  to  themselves  and  to  a more  or 
less  numerous  body  of  admirers,  know  nothing  whatever  of  the  methods  of 
physical  investigation  beyond  a few  precepts  which  they  continue  to  par- 
rot after  Bacon,  being  entirely  unaware  that  Bacon’s  conception  of  scien- 
. tific  inquiry  has  done  its  work,  and  that  science  has  now  advanced  into  a 
higher  stage,  there  are  probably  many  to  whom  such  remarks  as  the  fore- 
going may  still  be  useful.  In  an  age  in  which  chemistry  itself,  when  at- 
tempting- to  deal  with  the  more  complex  chemical  sequences — those  of  the 
animal  or  evei/the  vegetable  organism — has  found  it  necessary  to  become, 
and  has  succeeded  in  becoming,  a Deductive  Science,  it  is  not  to  be  ap- 
prehended that  any  person  of  scientific  habits,  who  has  kept  pace  with  the 
general  progress  of  the  knowledge  of  nature,  can  be  in  danger  of  applying 
the  methods  of  elementary  chemistry  to  explore  the  sequences  of  the  most 
complex  order  of  phenomena  in  existence. 


614 


LOGIC  OF  THE  MORAL  SCIENCES. 


CHAPTER  VIII. 

OF  THE  GEOMETRICAL,  OR  ABSTRACT,  METHOD. 

§ 1.  The  misconception  discussed  in  the  preceding  chapter  is,  as  we 
said,  chiefly  committed  by  persons  not  much  accustomed  to  scientific  in- 
vestigation : practitioners  in  politics,  who  rather  employ  the  commonplaces 
of  philosophy  to  justify  their  practice  than  seek  to  guide  their  practice  by 
philosophic  principles;  or  imperfectly  educated  persons,  who,  in  ignorance 
of  the  careful  selection  and  elaborate  comparison  of  instances  required  for 
the  formation  of  a sound  theory,  attempt  to  found  one  upon  a few  coinci- 
dences which  they  have  casually  noticed. 

The  erroneous  method  of  which  we  are  now  to  treat  is,  on  the  contrary, 
peculiar  to  thinking  and  studious  minds.  It  never  could  have  suggested 
itself  but  to  persons  of  some  familiarity  with  the  nature  of  scientific  re- 
search ; who,  being  aware  of  the  impossibility  of  establishing,  by  casual 
observation  or  direct  experimentation,  a true  theory  of  sequences  so  com- 
plex as  are  those  of  the  social  phenomena,  have  recourse  to  the  simpler 
laws  which  are  immediately  operative  in  those  phenomena,  and  which  are 
no  other  than  the  laws  of  the  nature  of  the  human  beings  therein  concern- 
ed. These  thinkers  perceive  (what  the  partisans  of  the  chemical  or  exper- 
imental theory  do  not)  that 'the  science  of  society  must  necessarily  be  de- 
ductive. 'But,  from  an  insufficient  consideration  of  the  specific  nature  of 
the  subject-matter — and  often  because  (their  own  scientific  education  hav- 
ing stopped  short  in  too  early  a stage)  geometry  stands  in  their  minds  as 
the  type  of  all  deductive  science  — it  is  to  geometry,  rather  than  to  as- 
tronomy and  natural  philosophy,  that  they  unconsciously  assimilate  the 
deductive  science  of  society. 

Among  the  differences  between  geometry  (a  science  of  co-existent  facts, 
altogether  independent  of  the  laws  of  the  succession  of  phenomena),  and 
those  physical  Sciences  of  Causation  which  have  been  rendered  deductive, 
the  following  is  one  of  the  most  conspicuous  : That  geometry  affords  no 
room  for  what  so  constantly  occurs  in  mechanics  and  its  applications,  the 
case  of  conflicting  forces ; of  causes  which  counteract  or  modify  one  an- 
other. In  mechanics  we  continually  find  two  or  more  moving  forces  pro- 
ducing, not  motion,  but  rest;  or  motion  in  a different  direction  from  that 
which  would  have  been  produced  by  either  of  the  generating  forces.  It 
is  true  that  the  effect  of  the  joint  forces  is  the  same  when  they  act  simul- 
taneously, as  if  they  had  acted  one  after  another,  or  by  turns ; and  it  is 
in  this  that  the  difference  between  mechanical  and  chemical  laws  consists. 
But  still  the  effects,  whether  produced  by  successive  or  by  simultaneous 
action,  do,  wholly  or  in  part,  cancel  one  another:  what  the  one  force  does, 
the  other,  partly,  or  altogether  undoes.  There  is  no  similar  state  of  things 
in  geometry.  The  result  which  follows  from  one  geometrical  principle  has 
nothing  that  conflicts  with  the  result  which  follows  from  another.  What 
is  proved  true  from  one  geometrical  theorem,  what  would  be  true  if  no 
other  geometrical  principles  existed,  can  not  be  altered  and  made  no  longer 
true  by  reason  of  some  other  geometrical  principle.  What  is  once  proved 
true  is  true  in  all  cases,  whatever  supposition  may  be  made  in  regard  to 
any  other  matter. 


THE  GEOMETRICAL  METHOD. 


615 


Now  a conception  similar  to  this  last  would  appear  to  have  been  form 
ed  of  the  social  science,  in  the  minds  of  the  earlier  of  those  who  have  at- 
tempted to  cultivate  it  by  a deductive  method.  Mechanics  would  be  a 
science  very  similar  to  geometry,  if  evSry  motion  resulted  from  one  force 
alone,  and  not  from  a conflict  of  forces.  In  the  geometrical  theory  of  so- 
ciety, it  seems  to  be  supposed  that  this  is  really  the  case  with  the  social 
phenomena;  that  each  of  them  results  always  from  only  one  force,  one 
single  property  of  human  nature. 

At  the  point  which  we  have  now  reached,  it  can  not  be  necessary  to  say 
any  thing  either  in  proof  or  in  illustration  of  the  assertion  that  such  is  not 
the  true  character  of  the  social  phenomena.  There  is  not,  among  these 
most  complex  and  (for  that  reason)  most  modifiable  of  all  phenomena,  any 
one  over  which  innumerable  forces  do  not  exercise  influence;  which  does 
not  depend  on  a conjunction  of  very  many  causes.  We  have  not,  there- 
fore, to  prove  the  notion  in  question  to  be  an  error,  but  to  prove  that  the 
error  has  been  committed ; that  so  mistaken  a conception  of  the  mode  in 
which  the  phenomena  of  society  are  produced  has  actually  been  ascertained. 

§ 2.  One  numerous  division  of  the  reasoners  who  have  treated  social 
facts  according  to  geometrical  methods,  not  admitting  any  modification  of 
one  law  by  another,  must  for  the  present  be  left  out  of  consideration,  be- 
cause in  them  this  error  is  complicated  with,  and  is  the  effect  of,  another 
fundamental  misconception,  of  which  we  have  already  taken  some  notice, 
and  which  will  be  further  treated  of  before  we  conclude.  I speak  of  those 
who  deduce  political  conclusions  not  from  laws  of  nature,  not  from  se- 
quences of  phenomena,  real  or  imaginary,  but  from  unbending  practical 
maxims.  Such,  for  example,  are  all  who  found  their  theory  of  politics  on 
what  is  called  abstract  right,  that  is  to  say,  on  universal  precepts;  a pre- 
tension of  which  we  have  already  noticed  the  chimerical  nature.  Such,  in 
like  manner,  are  those  who  make  the  assumption  of  a social  contract,  or 
any  other  kind  of  original  obligation,  and  apply  it  to  particular  cases  by 
mere  interpretation.  But  in  this  the  fundamental  error  is  the  attempt  to 
treat  an  art  like  a science,  and  to  have  a deductive  art;  the  irrationality 
of  which  will  be  shown  in  a future  chapter.  It  will  be  proper  to  take  our 
exemplification  of  the  geometrical  theory  from  those  thinkers  who  have 
avoided  this  additional  error,  and  who  entertain,  so  far,  a juster  idea  of 
the  nature  of  political  inquiry. 

We  may  cite,  in  the  first  instance,  those  who  assume  as  the  principle  of 
their  political  philosophy  that  government  is  founded  on  fear;  that  the 
dread  of  each  other  is  the  one  motive  by  which  human  beings  were  origi- 
nally brought  into  a state  of  society,  and  are  still  held  in  it.  Some  of  the 
earlier  scientific  inquirers  into  politics,  in  particular  Hobbes,  assumed  this 
proposition,  not  by  implication,  but  avowedly,  as  the  foundation  of  their 
doctrine,  and  attempted  to  build  a complete  philosophy  of  politics  there- 
upon. It  is  true  that  Hobbes  did  not  find  this  one  maxim  sufficient  to 
carry  him  through  the  whole  of  his  subject,  but  was  obliged  to  eke  it  out 
by  the  double  sophism  of  an  original  contract.  I call  this  a double  soph- 
ism; first,  as  passing  off  a fiction  for  a fact,  and,  secondly,  assuming  a 
practical  principle,  or  precept,  as  the  basis  of  a theory;  which  is  a petitio 
prihcipii,  since  (as  we  noticed  in  treating  of  that  Fallacy)  every  rule  of 
conduct,  even  though  it  be  so  binding  a one  as  the  observance  of  a prom- 
ise, must  rest  its  own  foundations  on  the  theory  of  the  subject;  and  the 
theory,  therefore,  can  not  rest  upon  it. 


616 


LOGIC  OF  THE  MORAL  SCIENCES. 


§ 3.  Passing  over  less  important  instances,  I shall  come  at  once  to  the 
most  remarkable  example  afforded  by  our  own  times  of  the  geometrical 
method  in  politics;  emanating  from  persons  who  are  well  aware  of  the 
distinction  between  science  and  artf;  who  knew  that  rules  of  conduct  must 
follow,  not  precede,  the  ascertainment  of  laws  of  nature,  and  that  the  lat- 
ter, not  the  former,  is  the  legitimate  field  for  the  application  of  the  deduct- 
ive method.  I allude  to  the  interest-philosophy  of  the  Benthain  school. 

The  profound  and  original  thinkers  who  are  commonly  known  under 
this  description,  founded  their  general  theory  of  government  on  one  com- 
prehensive premise,  namely,  that  men’s  actions  are  always  determined  by 
their  interests.  There  is  an  a«nbiguity  in  this  last  expression;  for,  as  the 
same  philosophers,  especially  Bentham,  gave  the  name  of  an  interest  to 
anything  which  a person  likes,  the  proposition  may  be  understood  to  mean 
only  this,  that  men’s  actions  are  always  determined  by  their  wishes.  In 
this  sense,  however,  it  would  not  bear  out  any  of  the  consequences  which 
these  writers  drew  from  it ; and  the  word,  therefore,  in  their  political 
reasonings,  must  be  understood  to  mean  (which  is  also  the  explanation  they 
themselves,  on  such  occasions  gave  of  it)  what  is  commonly  termed  private, 
or  worldly,  interest. 

Taking  the  doctrine,  then,  in  this  sense,  an  objection  presents  itself  in 
limine  which  might  be  deemed  a fatal  one,  namely,  that  so  sweeping  a 
proposition  is  far  from  being  universally  true.  Human  beings  are  not 
governed  in  all  their  actions  by  their  worldly  interests.  This,  however,  is 
by  no  means  so  conclusive  an  objection  as  it  at  first  appears;  because  in 
politics  we  are  for  the  most  part  concerned  with  the  conduct,  not  of  indi- 
vidual persons,  but  either  of  a series  of  persons  (as  a succession  of  kings), 
or  a body  or  mass  of  persons,  as  a nation,  an  aristocracy,  or  a representa- 
tive assembly.  And  whatever  is  true  of  a large  majority  of  mankind,  may 
without  much  error  be  taken  for  true  of  any  succession  of  persons),  con- 
sidered as  a whole,  or  of  any  collection  of  persons  in  which  the  act  of  the 
majority  becomes  the  act  of  the  whole  body.  Although,  therefore,  the 
maxim  is  sometimes  expressed  in  a manner  unnecessarily  paradoxical,  the 
consequences  drawn  from  it  will  hold  equally  good  if  the  assertion  be  lim- 
ited as  follows:  Any  succession  of  persons,  or  the  majority  of  any  body 
of  persons,  will  be  governed  in  the  bulk  of  their  conduct  by  their  personal 
interests.  We  are  bound  to  allow  to  this  school  of  thinkers  the  benefit  of 
this  more  rational  statement  of  their  fundamental  maxim,  which  is  also  in 
strict  conformity  to  the  explanations  which,  when  considered  to  be  called 
for,  have  been  given  by  themselves. 

The  theory  goes  on  to  infer,  quite  correctly,  that  if  the  actions  of  man- 
kind are  determined  in  the  main  by  their  selfish  interests,  the  only  rulers 
who  will  govern  according  to  the  interest  of  the  governed,  are  those  whose 
selfish  interests  are  in  accordance  with  it.  And  to  this  is  added  a third 
proposition,  namely,  that  no  rulers  have  their  selfish  interest  identical  with 
that  of  the  governed,  unless  it  be  rendered  so  by  accountability,  that  is, 
by  dependence  on  the  will  of  the  governed.  In  other  words  (and  as  the 
result  of  the  whole),  that  the  desire  of  retaining  or  the  fear  of  losing  their 
power,  and  whatever  is  thereon  consequent,  is  the  sole  motive  which  can 
be  relied  on  for  producing  on  the  part  of  rulers  a course  of  conduct  in  ac- 
cordance with  the  general  interest. 

We  have  thus  a fundamental  theorem  of  political  science,  consisting  of 
three  syllogisms,  and  depending  chiefly  on  two  general  premises,  in  each  of 
which  a certain  effect  is  considered  as  determined  only  by  one  cause,  not 


THE  GEOMETRICAL  METHOD. 


61V 


by  a concurrence  of  causes.  In  the  one,  it  is  assumed  that  the  actions  of 
average  rulers  are  determined  solely  by  self-interest;  in  the  other,  that  the 
sense  of  identity  of  interest  with  the  governed,  is  produced  and  producible 
by  no  other  cause  than  responsibility. 

Neither  of  these  propositions  is  by  any  means  true;  the  last  is  extreme- 
ly wide  of  the  truth. 

It  is  not  true  that  the  actions  even  of  average  rulers  are  wholly,  or  any 
thing  approaching  to  wholly,  determined  by  their  personal  interest,  or  even 
by  their  own  opinion  of  their  personal  interest.  I do  not  speak  of  the  in- 
fluence of  a sense  of  duty,  or  feelings  of  philanthropy,  motives  never  to  be 
mainly  relied  on,  though  (except  in  countries  or  during  periods  of  great 
moral  debasement)  they  influence  almost  all  rulers  in  some  degree,  and 
some  rulers  in  a very  great  degree.  But  I insist  only  on  what  is  true  of  all 
rulers,  viz.,  that  the  character  and  course  of  their  actions  is  largely  influ- 
enced (independently  of  personal  calculation)  by  the  habitual  sentiments 
and  feelings,  the  general  modes  of  thinking  and  acting,  which  prevail 
throughout  the  community  of  which  they  are  members;  as  well  as  by  the 
feelings,  habits,  and  modes  of  thought  which  characterize  the  particular  class 
in  that  community  to  which  they  themselves  belong.  And  no  one  will  un- 
derstand or  be  able  to  decipher  their  system  of  conduct,  who  does  not  take 
all  these  things  into  account.  They  are  also  much  influenced  by  the  max- 
ims and  traditions  which  have  descended  to  them  from  other  rulers,  their 
predecessors ; which  maxims  and  traditions  have  been  known  to  retain  an 
ascendancy  during  long  periods,  even  in  opposition  to  the  private  interests 
of  the  rulers  for  the  time  being.  I put  aside  the  influence  of  other  less  gen- 
eral causes.  Although,  therefore,  the  private  interest  of  the  rulers  or  of 
the  ruling  class  is  a very  powerful  force,  constantly  in  action,  and  exer- 
cising the  most  important  influence  upon  their  conduct,  there  is  also,  in 
what  they  do,  a large  portion  which  that  private  interest  by  no  means  af- 
fords a sufficient  explanation  of;  aud  even  the  particulars  which  constitute 
the  goodness  or  badness  of  their  government,  are  in  some,  and  no  small 
degree,  influenced  by  those  among  the  circumstances  acting  upon  them, 
which  can  not,  with  any  propriety,  be  included  in  the  term  self-interest. 

Turning  now  to  the  other  proposition,  that  responsibility  to  the  govern- 
ed is  the  only  cause  capable  of  producing  in  the  rulers  a sense  of  identity 
of  interest  with  the  community,  this  is  still  less  admissible  as  a universal 
truth,  than  even  the  former.  I am  not  speaking  of  perfect  identity  of  in- 
terest, which  is  an  impracticable  chimera;  which,  most  assuredly,  responsi- 
bility to  the  people  does  not  give.  I speak  of  identity  in  essentials;  and 
the  essentials  are  different  at  different  places  and  times.  There  are  a large 
number  of  cases  in  which  those  things  which  it  is  most  for  the  general  inter- 
est that  the  rulers  should  do,  are  also  those  which  they  are  prompted  to  do 
by  their  strongest  personal  interest,  the  consolidation  of  their  power.  The 
suppression,  for  instance,  of  anarchy  aud  resistance  to  law — the  complete 
establishment  of  the  authority  of  the  central  government,  in  a state  of  so- 
ciety like  that  of  Europe  in  the  Middle  Ages — is  one  of  the  strongest  inter- 
ests of  the  people,  and  also  of  the  rulers  simply  because  they  are  the  rul- 
ers ; and  responsibility  on  their  part  could  not  strengthen,  though  in  many 
conceivable  ways  it  might  weaken,  the  motives  prompting  them  to  pursue 
this  object.  During  the  greater  part  of  the  reign  of  Queen  Elizabeth,  and 
of  many  other  monarchs  who  might  be  named,  the  sense  of  identity  of  in- 
terest between  the  sovereign  and  the  majority  of  the  people  was  probably 
stronger  than  it  usually  is  in  responsible  governments ; every  thing  that 


LOGIC  OF  THE  MORAL  SCIENCES. 


61S 

the  people  had  most  at  heart,  the  monarch  had  at  heart  too.  Had  Peter 
the  Great,  or  the  rugged  savages  whom  he  began  to  civilize,  the  truest 
inclination  toward  the  things  which  were  for  the  real  interest  of  those 
savages  ? 

I am  not  here  attempting  to  establish  a theory  of  government,  and  am 
not  called  upon  to  determine  the  proportional  weight  which  ought  to  be 
given  to  the  circumstances  which  this  school  of  geometrical  politicians  left 
out  of  their  system,  and  those  which  they  took  into  it.  I am  only  con- 
cerned to  show  that  their  method  was  unscientific;  not  to  measure  the 
amount  of  error  which  may  have  affected  their  practical  conclusions. 

It  is  but  justice  to  them,  however,  to  remark,  that  their  mistake  was  not 
so  much  one  of  substance  as  of  form,  and  consisted  in  presenting  in  a 
systematic  shape,  and  as  the  scientific  treatment  of  a great  philosophical 
question,  what  should  have  passed  for  that  which  it  really  was,  the  mere 
polemics  of  the  day.  Although  the  actions  of  rulers  are  by  no  means 
wholly  determined  by  their  selfish  interests,  it  is  chiefly  as  a security 
against  those  selfish  interests  that  constitutional  checks  are  required;  and 
for  that  purpose  such  checks,  in  England,  and  the  other  nations  of  modern 
Europe,  can  in  no  manner  be  dispensed  with.  It  is  likewise  true,  that  in 
these  same  nations,  and  in  the  present  age,  responsibility  to  the  governed 
is  the  only  means  practically  available  to  create  a feeling  of  identity  of 
interest,  in  the  cases,  and  on  the  points,  where  that  feeling  does  not  suffi- 
ciently exist.  To  all  this,  and  to  the  arguments  which  may  be  founded  on 
it  in  favor  of  measures  for  the  correction  of  our  representative  system,  I 
have  nothing  to  object;  but  I confess  my  regret,  that  the  small  though 
highly  important  portion  of  the  philosophy  of  government,  which  was 
wanted  for  the  immediate  purpose  of  serving  the  cause  of  parliamentary 
reform,  should  have  been  held  forth  by  thinkers  of  such  eminence  as  a 
complete  theory. 

It  is  not  to  be  imagined  possible,  nor  is  it  true  in  point  of  fact,  that 
these  philosophers  regarded  the  few  premises  of  their  theory  as  including 
all  that  is  required  for  explaining  social  phenomena,  or  for  determining 
the  choice  of  forms  of  government  and  measures  of  legislation  and  admin- 
istration. They  were  too  highly  instructed,  of  too  comprehensive  intellect, 
and  some  of  them  of  too  sober  and  practical  a character,  for  such  an  error. 
They  would  have  applied,  and  did  apply,  their  principles  with  innumerable 
allowances.  But  it  is  not  allowances  that  are  wanted.  There  is  little 
chance  of  making  due  amends  in  the  superstructure  of  a theory  for  the 
want  of  sufficient  breadth  in  its  foundations.  It  is  unphilosophical  to  con- 
struct a science  out  of  a few  of  the  agencies  by  which  the  phenomena  are 
determined,  and  leave  the  rest  to  the  routine  of  practice  or  the  sagacity  of 
conjecture.  We  either  ought  not  to  pretend  to  scientific  forms,  or  we 
ought  to  study  all  the  determining  agencies  equally,  and  endeavor,  so  far 
as  it  can  be  done,  to  include  all  of  them  within  the  pale  of  the  science; 
else  we  shall  infallibly  bestow  a disproportionate  attention  upon  those 
which  our  theory  takes  into  account,  while  we  misestimate  the  rest,  and 
probably  underrate  their  importance.  That  the  deductions  should  be 
from  the  whole  and  not  from  a part  only  of  the  laws  of  nature  that  are 
concerned,  would  be  desirable  even  if  those  omitted  were  so  insignificant 
in  comparison  with  the  others,  that  they  might,  for  most  purposes  and  on 
most  occasions,  be  left  out  of  the  account.  But  this  is  far  indeed  from  be- 
ing true  in  the  social  science.  The  phenomena  of  society  do  not  depend, 
in  essentials,  on  some  one  agency  or  law  of  human  nature,  with  only  incon- 


PHYSICAL  METHOD. 


619 


siderable  modifications  from  others.  The  whole  of  the  qualities  of  human 
nature  influence  those  phenomena,  and  there  is  not  one  which  influences 
them  in  a small  degree.  There  is  not  one,  the  removal  or  any  great  alter- 
ation of  which,  would  not  materially  affect  the  whole  aspect  of  society, 
and  change  more  or  less  the  sequences  of  social  phenomena  generally. 

The  theory  which  has  been  the  subject  of  these  remarks  is,  in  this  coun- 
try at  least,  the  principal  contemporary  example  of  what  I have  styled  the 
geometrical  method  of  philosophizing  in  the  social  science;  and  our  exj 
animation  of  it  has,  for  this  reason,  been  more  detailed  than  would  other-i 
wise  have  been  suitable  to  a work  like  the  present.  Having  now  suffi- 
ciently illustrated  the  two  erroneous  methods,  we  shall  pass  without  fur- 
ther  preliminary  to  the  true  method ; that  which  proceeds  (conformably 
to  the  practice  of  the  more  complex  physical  sciences)  deductively  indeed, 
but  by  deduction  from  many,  not  from  one  or  a very  few,  original  prem- 
ises ; considering  each  effect  as  (what  it  really  is)  an  aggregate  result  of 
many  causes,  operating  sometimes  through  the  same,  sometimes  through 
different  mental  agencies,  or  laws  of  human  nature. 


CHAPTER  IX. 

OF  THE  PHYSICAL,  OR  CONCRETE  DEDUCTIVE,  METHOD. 

§ 1.  After  what  has  been  said  to  illustrate  the  nature  of  the  inquiry 
into  social  phenomena,  the  general  character  of  the  method  proper  to  that 
inquiry  is  sufficiently  evident,  and  needs  only  to  be  recapitulated,  not 
proved.  However  complex  the  phenomena,  all  their  sequences  and  co-ex- 
istences  result  from  the  laws  of  the  separate  elements.  The  effect  pro- 
duced, in  social  phenomena,  by  any  complex  set  of  circumstances,  amounts 
precisely  to  the  sum  of  the  effects  of  the  circumstances  taken  singly;  and 
the  complexity  does  not  arise  from  the  number  of  the  laws  themselves, 
which  is  not  remarkably  great,  but  from  the  extraordinary  number  and 
variety  of  the  data  or  elements — of  the  agents  which,  in  obedience  to  that 
small  number  of  laws,  co-operate  toward  the  effect.  The  Social  Science, 
therefore  (which,  by  a convenient  barbarism,  has  been  termed  Sociology), 
is  a deductive  science ; not,  indeed,  after  the  model  of  geometry,  but  after 
that  of  the  more  complex  physical  sciences.  •'It  infers  the  law  of  each  ef- 
fect from  the  laws  of  causation  on  which  that  effect  depends ; not,  how- 
ever, from  the  law  merely  of  one  cause,  as  in  the  geometrical  method,  but 
by  considering  all  the  causes  which  conjunctly  influence  the  effect,  and 
compounding  their  laws  with  one  another.  Its  method,  in  short,  is  the 
Concrete  Deductive  Method : that  of  which  astronomy  furnishes  the  most 
perfect,  natural  philosophy  a somewhat  less  perfect,  example,  and  the  em- 
ployment of  which,  with  the  adaptations  and  precautions  required  by  the 
subject,  is  beginning  to  regenerate  physiology. 

Nor  does  it  admit  of  doubt,  that  similar  adaptations  and  precautions  are 
indispensable  in  sociology.  In  applying  to  that  most  complex  of  all  stud- 
ies what  is  demonstrably  the  sole  method  capable  of  throwing  the  light 
of  science  even  upon  phenomena  of  a far  inferior  degree  of  complication, 
we  ought  to  be  aware  that  the  same  superior  complexity  which  renders  the 
instrument  of  Deduction  more  necessary,  renders  it  also  more  precarious; 
and  we  must  be  prepared  to  meet,  by  appropriate  contrivances,  this  in- 
crease of  difficulty. 


620 


LOGIC  OF  THE  MORAL  SCIENCES. 


The  actions  and  feelings  of  human  beings  in  the  social  state,  are,  no 
doubt,  entirely  governed  by  psychological  and  ethological  laws:  whatever 
influence  any  cause  exercises  upon  the  social  phenomena,  it  exercises 
through  those  laws.  Supposing  therefore  the  laws  of  human  actions  and 
feelings  to  be  sufficiently  known,  there  is  no  extraordinary  difficulty  in  de- 
termining from  those  laws,  the  nature  of  the  social  effects  which  any  given 
cause  tends  to  produce.  But  when  the  question  is  that  of  compounding 
several  tendencies  together,  and  computing  the  aggregate  result  of  many 
co-existent  causes;  and  especially  when, by  attempting  to  predict  what  will 
actually  occur  in  a given  case,  we  incur  the  obligation  of  estimating  and 
compounding  the  influences  of  all  the  causes  which  happen  to  exist  in  that 
case,  we  attempt  a task  to  proceed  far  in  which,  surpasses  the  compass  of 
the  human  faculties. 

If  all  the  resources  of  science  are  not  sufficient  to  enable  us  to  calculate, 
a priori,  with  complete  precision,  the  mutual  action  of  three  bodies  gravita- 
ting toward  one  another,  it  may  be  judged  with  what  prospect  of  success 
we  should  endeavor  to  calculate  the  result  of  the  conflicting  tendencies 
which  are  acting  in  a thousand  different  directions  and  promoting  a thou- 
sand different  changes  at  a given  instant  in  a given  society;  although  we 
might  and  ought  to  be  able,  from  the  laws  of  human  nature,  to  distinguish 
correctly  enough  the  tendencies  themselves,  so  far  as  they  depend  on  causes 
accessible  to  our  observation ; and  to  determine  the  direction  which  each 
of  them,  if  acting  alone,  would  impress  upon  society,  as  well  as,  in  a gener- 
al way  at  least,  to  pronounce  that  some  of  these  tendencies  are  more  pow- 
erful than  others. 

But,  without  dissembling  the  necessary  imperfections  of  the  a priori 
method  when  applied  to  such  a subject,  neither  ought  we,  on  the  other 
hand,  to  exaggerate  them.  The  same  objections  which  apply  to  the  Meth- 
od of  Deduction  in  this  its  most  difficult  employment,  apply  to  it,  as  we 
formerly  showed',*  in  its  easiest;  and  would  even  there  have  been  insuper- 
able, if  there  had  not  existed,  as  was  then  fully  explained,  an  appropriate 
remedy.  This  remedy  consists  in  the  process  which,  under  the  name  of 
Verification,  we  have  characterized  as  the  third  essential  constituent  part 
of  the  Deductive  Method ; that  of  collating  the  conclusions  of  the  ratioci- 
nation either  with  the  concrete  phenomena  themselves,  or,  when  such  are 
obtainable,  with  their  empirical  laws.  The  ground  of  confidence  in  any 
concrete  deductive  science  is  not  the  a priori  reasoning  itself,  but  the  ac- 
cordance between  its  results  and  those  of  observation  a posteriori.  Either 
of  these  processes,  apart  from  the  other,  diminishes  in  value  as  the  subject 
increases  in  complication,  and  this  is  in  so  rapid  a ratio  as  soon  to  become 
entirely  worthless;  but  the  reliance  to  be  placed  in  the  concurrence  of  the 
two  sorts  of  evidence,  not  only  does  not  diminish  in  any  thing  like  the 
same  proportion,  but  is  not  necessarily  much  diminished  at  all.  Nothing 
more  results  than  a disturbance  in  the  order  of  precedency  of  the  two 
processes,  sometimes  amounting  to  its  actual  inversion:  insomuch  that  in- 
stead of  deducing  our  conclusions  by  reasoning,  and  verifying  them  by  ob- 
servation, we  in  some  cases  begin  by  obtaining  them  provisionally  from 
specific  experience,  and  afterward  connect  them  with  the  principles  of  hu- 
man nature  by  a priori  reasonings,  which  reasonings  are  thus  a real  Verifi- 
cation. 

The  only  thinker  who,  with  a competent  knowledge  of  scientific  methods 

* Supra , p.  321. 


PHYSICAL  METHOD. 


621 


in  general,  "has  attempted  to  characterize  the  Method  of  Sociology,  M. 
Comte,  considers  this  inverse  order  as  inseparably  inherent  in  the  nature  of 
sociological  speculation.  He  looks  upon  the  social  science  as  essentially 
consisting  of  generalizations  from  history,  verified,  not  originally  suggest- 
ed, by  deduction  from  the  laws  of  human  nature.  Though  there  is  a truth 
contained  in  this  opinion,  >of  which  I shall  presently  endeavor  to  show  the 
importance,  I can  not  but  think  that  this  truth  is  enunciated  in  too  unlim- 
ited a manner,  and  that  there  is  considerable  scope  in  sociological  inquiry 
for  the  direct,  as  well  as  for  the  inverse,  Deductive  Method. 

It  will,  in  fact,  be  shown  in  the  next  chapter,  that  there  is  a kind  of  soci- 
ological inquiries  to  which,  from  their  prodigious  complication,  the  method 
of  direct  deduction  is  altogether  inapplicable,  while  by  a happy  compensa- 
tion it  is  precisely  in  these  cases  that  we  are  able  to  obtain  the  best  empir- 
ical laws : to  these  inquiries,  therefore,  the  Inverse  Method  is  exclusively 
adapted.  But  there  are  also,  as  will  presently  appear,  other  cases  in  which 
it  is  impossible  to  obtain  from  direct  observation  any  thing  worthy  the 
name  of  an  empirical  law;  and  it  fortunately  happens  that  these  are  the 
very  cases  in  which  the  Direct  Method  is  least  affected  by  the  objection 
which  undoubtedly  must  always  affect  it  in  a certain  degree. 

We  shall  begin,  then,  by  looking  at  the  Social  Science  as  a science  of  di- 
rect Deduction,  and  considering  what  can  be  accomplished  in  it,  and  under 
what  limitations,  by  that  mode  of  investigation.  We  shall,  then,  in  a sep- 
arate chapter,  examine  and  endeavor  to  characterize  the  inverse  process. 

§ 21'  It  is  evident,  in  the  first  place,  that  Sociology,  considered  as  a sys- 
tem of  deductions  a priori,  can  not  be  a science  of  positive  predictions, 
but  only  of  tendencies.  'We  may  be  able  to  conclude, from  the  laws  of  hu- 
man nature  applied  to  the  circumstances  of  a given  state  of  society,  that  a 
particular  cause  will  operate  in  a certain  manner  unless  counteracted ; but 
we  can  never  be  assured  to  what  extent  or  amount  it  will  so  operate,  or 
affirm  with  certainty  that  it  will  not  be  counteracted  ; because  we  can  sel- 
dom know,  even  approximately,  all  the  agencies  which  may  co-exist  with  it, 
.and  still  less  calculate  the  collective  result  of  so  many  combined  elements. 
The  remark,  however,  must  here  be  once  more  repeated,  that  knowledge 
insufficient  for  prediction  may  be  most  valuable  for  guidance.  It  is  not 
necessary  for  the  wise  conduct  of  the  affairs  of  society,  no  more  than  of 
any  one’s  private  concerns,  that  we  should  be  able  to  foresee  infallibly  the 
results  of  what  we  do.  We  must  seek  our  objects  by  means  which  may 
perhaps  be  defeated,  and  take  precautions  against  dangers  which  possibly, 
may  never  be  realized.  ''The  aim  of  practical  politics  is  to  surround  any 
given  society  with  the  greatest  possible  number  of  circumstances  of  which 
the  tendencies  are  beneficial,  and  to  remove  or  counteract,  as  far  as  practi- 
cable, those  of  which  the  tendencies  are  injurious.  A knowledge  of  the 
tendencies  only,  though  without  the  power  of  accurately  predicting  their 
conjunct  result,  gives  us  to  a considerable  extent  this  power. 

It  would,  however,  be  an  error  to  suppose  that  even  with  respect  to  tend- 
encies we  could  arrive  in  this  manner  at  any  great  number  of  proposi- 
tions which  will  be  true  in  all  societies  without  exception.  Such  a suppo- 
sition would  be  inconsistent  with  the  eminently  modifiable  nature  of  the 
social  phenomena,  and  the  multitude  and  variety  of  the  circumstances  by 
which  they  are  modified — circumstances  never  the  same,  or  even  nearly  the 
same,  in  two  different  societies,  or  in  two  different  periods  of  the  same 
society.  This  would  not  be  so  serious  an  obstacle  if,  though  the  causes 


622 


LOGIC  OF  THE  MORAL  SCIENCES. 


acting  upon  society  in  general  are  numerous,  those  which  influence  any  one 
feature  of  society  were  limited  in  number;  for  we  might  then  insulate  any 
particular  social  phenomenon,  and  investigate  its  laws  without  disturbance 
from  the  rest.  But  the  truth  is  the  very  opposite  of  this.  Whatever  af- 
fects, in  an  appreciable  degree,  any  one  element  of  the  social  state,  affects 
through  it  all  the  other  elements.  The  mode  of  production  of  all  social 
phenomena  is  one  great  case  of  Intermixture  of  Laws.  We  can  never  ei- 
ther understand  in  theory  or  command  in  practice  the  condition  of  a so- 
ciety in  any  one  respect,  without  taking  into  consideration  it£  condition  in 
all  other  respects.  There  is  no  social  phenomenon  which  is  not  more  or 
less  influenced  by  every  other  part  of  the  condition  of  the  same  society, 
and  therefore  by  every  cause  which  is  influencing  any  other  of  the  contem- 
poraneous social  phenomena.  There  is,  in  short,  what  physiologists  term 
a consensus,  similar  to  that  existing  among  the  various  organs  and  func- 
tions of  the  physical  frame  of  man  and  the  more  perfect  animals;  and  con- 
stituting one  of  the  many  analogies  which  have  rendered  universal  such 
expressions  as  the  “body  politic”  and  “body  natural.”  It  follows  from 
this  consensus,  that  unless  two  societies  could  be  alike  in  all  the  circum- 
stances which  surround  and  influence  them  (which  would  imply  their  be- 
ing alike  in  their  previous  history),  no  portion  whatever  of  the  phenomena 
/will,  unless  by  accident,  precisely  correspond ; no  one  cause  will  produce 
exactly  the  same  effects  in  both.  Every  cause,  as  its  effect  spreads  through 
society,  comes  somewhere  in  contact  with  different  sets  of  agencies,  and 
thus  has  its  effects  on  some  of  the  social  phenomena  differently  modified; 
and  these  differences,  by  their  reaction,  produce  a difference  even  in  those 
of  the  effects  which  would  otherwise  have  been  the  same.  We  can  never, 
therefore,  affirm  with  certainty  that  a cause  which  has  a particular  tend- 
ency in  one  people  or  in  one  age  will  have  exactly  the  same  tendency  in 
another,  without  referring  back  to  our  premises,  and  performing  over  again 
for  the  second  age  or  nation,  that  analysis  of  the  whole  of  its  influencing 
circumstances  which  we  had  already  performed  for  the  first.  The  deduct- 
ive science  of  society  will  not  lay  down  a theorem,  asserting  in  a univer- 
sal manner  the  effect  of  any  cause ; but  will  rather  teach  us  how  to  frame 
the  proper  theorem  for  the  circumstances  of  any  given  case.  It  will  not 
give  the  laws  of  society  in  general,  but  the  means  of  determining  the  phe- 
nomena of  any  given  society  from  the  particular  elements  or  data  of  that 
society. 

All  the  general  propositions  which  can  be  framed  by  the  deductive  sci- 
ence, are  therefore,  in  the  strictest  sense  of  the  word,  hypothetical.  They 
are  grounded  on  some  suppositious  set  of  circumstances,  and  declare  how 
some  given  cause  would  operate  in  those  circumstances,  supposing  that  no 
others  were  combined  with  them.  If  the  set  of  circumstances  supposed 
have  been  copied  from  those  of  any  existing  society,  the  conclusions  will 
be  true  of  that  society,  provided,  and  in  as  far  as,  the  effect  of  those  cir- 
cumstances shall  not  be  modified  by  others  which  have  not  been  taken  into 
the  account.  If  we  desire  a nearer  approach  to  concrete  truth,  we  can  only 
aim  at  it  by  taking,  or  endeavoring  to  take,  a greater  number  of  individ- 
ualizing circumstances  into  the  computation. 

Considering,  however,  in  how  accelerating  a ratio  the  uncertainty  of  our 
conclusions  increases  as  we  attempt  to  take  the  effect  of  a greater  number 
of  concurrent  causes  into  our  calculations,  the  hypothetical  combinations 
of  circumstances  on  which  we  construct  the  general  theorems  of  the  sci- 
ence, can  not  be  made  very  complex,  without  so  rapidly  accumulating  a 


PHYSICAL  METHOD. 


623 


liability  to  error  as  must  soon  deprive  our  conclusions  of  all  value.  This 
mode  of  inquiry,  considered  as  a means  of  obtaining  general  propositions, 
must,  therefore,  on  pain  of  frivolity,  be  limited  to  those  classes  of  social 
facts  which,  though  influenced  like  the  rest  by  all  sociological  agents,  are 
under  the  immediate  influence,  principally  at  least,  of  a few  only. 

§ 3.  Notwithstanding  the  universal  consensus  of  the  social  phenomena, 
whereby  nothing  which  takes  place  in  any  part  of  the  operations  of  society 
is  without  its  share  of  influence  on  every  other  part;  and  notwithstanding 
the  paramount  ascendancy  which  the  general  state  of  civilization  and  social 
progress  in  any  given  society  must  hence  exercise  over  all  the  partial  and 
subordinate  phenomena;  it  is  not  the  less  true  that  different  species  of  so- 
cial facts  are  in  the  main  dependent,  immediately  and  in  the  first  resort, 
on  different  kinds  of  causes  ; and  therefore  not  only  may  with  advantage, 
but  must,  be  studied  apart*  just  as  in  the  natural  body  we  study  separate- 
ly the  physiology  and  pathology  of  each  of  the  principal  organs  and  tis- 
sues, though  every  one  is  acted  upon  by  the  state  of  all  the  others;  and 
though  the  peculiar  constitution  and  general  state  of  health  of  the  organ- 
ism co-operates  with,  and  often  preponderates  over,  the  local  causes,  in  de- 
termining the  state  of  any  particular  organ. 

On  these  considerations  is  grounded  the  existence  of  distinct  and  sep- 
arate, though  not  independent,  branches  or  departments  of  sociological 
speculation. 

There  is,  for  example,  one  large  class  of  social  phenomena  in  which  the 
immediately  determining  causes  are  principally  those  which  act  through 
the  desire  of  wealth,  and  in  which  the  psychological  law  mainly  concerned 
is  the  familiar  one,  that  a greater  gain  is  preferred  to  a smaller.  I mean, 
of  course,  that  portion  of  the  phenomena  of  society  which  emanate  from 
the  industrial,  or  productive,  operations  of  mankind;  and  from  those  of 
their  acts  through  which  the  distribution  of  the  products  of  those  indus- 
trial operations  takes  place,  in  so  far  as  not  effected  by  force,  or  modified 
by  voluntary  gift.  By  reasoning  from  that  one  law  of  human  nature,  and 
from  the  principal  outward  circumstances  (whether  universal  or  confined 
to  particular  states  of  society)  which  operate  upon  the  human  mind  through 
that  law,  we  may  be  enabled  to  explain  and  predict  this  portion  of  the  phe- 
nomena of  society,  so  far  as  they  depend  on  that  class  of  circumstances 
only;  overlooking  the  influence  of  any  other  of  the  circumstances  of  socie- 
ty ; and  therefore  neither  tracing  back  the  circumstances  which  we  do  take 
into  account,  to  their  possible  origin  in  some  other  facts  in  the  social  state, 
nor  making  allowance  for  the  manner  in  which  any  of  those  other  circum- 
stances may  interfere  with,  and  counteract  or  modify,  the  effect  of  the 
former.  A department  of  science  may  thus  be  constructed,  which  has  re- 
ceived the  name  of  Political  Economy. 

The  motive  which  suggests  the  separation  of  this  portion  of  the  social 
phenomena  from  the  rest,  and  the  creation  of  a distinct  branch  of  science 
relating  to  them  is — that  they  do  mainly  depend,  at  least  in  the  first  resort, 
on  one  class  of  circumstances  only;  and  that  even  when  other  circum- 
stances interfere,  the  ascertainment  of  the  effect  due  to  the  one  class  of 
circumstances  alone,  is  a sufficiently  intricate  and  difficult  business  to  make 
it  expedient  to  perform  it  once  for  all,  and  then  allow  for  the  effect  of  the 
modifying  circumstances  ; especially  as  certain  fixed  combinations  of  the 
former  are  apt  to  recur  often,  in  conjunction  with  ever-varying  circum- 
stances of  the  latter  class. 


624 


LOGIC  OF  THE  MORAL  SCIENCES. 


Political  Economy,  as  I have  said  on  another  occasion,  concerns  itself 
only  with  “such  of  the  phenomena  of  the  social  state  as  take  place  in  con- 
sequence of  the  pursuit  of  wealth.  It  makes  entire  abstraction  of  every 
other  human  passion  or  motive;  except  those  which  may  be  regarded  as 
perpetually  antagonizing  principles  to  the  desire  of  wealth,  namely,  aversion 
to  labor,  and  desire  of  the  present  enjoyment  of  costly  indulgences.  These 
it  takes,  to  a certain  extent,  into  its  calculations,  because  these  do  not 
merely,  like  our  other  desires,  occasionally  conflict  with  the  pursuit  of 
wealth,  but  accompany  it  always  as  a drag  or  impediment,  and  are  there- 
fore inseparably  mixed  up  in  the  consideration  of  it.  Political  Economy 
considers  mankind  as  occupied  solely  in  acquiring  and  consuming  wealth; 
and  aims  at  showing  what  is  the  course  of  action  into  which  mankind, 
living  in  a state  of  society,  would  be  impelled,  if  that  motive,  except  in  the 
degree  in  which  it  is  checked  by  the  two  perpetual  counter-motives  above 
adverted  to,  were  absolute  ruler  of  all  their  actions.  Under  the  influ- 
ence of  this  desire,  it  shows  mankind  accumulating  wealth,  and  employing 
that  wealth  in  the  production  of  other  wealth ; sanctioning  by  mutual 
agreement  the  institution  of  property;  establishing  laws  to  prevent  indi- 
viduals from  encroaching  upon  the  property  of  others  by  force  or  fraud ; 
adopting  various  contrivances  for  increasing  the  productiveness  of  their 
labor;  settling  the  division  of  the  produce  by  agreement,  under  the  influ- 
ence of  competition  (competition  itself  being  governed  by  certain  laws, 
which  laws  are  therefore  the  ultimate  regulators  of  the  division  of  the 
produce) ; and  employing  certain  expedients  (as  money,  credit,  etc.)  to 
facilitate  the  distribution.  All  these  operations,  though  many  of  them  are 
really  the  result  of  a plurality  of  motives,  are  considered  by  political  econ- 
omy as  flowing  solely  from  the  desire  of  wealth.  The  science  then  pro- 
ceeds to  investigate  the  laws  which  govern  these  several  operations,  under 
the  supposition  that  man  is  a being  who  is  determined,  by  the  necessity 
of  Ids  nature,  to  prefer  a greater  portion  of  wealth  to  a smaller,  in  all  cases, 
without  any  other  exception  than  that  constituted  by  the  two  counter- 
motives  already  specified.  Not  that  any  political  economist  was  ever  so 
absurd  as  to  suppose  that  mankind  are  really  thus  constituted,  but  because 
vthis  is  the  mode  in  which  science  must  necessarily  proceed.  - When  an 
effect  depends  on  a concurrence  of  causes,  these  causes  must  be  studied 
one  at  a time,  and  their  laws  separately  investigated,  if  we  wish,  through 
the  causes,  to  obtain  the  power  of  either  predicting  or  controlling  the 
effect;  since  the  law  of  the  effect  is  compounded  of  the  laws  of  all  the 
causes  which  determine  it.  The  law  of  the  centripetal  and  that  of  the 
projectile  force  must  have  been  known,  before  the  motions  of  the  earth 
and  planets  could  be  explained,  or  many  of  them  predicted.  The  same  is 
the  case  with  the  conduct  of  man  in  society.  In  order  to  judge  how  he 
will  act  under  the  variety  of  desires  and  aversions  which  are  concurrently 
operating  upon  him,  we  must  know  how  he  would  act  under  the  exclusive 
influence  of  each  one  in  particular.  There  is,  perhaps,  no  action  of  a man’s 
life  in  which  he  is  neither  under  the  immediate  nor  under  the  remote  in- 
fluence of  any  impulse  but  the  mere  desire  of  wealth.  With  respect  to 
those  parts  of  human  conduct  of  which  wealth  is  not  even  the  principal 
object,  to  these  political  economy  does  not  pretend  that  its  conclusions  are 
applicable.  But  there  are  also  certain  departments  of  human  affairs,  in 
which  the  acquisition  of  wealth  is  the  main  and  acknowledged  end.  It  is 
only  of  these  that  political  economy  takes  notice.  The  manner  in  which  it 
necessarily  proceeds  is  that  of  treating  the  main  and  acknowledged  end  as 


PHYSICAL  METHOD. 


625 


if  it  were  the  sole  end  ; which,  of  all  hypotheses  equally  simple,  is  the  near- 
est to  the  truth.  The  political  economist  inquires,  what  are  the  actions 
which  would  be  produced  by  this  desire,  if  within  the  departments  in 
question  it  were  unimpeded  by  any  other.  In  this  way  a nearer  approx- 
imation is  obtained  than  would  otherwise  be  practicable  to  the  real  order 
of  human  affairs  in  those  departments.  This  approximation  has  then  to 
be  corrected  by  making  proper  allowance  for  the  effects  of  any  impulses 
of  a different  description,  which  can  be  shown  to  interfere  with  the  result 
in  any  particular  case.  Only  in  a few  of  the  most  striking  cases  (such  as 
the  important  one  of  the  principle  of  population)  are  these  corrections  in- 
terpolated into  the  expositions  of  political  economy  itself;  the  strictness 
of  purely  scientific  arrangement. being  thereby  somewhat  departed  from, 
for  the  sake  of  practical  utility.  So  far  as  it  is  known,  or  may  be  pre- 
sumed, that  the  conduct  of  mankind  in  the  pursuit  of  wealth  is  under  the 
collateral  influence  of  any  other  of  the  properties  of  our  nature  than  the 
desire  of  obtaining  the  greatest  quantity  of  wealth  with  the  least  labor 
and  self-denial,  the  conclusions  of  political  economy  will  so  far  fail  of  being 
applicable  to  the  explanation  or  prediction  of  real  events,  until  they  are 
modified  by  a correct  allowance  for  the  degree  of  influence  exercised  by 
the  other  cause.”* 

Extensive  and  important  practical  guidance  may  be  derived,  in  any  given 
state  of  society,  from  general  propositions  such  as  those  above  indicated; 
even  though  the  modifying  influence  of  the  miscellaneous  causes  which  the 
theory  does  not  take  into  account,  as  well  as  the  effect  of  the  general  social 
changes  in  progress,  be  provisionally  overlooked.  And  though  it  has  been 
a very  common  error  of  political  economists  to  draw  conclusions  from  the 
elements  of  one  state  of  society,  and  apply  them  to  other  states  in  which 
many  of  the  elements  are  not  the  same,  it  is  even  then  not  difficult,  by 
tracing  back  the  demonstrations,  and  introducing  the  new  premises  in 
their  proper  places,  to  make  the  same  general  course  of  argument  which 
served  for  the  one  case,  serve  for  the  others  too. 

For  example,  it  has  been  greatly  the  custom  of  English  political  econ- , 
omists  to  discuss  the  laws  of  the  distribution  of  the  produce  of  industry, 
on  a supposition  which  is  scarcely  realized  anywhere  out  of  England  and 
Scotland,  namely,  that  the  produce  is  “ shared  among  three  classes,  altogeth- 
er distinct  from,  one  another,  laborers,  capitalists,  and  landlords ; and  that 
all  these  are  free  agents,  permitted  in  law  and  in  fact  to  set  upon  their  la- 
bor, their  capital,  and  their  land,  whatever  price  they  are  able  to  get  for  it. 
The  conclusions  of  the  science,  being  all  adapted  to  a society  thus  consti- 
tuted, require  to  be  revised  whenever  they  are  applied  to  any  other.  They 
are  inapplicable  where  the  only  capitalists  are  the  landlords,  and  the  labor- 
ers are  their  property,  as  in  slave  countries.  They  are  inapplicable  where 
the  almost  universal  landlord  is  the  state,  as  in  India.  They  are  inappli- 
cable where  the  argricultural  laborer  is  generally  the  owner  both  of  the  land 
itself  and  of  the  capital,  as  frequently  in  France,  or  of  the  capital  only,  as 
in  Ireland.”  But  though  it  may  often  be  very  justly  objected  to  the  ex- 
isting race  of  political  economists  “ that  they  attempt  to  construct  a per- 
manent fabric  out  of  transitory  materials ; that  they  take  for  granted  the 
immutability  of  arrangements  of  society,  many  of  which  are  in  their  nature 
fluctuating  or  progressive,  and  enunciate  with  as  little  qualification  as  if 
they  were  universal  and  absolute  truths,  propositions  which  are  perhaps 


Essays  on  some  Unsettled  Questions  of  Political  Economy , pp.  137-140. 

40 


626 


LOGIC  OF  THE  MORAL  SCIENCES. 


applicable  to  no  state  of  society  except  the  particular  one  in  which  the 
writer  happened  to  live this  does  not  take  away  the  value  of  the  proposi- 
tions, considered  with  reference  to  the  state  of  society  from  which  they 
were  drawn.  And  even  as  applicable  to  other  states  of  society,  “ it  must 
not  be  supposed  that  the  science  is  so  incomplete  and  unsatisfactory  as  this 
might  seem  to  prove.  Though  many  of  its  conclusions  are  only  locally 
true,  its  method  of  investigation  is  applicable  universally;  and  as  whoever 
has  solved  a certain  number  of  algebraic  equations,  can  without  difficulty 
solve  all  others  of  the  same  kind,  so  whoever  knows  the  political  economy 
of  England,  or  even  of  Yorkshire,  knows  that  of  all  nations,  actual  or  pos- 
sible, provided  he  have  good  sense  enough  not  to  expect  the  same  conclu- 
sion to  issue  from  varying  premises.”  Whoever  has  mastered  with  the 
degree  of  precision  which  is  attainable  the  laws  which,  under  free  competi- 
tion, determine  the  rent,  profits,  and  wages,  received  by  landlords,  capital- 
ists, and  laborers,  in  a state  of  society  in  which  the  three  classes  are  com- 
pletely separate,  will  have  no  difficulty  in  determining  the  very  different 
laws  which  regulate  the  distribution  of  the  produce  among  the  classes  in- 
terested in  it  in  any  of  the  states  of  cultivation  and  landed  property  set 
forth  in  the  foregoing  extract.* 

§ 4.  I would  not  here  undertake  to  decide  what  other  hypothetical  or 
abstract  sciences  similar  to  Political  Economy,  may  admit  of  being  carved 
out  of  the  general  body  of  the  social  science*  what  other  portions  of  the 
social  phenomena  are  in  a sufficiently  close  and  complete  dependence,  in  the 
first  resort,  on  a peculiar  class  of  causes,  to  make  it  convenient  to  create  a 
preliminary  science  of  those  causes;  postponing  the  consideration  of  the 
causes  which  act  through  them,  or  in  concurrence  with  them,  to  a later 
period  of  the  inquiry.  There  is,  however,  among  these  separate  depart- 
ments one  which  can  not  be  passed  over  in  silence,  being  of  a more  com- 
prehensive and  commanding  character  than  any  of  the  other  branches  into 
which  the  social  science  may  admit  of  being  divided.  Like  them,  it  is  di- 
rectly conversant  with  the  causes  of  only  one  class  of  social  facts,  but  a class 
which  exercises,  immediately  or  remotely,  a paramount  influence  over  the 
test.  I allude  to  what  may  be  termed  Political  Ethology,  or  the  theory  of 
the  causes  which  determine  the  type  of  character  belonging  to  a people  or 
to  an  age.  Of  all  the  subordinate  branches  of  the  social  science,  this  is 
the  most  completely  in  its  infancy.  The  causes  of  national  character  are 
scarcely  at  all  understood,  and  the  effect  of  institutions  or  social  arrange- 
ments upon  the  character  of  the  people  is  generally  that  portion  of  their 
effects  which  is  least  attended  to,  and  least  comprehended.  Nor  is  this 
wonderful,  when  we  consider  the  infant  state  of  the  science  of  Ethology 
itself,  from  whence  the  laws  must  be  drawn,  of  which  the  truths  of  polit- 
ical ethology  can  be  but  results  and  exemplifications. 

Yet,  to  whoever  well  considers  the  matter,  it  must  appear  that  the  laws 
of  national  (or  collective)  character  are  by  far  the  most  important  class  of 
sociological  laws.  In  the  first  place,  the  character  which  is  formed  by  any 
state  of  social  circumstances  is  in  itself  the  most  interesting  phenomenon 
which  that  state  of  society  can  possibly  present.  Secondly,  it  is  also  a fact 
which  enters  largely  into  the  production  of  all  the  other  phenomena.  And 
above  all,  the  character,  that  is,  the  opinions,  feelings,  and  habits,  of  the 
people,  though  greatly  the  results  of  the  state  of  society  which  precedes 

* The  quotations  in  this  paragraph  are  from  a paper  written  by  the  author,  and  published 
in  a periodical  in  1834. 


PHYSICAL  METHOD. 


627 


them,  are  also  greatly  the  causes  of  the  state  of  society  which  follows  them ; 
and  are  the  power  by  which  all  those  of  the  circumstances  of  society  which 
are  artificial,  laws  and  customs  for  instance,  are  altogether  moulded:  cus- 
toms evidently,  laws  no  less  really,  either  by  the  direct  influence  of  public 
sentiment  upon  the  ruling  powers,  or  by  the  effect  which  the  state  of  na- 
tional opinion  and  feeling  has  in  determining  the  form  of  government  and 
shaping  the  character  of  the  governors. 

As  might  be  expected,  the  most  imperfect  part  of  those  branches  of  social 
inquiry  which  have  been  cultivated  as  separate  sciences,  is  the  theory  of  the 
manner  in  which  their  conclusions  are  affected  by  ethological  considerations. 
The  omission  is  no  defect  in  them  as  abstract  or  hypothetical  sciences,  but 
it  vitiates  them  in  their  practical  application  as  branches  of  a comprehen- 
sive social  science.  In  political  economy,  for  instance,  empirical  laws  of  hu- 
man nature  are  tacitly  assumed  by  English  thinkers,  which  are  calculated 
only  for  Great  Britain  and  the  United  States.  Among  other  things,  an  in- 
tensity of  competition  is  constantly  supposed,  which,  as  a general  mercan- 
tile fact,  exists  in  no  country  in  the  world  except  those  two.  An  English 
political  economist,  like  his  countrymen  in  general,  has  seldom  learned  that 
it  is  possible  that  men,  in  conducting  the  business  of  selling  their  goods 
over  a counter,  should  care  more  about  their  ease  or  their  vanity  than  about 
their  pecuniary  gain.  Yet  those  who  know  the  habits  of  the  continent  of 
Europe  are  aware  how  apparently  small  a motive  often  outweighs  the  desire 
of  money  getting,  even  in  the  operations  which  have  money  getting  for  their 
direct  object.  The  more  highly  the  science  of  ethology  is  cultivated,  and 
the  better  the  diversities  of  individual  and  national  character  are  under- 
stood, the  smaller,  probably,  will  the  number  of  propositions  become,  which 
it  will  be  considered  safe  to  build  on  as  universal  principles  of  human  na- 
ture. 

These  considerations  show  that  the  process  of  dividing  off  the  social 
science  into  compartments,  in  order  that  each  may  be  studied  separately, 
and  its  conclusions  afterward  corrected  for  practice  by  the  modifications 
supplied  by  the  others,  must  be  subject  to  at  least  one  important  limitation. 
Those  portions  alone  of  the  social  phenomena  can  with  advantage  be  made 
the  subjects,  even  provisionally,  of  distinct  branches  of  science,  into  which 
the  diversities  of  character  between  different  nations  or  different  times  en- 
ter as  influencing  causes  only  in  a secondary  degree.  Those  phenomena, 
on  the  contrary,  with  which  the  influences  of  the  ethological  state  of  the 
people  are  mixed  up  at  every  step  (so  that  the  connection  of  effects  and 
causes  can  not  be  even  rudely  marked  out  without  taking  those  influences 
into  consideration)  could  not  writh  any  advantage,  nor  without  great  disad- 
vantage, be  treated  independently  of  political  ethology,  nor,  therefore,  of  all 
the  circumstances  by  which  the  qualities  of  a people  are  influenced.  For 
this  reason  (as  well  as  for  others  which  will  hereafter  appear)  there  can  be 
no  separate  Science  of  Government ; that  being  the  fact  which,  of  all  oth- 
ers, is  most  mixed  up,  both  as  cause  and  effect,  with  the  qualities  of  the  par- 
ticular people  or  of  the  particular  age.  All  questions  respecting  the  tend- 
encies of  forms  of  government  must  stand  part  of  the  general  science  of 
society,  not  of  any  separate  branch  of  it. 

This  general  Science  of  Society,  as  distinguished  from  the  separate  de- 
partments of  the  science  (each  of  which  asserts  its  conclusions  only  con- 
ditionally, subject  to  the  paramount  control  of  the  laws  of  the  general  sci- 
ence) now  remains  to  be  characterized.  And  as  will  be  shown  presently, 
nothing  of  a really  scientific  character  is  here  possible,  except  by  the  inverse 


628  LOGIC  OF  THE  MORAL  SCIENCES. 

deductive  method.  But  before  we  quit  the  subject  of  those  sociological 
speculations  which  proceed  by  wav  of  direct  deduction,  we  must  examine 
in  what  relation  they  stand  to  that  indispensable  element  in  all  deductive 
sciences,  Verification  by  Specific  Experience — comparison  between  the  con- 
clusions of  reasoning  and  the  results  of  observation. 

§ 5.  We  have  seen  that,  in  most  deductive  sciences,  and  among  the  rest 
in  Ethology  itself,  which  is  the  immediate  foundation  of  the  Social  Science, 
a preliminary  work  of  preparation  is  performed  on  the  observed  facts,  to 
fit  them  for  being  rapidly  and  accurately  collated  (sometimes  even  for 
being  collated  at  all)  with  the  conclusions  of  theory.  This  preparatory 
treatment  consists  in  finding  general  propositions  which  express  concisely 
what  is  common  to  large  classes  of  observed  facts;  and  these  are  called  the 
empirical  laws  of  the  phenomena.  We  have,  therefore,  to  inquire,  whether 
any  similar  preparatory  process  can  be  performed  on  the  facts  of  the  social 
science;  whether  there  are  any  empirical  laws  in  history  or  statistics. 

In  statistics,  it  is  evident  that  empirical  laws  may  sometimes  be  traced; 
and  the  tracing  them  forms  an  important  part  of  that  system  of  indirect 
observation  on  which  we  must  often  rely  for  the  data  of  the  Deductive 
Science.  The  process  of  the  science  consists  in  inferring  effects  from  their 
causes  ; but  we  have  often  no  means  of  observing  the  causes,  except  through 
the  medium  of  their  effects.  In  such  cases  the  deductive  science  is  unable 
to  predict  the  effects,  for  want  of  the  necessary  data;  it  can  determine 
what  causes  are  capable  of  producing  any  given  effect,  but  not  with  what 
frequency  and  in  what  quantities  those  causes  exist.  An  instance  in  point 
is  afforded  by  a newspaper  now  lying  before  me.  A statement  was  fur- 
nished by  one  of  the  official  assignees  in  bankruptcy  showing  among  the 
various  bankruptcies  which  it  had  been  his  duty  to  investigate,  in  how 
many  cases  the  losses  had  been  caused  by  misconduct  of  different  kinds, 
and  in  how  many  by  unavoidable  misfortunes.  The  result  was,  that  the 
number  of  failures  caused  by  misconduct  greatly  preponderated  over  those 
arising  from  all  other  causes  whatever.  Nothing  but  specific  experience 
could  have  given  sufficient  ground  for  a conclusion  to  this  purport.  To 
collect,  therefore,  such  empirical  laws  (which  are  never  more  than  approx- 
imate generalizations)  from  direct  observation,  is  an  important  part  of  the 
process  of  sociological  inquiry. 

The  experimental  process  is  not  here  to  be  regarded  as  a distinct  road  to 
the  truth,  but  as  a means  (happening  accidentally  to  be  the  only,  or  the  best, 
available)  for  obtaining  the  necessary  data  for  the  deductive  science.  - When 
the  immediate  causes  of  social  facts  are  not  open  to  direct  observation,  the 
/empirical  law  of  the  effects  gives  us  the  empirical  law  (which  in  that  case 
is  all  that  we  can  obtain)  of  the  causes  likewise.  But  those  immediate 
causes  depend  on  remote  causes ; and  the  empirical  law,  obtained  by  this 
indirect  mode  of  observation,  can  only  be  relied  on  as  applicable  to  unob- 
served cases,  so  long  as  there  is  reason  to  think  that  no  change  has  taken 
place  in  any  of  the  remote  causes  on  which  the  immediate  causes  depend. 
In  making  use,  therefore,  of  even  the  best  statistical  generalizations  for  the 
purpose  of  inferring  (though  it  be  only  conjecturally)  that  the  same  em- 
pirical laws  will  hold  in  any  new  case,  it  is  necessary  that  wo  be  well  ac- 
quainted with  the  remoter  causes,  in  order  that  we  may  avoid  applying  the 
empirical  law  to  cases  which  differ  in  any  of  the  circumstances  on  which 
the  truth  of  the  law  ultimately  depends.  And  thus,  even  where  conclu- 
sions derived  from  specific  observation  are  available  for  practical  infer- 


\ 

i 


PHYSICAL  METHOD. 


629 


ences  in  new  cases,  it  is  necessary  that  the  deductive  science  should  stand 
sentinel  over  the  whole  process ; that  it  should  be  constantly  referred  to, 
and  its  sanction  obtained  to  every  inference. 

The  same  thing  holds  true  of  all  generalizations  which  can  be  grounded 
on  history.  Not  only  there  are  such  generalizations,  but  it  will  presently 
be  shown  that  the  general  science  of  society,  which  inquires  into  the  laws 
of  succession  and  co-existence  of  the  great  facts  constituting  the  state  of 
society  and  civilization  at  any  time,  can  proceed  in  no  other  manner  than 
by  making  such  generalizations — afterward  to  be  confirmed  by  connecting 
them  with  the  psychological  and  ethological  laws  on  which  they  must 
really  depend. 

§ 6.  But  (reserving  this  question  for  its  proper  place)  in  those  more  special 
inquiries  which  form  the  subject  of  the  separate  branches  of  the  social  sci- 
ence, this  twofold  logical  process  and  reciprocal  verification  is  not  possible ; 
specific  experience  affords  nothing  amounting  to  empirical  laws.  This  is 
particularly  the  case  where  the  obj’ect  is  to  determine  the  effect  of  any  one 
social  cause  among  a great  number  acting  simultaneously;  the  effect,  for 
example,  of  corn  laws,  or  of  a prohibitive  commercial  system  generally. 
Though  it  may  be  perfectly  certain,  from  theory,  what  kind  of  effects  corn 
laws  must  produce,  and  in  what  general  direction  their  influence  must  tell 
upon  industrial  prosperity,  their  effect  is  yet  of  necessity  so  much  dis- 
guised by  the  similar  or  contrary  effects  of  other  influencing  agents,  that 
specific  experience  can  at  most  only  show  that  on  the  average  of  some 
great  number  of  instances,  the  cases  where  there  were  corn  laws  exhibited 
the  effect  in  a greater  degree  than  those  where  there  were  not.  Now  the 
number  of  instances  necessary  to  exhaust  the  whole  round  of  combinations 
of  the  various  influential  circumstances,  and  thus  afford  a fair  average,  nev- 
er can  be  obtained.  Not  only  we  can  never  learn  with  sufficient  authen- 
ticity the  facts  of  so  many  instances,  but  the  world  itself  does  not  afford 
them  in  sufficient  numbers,  within  the  limits  of  the  given  state  of  society 
and  civilization  which  such  inquiries  always  presuppose.  Having  thus  no 
previous  empirical  generalizations  with  which  to  collate  the  conclusions  of 
theory,  the  only  mode  of  direct  verification  which  remains  is  to  compare 
those  conclusions  with  the  result  of  an  individual  experiment  or  instance. 
But  here  the  difficulty  is  equally  great.  For  in  order  to  verify  a theory  by 
an  experiment,  the  circumstances  of  the  experiment  must  be  exactly  the 
same  with  those  contemplated  in  the  theory.  But  in  social  phenomena  the 
circumstances  of  no  two  cases  are  exactly  alike.  A trial  of  corn  laws  in  an-, 
other  country,  or  in  a former  generation,  would  go  a very  little  way  toward, 
verifying  a conclusion  drawn  respecting  their  effect  in  this  generation  and 
in  this  country.  It  thus  happens,  in  most  cases,  that  the  only  individual 
instance  really  fitted  to  verify  the  predictions  of  theory  is  the  very  instance 
for  which  the  predictions  were  made;  and  the  verification  comes  too  late 
to  be  of  any  avail  for  practical  guidance. 

Although,  however,  direct  verification  is  impossible,  there  is  an  indirect 
verification,  which  is  scarcely  of  less  value,  and  which  is  always  practica- 
ble. The  conclusion  drawn  as  to  the  individual  case  can  only  be  directly 
verified  in  that  case;  but  it  is  verified  indirectly,  by  the  verification  of  other 
conclusions,  drawn  in  other  individual  cases  from  the  same  laws.  ' The  ex- 
perience which  comes  too  late  to  verify  the  particular  proposition  to  which 
it  refers,  is  not  too  late  to  help  toward  verifying  the  general  sufficiency 
of  the  theory.  ' The  test  of  the  degree  in  which  the  science  affords  safe 


630 


LOGIC  OF  THE  MORAL  SCIENCES. 


ground  for  predicting  (and  consequently  for  practically  dealing  with)  what 
lias  not  yet  happened,  is  the  degree  in  which  it  would  have  enabled  us  to 
predict  what  has  actually  occurred.  Before  our  theory  of  the  influence  of 
a particular  cause,  in  a given  state  of  circumstances,  can  be  entirely  trust- 
ed, we  must  be  able  to  explain  and  account  for  the  existing  state  of  all 
that  portion  of  the  social  phenomena  which  that  cause  has  a tendency  to 
influence.  If,  for  instance,  we  would  apply  our  speculations  in  political 
economy  to  the  prediction  or  guidance  of  the  phenomena  of  any  country, 
we  must  be  able  to  explain  all  the  mercantile  or  industrial  facts  of  a gen- 
eral character,  appertaining  to  the  present  state  of  that  country ; to  point 
out  causes  sufficient  to  account  for  all  of  them,  and  prove,  or  show  good 
ground  for  supposing,  that  these  causes  have  really  existed.  If  we  can 
not  do  this,  it  is  a proof  either  that  the  facts  which  ought  to  be  taken  into 
account  are  not  yet  completely  known  to  us,  or  that  although  we  know  the 
facts,  we  are  not  masters  of  a sufficiently  perfect  theory  to  enable  us  to 
assign  their  consequences.  In  either  case  we  are  not,  in  the  present  state 
of  our  knowledge,  fully  competent  to  draw  conclusions,  speculative  or 
practical,  for  that  country.  In  like  manner,  if  we  would  attempt  to  judge 
of  the  effect  which  any  political  institution  would,  have,  supposing  that  it 
could  be  introduced  into  any  given  country,  we  must  be  able  to  show  that 
the  existing  state  of  the  practical  government  of  that  country,  and  of 
whatever  else  depends  thereon,  together  with  the  particular  character  and 
tendencies  of  the  people,  and  their  state  in  respect  to  the  various  elements 
of  social  well-being,  are  such  as  the  institutions  they  have  lived  under,  in 
conjunction  with  the  other  circumstances  of  their  nature  or  of  their  posi- 
tion, were  calculated  to  produce. 

To  prove,  in  short,  that  our  science,  and  our  knowledge  of  the  particu- 
lar case,  render  us  competent  to  predict  the  future,  we  must  show  that 
they  would  have  enabled  us  to  predict  the  present  and  the  past.  If  there 
be  any  thing  which  we  could  not  have  predicted,  this  constitutes  a resid- 
ual phenomenon,  requiring  further  study  for  the  purpose  of  explanation; 
and  we  must  either  search  among  the  circumstances  of  the  particular  case 
until  we  find  one  which,  on  the  principles  of  our  existing  theory,  accounts 
for  the  unexplained  phenomenon,  or  we  must  turn  back,  and  seek  the  ex- 
planation by  an  extension  and  improvement  of  the  theory  itself. 


CHAPTER  X. 

OF  THE  INVERSE  DEDUCTIVE,  OR  HISTORICAL,  METHOD. 

§ 1.  There  are  two  kinds  of  sociological  inquiry.  Tn  the  first  kind,  the 
question  proposed  is,  what  effect  will  follow  from  a given  cause,  a certain 
general  condition  of  social  circumstances  being  presupposed.  As,  for  ex- 
ample, what  would  be  the  effect  of  imposing  or  of  repealing  corn  laws,  of 
abolishing  monarchy  or  introducing  universal  suffrage,  in  the  present  con- 
dition of  society  and  civilization  in  any  European  country,  or  under  any 
other  given  supposition  with  regard  to  the  circumstances  of  society  in  gen- 
eral, without  reference  to  the  changes  which  might  jnke  place,  or  which 
may  already  be  in  progress,  in  those  circumstances.  But  there  is  also  a 
second  inquiry,  namely,  wh^t  are  the  laws  which  determine  those  general 
circumstances  themselves.  In  this  last  the  question  is,  not  what  will  be 
the  effect  of  a given  cause  in  a certain  state  of  society,  but  what  are  the 


HISTORICAL  METHOD. 


631 


causes  which  produce,  and  the  phenomena  which  characterize,  states  of 
society  generally.  * In  the  solution  of  this  question  consists  the  general 
Science  of  Society ; by  which  the  conclusions  of  the  other  and  more  spe- 
cial kind  of  inquiry  must  be  limited  and  controlled. 

§ 2.  In  order  to  conceive  correctly  the  scope  of  this  general  science,  and 
distinguish  it  from  the  subordinate  departments  of  sociological  specula- 
tion, it  is  necessary  to  fix  the  ideas  attached  to  the  phrase,  “A  State  of  So- 
ciety.” What  is  called  a state  of  society,  is  the  simultaneous  state  of  all 
the  greater  social  facts  or  phenomena.  Such  are : the  degree  of  knowl- 
edge, and  of  intellectual  and  moral  culture,  existing  in  the  community,  and 
in  every  class  of  it;  the  state  of  industry,  of  wealth  and  its  distribution; 
the  habitual  occupations  of  the  community  ; their  division  into  classes,  and 
the  relations  of  those  classes  to  one  another;  the  common  beliefs  which 
they  entertain  on  all  the  subjects  most  important  to  mankind,  and  the  de- 
gree of  assurance  with  which  those  beliefs  are  held ; their  tastes,  and  the 
character  and  degree  of  their  esthetic  development;  their  form  of  govern- 
ment, and  the  more  important  of  their  laws  and  customs.  The  condition  of 
all  these  things,  and  of  many  more  which  will  readily  suggest  themselves, 
constitute  the  state  of  society,  or  the  state  of  civilization,  at  any  given  time. 

When  states  of  society,  and  the  causes  which  produce  them,  are  spoken 
of  as  a subject  of  science,  it  is  implied  that  there  exists  a natural  correla- 
tion among  these  different  elements ; that  not  every  variety  of  combina- 
tion of  these  general  social  facts  is  possible,  but  only  certain  combinations; 
that,  in  short,  there  exist  Uniformities  of  Co-existence  between  the  states 
of  the  various  social  phenomena.  And  such  is  the  truth;  as  is  indeed  a 
necessary  consequence  of  the  influence  exercised  by  every  one  of  those 
phenomena  over  every  other.  It  is  a fact  implied  in  the  consensus  of  the 
various  parts  of  the  social  body. 

States  of  society  are  like  different  constitutions  or  different  ages  in  the 
physical  frame ; they  are  conditions  not  of  one  or  a few  organs  or  func- 
tions, but  of  the  whole  organism.  Accordingly,  the  information  which  we 
possess  respecting  past  ages,  and  respecting  the  various  states  of  society 
now  existing  in  different  regions  of  the  earth,  does,  when  duly  analyzed, 
exhibit  uniformities.  It  is  found  that  when  one  of  the  features  of  society 
is  in  a particular  state,  a state  of  many  other  features,  more  or  less  precise- 
ly determinate,  always  or  usually  co-exists  with  it. 

But  the  uniformities  of  co-existence  obtaining  among  phenomena  which 
are  effects  of  causes,  must  (as  we  have  so  often  observed)  be  corollaries 
from  the  laws  of  causation  by  which  these  phenomena  are  really  deter- 
mined. The  mutual  correlation  between  the  different  elements  of  each 
state  of  society,  is,  therefore,  a derivative  law,  resulting  from  the  laws 
which  regulate  the  succession  between  one  state  of  society  and  another; 
for  the  proximate  cause  of^every  state  of  society  is  the  state  of  society 
immediately  preceding  it.  The  fundamental  problem,  therefore,  of  the 
social  science,  is  to  find  the  laws  according  to  which  any  .state  of  society 
produces  the  state  which  succeeds  it  and  takes  its  place.  This  opens  the 
great  .and  vexed  question  of  the  progressiveness  of  man  and  society;  an 
idea  involved  in  every  just  conception  of  social  phenomena  as  the  subject 
of  a science. 

§ 3.  It  is  one  of  the  characters,  not  absolutely  peculiar  to  the  sciences 
of  human  nature  and  society,  but  belonging  to  them  in  a peculiar  degree, 


(532 


LOGIC  OF  THE  MORAL  SCIENCES. 


to  be  conversant  with  a subject-matter  whose  properties  are  changeable. 
I do  not  mean  changeable  from  day  to  day,  but  from  age  to  age;  so  that 
not  only  the  qualities  of  individuals  vary,  but  those  of  the  majority  are 
not  the  same  in  one  age  as  in  another. 

The  principal  cause  of  this  peculiarity  is  the  extensive  and  constant  re- 
action of  the  effects  upon  their  causes.  **The  circumstances  in  which  man- 
kind are  placed,  operating  according  to  their  own  laws  and  to  the  laws 
of  human  nature,  form  the  characters  of  the  human  beings;  but  the  human 
beings,  in  their  turn,  mould  and  shape  the  circumstances  for  themselves 
and  for  those  who  come  after  them.  ^ From  this  reciprocal  action  there 
must  necessarily  result  either  a cycle  or  a progress.  In  astronomy  also, 
every  fact  is  at  once  effect  and  cause ; the  successive  positions  of  the  vari- 
ous heavenly  bodies  produce  changes  both  in  the  direction  and  in  the  inten- 
sity of  the  forces  by  which  those  positions  are  determined.  But  in  the 
case  of  the  solar  system,  these  mutual  actions  bring  around  again,  after  a 
certain  number  of  changes,  the  former  state  of  circumstances ; which,  of 
course,  leads  to  the  perpetual  recurrence  of  the  same  series  in  an  unvarying 
order.  Those  bodies,  in  short,  revolve  in  orbits  : but  there  are  (or,  con- 
formably to  the  laws  of  astronomy,  there  might  be)  others  which,  instead  of 
an  orbit,  describe  a trajectory — a course  not  returning  into  itself.  One  or 
other  of  these  must  be  the  type  to  which  human  affairs  must  conform. 

One  of  the  thinkers  who  earliest  conceived  the  succession  of  historical 
events  as  subject  to  fixed  laws,  and  endeavored  to  discover  these  laws  by 
an  analytical  survey  of  history,  Vico,  the  celebrated  author  of  the  Scienza 
JVuova,  adopted  the  former  of  these  opinions.  He  conceived  the  phenom- 
ena of  human  society  as  revolving  in  an  orbit;  as  going  through  periodic- 
ally the  same  series  of  changes.  Though  there  were  not  wanting  circum- 
stances tending  to  give  some  plausibility  to  this  view,  it  would  not  bear 
a close  scrutiny:  and  those  who  have  succeeded  Vico  in  this  kind  of  spec- 
ulations have  universally  adopted  the  idea  of  a trajectory  or  progress,  in 
lieu  of  an  orbit  or  cycle. 

The  words  Progress  and  Progressiveness  are  not  here  to  be  understood 
as  synonymous  with  improvement  and  tendency  to  improvement.  It  is 
conceivable  that  the  laws  of  human  nature  might  determine,  and  even  ne- 
cessitate, a certain  series  of  changes  in  man  and  society,  which  might  not 
in  every  case,  or  which  might  not  on  the  whole,  be  improvements.  It  is 
tiiy  belief,  indeed,  that  the  general  tendency  is,  and  will  continue  to  be, 
(saving  occasional  and  temporary  exceptions,  one  of  improvement ; a tend- 
ency toward  a better  and  happier  state.  This,  however,  is  not  a question 
of  the  method  of  the  social  science,  but  a theorem  of  the  science  itself. 
"For  our  purpose  it  is  sufficient  that  there  is  a progressive  change  both  in 
the  character  of  the  human  race  and  in  their  outward  circumstances,  so  far 
as  moulded  by  themselves;  that  in  each  successive  age  the  principal  phe- 
nomena of  society  are  different  from  what  they  were  in  the  age  preceding, 
and  still  more  different  from  any  previous  age:  the  periods  which  most 
distinctly  mark  these  successive  changes  being  intervals  of  one  generation, 
during  which  a new  set  of  human  beings  have  been  educated,  have  grown 
up  from  childhood,  and  taken  possession  of  society. 

^The  progressiveness  of  the  human  race  is  the  foundation  on  which  a 
method  of  philosophizing  in  the  social  science  has  been  of  late  years  erect- 
ed, far  superior  to  either  of  the  two  modes  which  had  previously  been 
prevalent,  the  chemical  or  experimental,  and  the  geometrical  modes.  This 
method,  which  is  now  generally  adopted  by  the  most  advanced  thinkers 


HISTORICAL  METHOD. 


633 


on  the  Continent,  consists  in  attempting,  by  a study  and  analysis  of  the 
general  facts  of  history,  to  discover  (what  these  philosophers  term)  the  law 
of  progress : which  law,  once  ascertained,  must  according  to  them  enable 
us  to  predict  future  events,  just  as  after  a few  terms  of  an  infinite  series 
in  algebra  we  are  able  to  detect  the  principle  of  regularity  in  their  forma- 
tion, and  to  predict  the  rest  of  the  series  to  any  number  of  terms  we  please. 
The  principal  aim  of  historical  speculation  in  France,  of  late  years,  has  , 
been  to  ascertain  this  law.  But  while  I gladly  acknowledge  the  great  serv- 
ices which  have  been  rendered  to  historical  knowledge  by  this  school,  I 
can  not  but  deem  them  to  be  mostly  chargeable  with  a fundamental  mis- 
conception of  the  true  method  of  social  philosophy.  The  misconception 
consists  in  supposing  that  the  order  of  succession  which  we  may  be  able 
to  trace  among  the  different  states  of  society  and  civilization  which  history 
presents  to  us,  even  if  that  order  were  more  rigidly  uniform  than  it  has 
yet  been  proved  to  be,  could  ever  amount  to  a law  of  nature.  It  can  only 
be  an  empirical  law.  The  succession  of  states  of  the  human  mind  and  of 
human  society  can  not  have  an  independent  law  of  its  own;  it  must  de- 
pend on  the  psychological  and  ethological  laws  which  govern  the  action  of 
circumstances  on  men  and  of  men  on  circumstances.  It  is  conceivable 
that  those  laws  might  be  such,  and  the  general  circumstances  of  the  human 
race  such,  as  to  determine  the  successive  transformations  of  man  and  society 
to  one  given  and  unvarying  order.  But  even  if  the  case  were  so,  it  can  not 
be  the  ultimate  aim  of  science  to  discover  an  empirical  law.  Until  that' 
law  could  be  connected  with  the  psychological  and  ethological  laws  on 
which  it  must  depend,  and,  by  the  consilience  of  deduction  a priori  with 
historical  evidence,  could  be  converted  from  an  empirical  law  into  a scien- 
tific one,  it  could  not  be  relied  on  for  the  prediction  of  future  events,  be- 
yond, at  most,  strictly  adjacent  cases,  M.  Comte  alone,  among  the  new 
historical  school,  has  seen  the  necessity  of  thus  connecting  all  our  generali- 
zations from  history  with  the  laws  of  human  nature. 

§ 4.  But,  while  it  is  an  imperative  rule  never  to  introduce  any  generali- 
zation from  history  into  the  social  science  unless  sufficient  grounds  can 
be  pointed  out  for  it  in  human  nature,  I do  not  think  any  one  will  contend 
that  it  would  have  been  possible,  setting  out  from  the  principles  of  human 
nature  and  from  the  general  circumstances  of  the  position  of  our  species,  to 
determine  a priori  order  in  which  human  development  must  take  place, 
and  to  predict,  consequently,  the  general  facts  of  history  up  to  the  presf 
ent  time.  After  the  first  few  terms  of  the  series,  the  influence  exercised 
over  each  generation  by  the  generations  which  preceded  it,  becomes  (as  is 
well  observed  by  the  writer  last  referred  to)  more  and  more  preponder- 
ant over  all  other  influences ; until  at  length  what  we  now  are  and  do,  is  in 
a very  small  degree  the  result  of  the  universal  circumstances  of  the  human 
race,  or  even  of  our  own  circumstances  acting  through  the  original  quali- 
ties of  our  species,  but  mainly  of  the  qualities  produced  in  us  by  the  whole 
previous  history  of  humanity.  So  long  a series  of  actions  and  reactions 
between  Circumstances  and  Man,  each  successive  term  being  composed  of 
an  ever  greater  number  and  variety  of  parts,  could  not  possibly  be  com- 
puted by  human  faculties  from  the  elementary  laws  which  produce  it.  The 
mere  length  of  the  series  would  be  a sufficient  obstacle,  since  a slight  error 
in  any  one  of  the  terms  would  augment  in  rapid  progression  at  every  sub- 
sequent step. 

If,  therefore,  the  series  of  the  effects  themselves  did  not,  when  examined 


634 


LOGIC  OF  THE  MORAL  SCIENCES. 


as  a whole,  manifest  any  regularity,  we  should  in  vain  attempt  to  construct 
a general  science  of  society.  We  must  in  that  case  have  contented  our- 
selves with  that  subordinate  order  of  sociological  speculation  formerly  no- 
ticed, namely,  with  endeavoring  to  ascertain  what  would  be  the  effect  of 
'the  introduction  of  any  new  cause,  in  a state  of  society  supposed  to  be  fix- 
'ed — a knowledge  sufficient  for  the  more  common  exigencies  of  daily  polit- 
ical practice,  but  liable  to  fail  in  all  cases  in  which  the  progressive  move- 
ment of  society  is  one  of  the  influencing  elements ; and  therefore  more 
precarious  in  proportion  as  the  case  is  more  important.  But  since  both  the 
natural  varieties  of  mankind,  and  the  original  diversities  of  local  circum- 
stances, are  much  less  considerable  than  the  points  of  agreement,  there  will 
naturally  be  a certain  degree  of  uniformity  in  the  progressive  development 
of  the  species  and  of  its  works.  And  this  uniformity  tends  to  become 
greater,  not  less,  as  society  advances ; since  the  evolution  of  each  people, 
which  is  at  first  determined  exclusively  by  the  nature  and  circumstances 
of  that  people,  is  gradually  brought  under  the  influence  (which  becomes 
stronger  as  civilization  advances)  of  the  other  nations  of  the  earth,  and  of 
the  circumstances  by  which  they  have  been  influenced.  History  accord- 
ingly does,  when  judiciously  examined,  afford  Empirical  Laws  of  Society. 
And  the  problem  of  general  sociology  is  to  ascertain  these,  and  connect 
them  with  the  laws  of  human  nature,  by  deductions  showing  that  such 
were  the  derivative  laws  naturally  to  be  expected  as  the  consequences  of 
those  ultimate  ones. 

It  is,  indeed,  hardly  ever  possible,  even  after  history  has  suggested  the 
derivative  law,  to  demonstrate  a priori  that  such  was  the  only  order  of 
succession  or  of  co-existence  in  which  the  effects  could,  consistently  with 
the  laws  of  human  nature,  have  been  produced.  We  can  at  most  make  out 
that  there  were  strong  a priori  reasons  for  expecting  it,  and  that  no  other 
order  of  succession  or  co-existence  would  have  been  so  likely  to  result  from 
the  nature  of  man  and  the  general  circumstances  of  his  position.  Often 
we  can  not  do  even  this;  we  can  not  even  show  that  what  did  take  place 
was  probable  a priori , but  only  that  it  was  possible.  This,  however — 
which,  in  the  Inverse  Deductive  Method  that  we  are  now  characterizing,  is 
a real  process  of  verification — -is  as  indispensable,  as  verification  by  specific 
experience  has  been  shown  to  be,  where  the  conclusion  is  originally  obtain- 
ed by  the  direct  way  of  deduction.  The  empirical  laws  must  be  the  result 
of  but  a few  instances,  since  few  nations  have  ever  attained  at  all,  and  still 
fewer  by  their  own  independent  development,  a high  stage  of  social  prog- 
ress. If,  therefore,  even  one  or  two  of  these  few  instances  be  insufficiently 
known,  or  imperfectly  analyzed  into  their  elements,  and  therefore  not  ade- 
quately compared  with  other  instances,  nothing  is  more  probable  than  that 
a wrong  empirical  law  will  emerge  instead  of  the  right  one.  Accordingly, 
the  most  erroneous  generalizations  are  continually  made  from  the  course  of 
history ; not  only  in  this  country,  where  history  can  not  yet  be  said  to  be 
at  all  cultivated  as  a science,  but  in  other  countries  where  it  is  so  culti- 
vated, and  by  persons  well  versed  in  it.  The  only  check  or  corrective  is, 
constant  verification  by  psychological  and  ethological  laws.  We  may  add 
to  this,  that  no  one  but  a person  competently  skilled  in  those  laws  is 
capable  of  preparing  the  materials  for  historical  generalization,  by  analyz- 
ing the  facts  of  history,  or  even  by  observing  the  social  phenomena  of  his 
own  time.  No  other  will  be  aware  of  the  comparative  importance  of  dif- 
ferent facts,  nor  consequently  know  what  facts  to  look  for,  or  to  observe ; 
still  less  will  he  be  capable  of  estimating  the  evidence  of  facts  which,  as  is 


HISTORICAL  METHOD. 


635 


the  case  with  most,  can  not  be  ascertained  by  direct  observation  or  learned 
from  testimony,  but  must  be  inferred  from  marks. 

§ 5.  The  Empirical  Laws  of  Society  are  of  two  kinds ; some  are  uni- 
formities of  co-existence,  some  of  succession.  According  as  the  science  is 
occupied  in  ascertaining  and  verifying  the  former  sort  of  uniformities  or 
the  latter,  M.  Comte  gives  it  the  title  of  Social  Statics,  or  of  Social  Dy- 
namics ; conformably  to  the  distinction  in  mechanics  between  the  condi- 
tions of  equilibrium  and  those  of  movement;  or  in  biology,  between  the 
laws  of  organization  and  those  of  life.  The  first  branch  of  the  science  as- 
certains the  conditions  of  stability  in  the  social  union ; the  second,  the  laws 
of  progress.  Social  Dynamics  is  the  theory  of  Society  considered  in  a 
state  of  progressive  movement;  while  Social  Statics  is  the  theory  of  the 
cojisensus  already  spoken  of  as  existing  among  the  different  parts  of  the 
social  organism ; in  other  words,  the  theory  of  the  mutual  actions  and  re- 
actions of  contemporaneous  social  phenomena;  “ making*  provisionally,  as 
far  as  possible,  abstraction,  for  scientific  purposes,  of  the  fundamental  move- 
ment which  is  at  all  times  gradually  modifying  the  whole  of  them. 

“ In  this  first  point  of  view,  the  provisions  of  sociology  will  enable  us  to 
infer  one  from  another  (subject  to  ulterior  verification  by  direct  observa- 
tion) the  various  characteristic  marks  of  each  distinct  mode  of  social  ex- 
istence, in  a manner  essentially  analogous  to  what  is  now  habitually  prac- 
ticed in  the  anatomy  of  the  physical  body.  This  preliminary  aspect,  there- 
fore, of  political  science,  of  necessity  supposes  that  (contrary  to  the  exist- 
ing habits  of  philosophers)  each  of  the  numerous  elements  of  the  social 
state,  ceasing  to  be  looked  at  independently  and  absolutely,  shall  be  al- 
ways and  exclusively  considered  relatively  to  all  the  other  elements,  with 
the  whole  of  which  it  is  united  by  mutual  interdependence.  It  would  be 
superfluous  to  insist  here  upon  the  great  and  constant  utility  of  this  branch 
of  sociological  speculation.  It  is,  in  the  first  place,  the  indispensable  basis 
of  the  theory  of  Social  progress.  It  may,  moreover,  be  employed,  immedi- 
ately, and  of  itself,  to  supply  the  place,  provisionally  at  least,  of  direct  ob- 
servation, which  in  many  cases  is  not  always  practicable  for  some  of  the 
elements  of  society,  the  real  condition  of  which  may,  however,  be  sufficient- 
ly judged  of  by  means  of  the  relations  which  connect  them  with  others 
previously  known.  The  history  of  the  sciences  may  give  us  some  notion 
of  the  habitual  importance  of  this  auxiliary  resource,  by  reminding  us,  for 
example,  how  the  vulgar  errors  of  mere  erudition  concerning  the  pretend) 
ed  acquirements  of  the  ancient  Egyptians  in  the  higher  astronomy  were 
irrevocably  dissipated  (even  before  sentence  had  been  passed  on  them  by 
a sounder  erudition)  from  the  single  consideration  of  the  inevitable  con- 
nection between  the  general  state  of  astronomy  and  that  of  abstract  ge- 
ometry, then  evidently  in  its  infancy.  It  would  be  easy  to  cite  a multi- 
tude of  analogous  cases,  the  character  of  which  could  admit  of  no  dispute. 
In  order  to  avoid  exaggeration,  however,  it  should  be  remarked,  that  these 
necessary  relations  among  the  different  aspects  of  society  can  not,  from 
their  very  nature,  be  so  simple  and  precise  that  the  results  observed  could 
only  have  arisen  from  some  one  mode  of  mutual  co-ordination.  Such  a 
notion,  already  too  narrow  in  the  science  of  life,  would  be  completely  at 
variance  with  the  still  more  complex  nature  of  sociological  speculations. 
But  the  exact  estimation  of  these  limits  of  variation,  both  in  the  healthy 


Cours  de  Philosophie  Positive,  iv.,  325-29. 


G36 


LOGIC  OF  THE  MORAL  SCIENCES. 


find  in  the  morbid  state,  constitutes,  at  least  as  much  as  in  the  anatomy  of 
the  natural  body,  an  indispensable  complement  to  every  theory  of  Socio- 
logical Statics;  without  which  the  indirect  exploration  above  spoken  of 
would  often  lead  into  error. 

^ “This  is  not  the  place  for  methodically  demonstrating  the  existence  of 
a necessary  relation  among  all  the  possible  aspects  of  the  same  social  or- 
ganism ; a point  on  which,  in  principle  at  least,  there  is  now  little  difference 
of  opinion  among  sound  thinkers.  ^ From  whichever  of  the  social  elements 
we  choose  to  set  out,  we  may  easily  recognize  that  it  has  always  a connec- 
tion, more  or  less  immediate,  with  all  the  other  elements,  even  with  those 
which  at  first  sight  appear  the  most  independent  of  it.  The  dynamic- 
al consideration  of  the  progressive  development  of  civilized  humanity,  af- 
fords, no  doubt,  a still  more  efficacious  means  of  effecting  this  interesting 
verification  of  the  consensus  of  the  social  phenomena,  by  displaying  the 
manner  in  which  every  change  in  any  one  part,  operates  immediately,  or 
very  speedily,  upon  all  the  rest.  But  this  indication  may  be  preceded,  or 
at  all  events  followed,  by  a confirmation  of  a purely  statical  kind ; for,  in 
politics  as  in  mechanics,  the  communication  of  motion  from  one  object  to 
another  proves  a connection  between  them.  ^Without  descending  to  the 
minute  interdependence  of  the  different  branches  of  any  one  science  or 
art,  is  it  not  evident  that  among  the  different  sciences,  as  well  as  among 
most  of  the  arts,  there  exists  such  a connection,  that  if  the  state  of  any  one 
well-marked  division  of  them  is  sufficiently  known  to  us,  we  can  with  real 
scientific  assurance  infer,  from  their  necessary  correlation,  the  contempo- 
raneous state  of  every  one  of  the  others  ? By  a further  extension  of  this 
consideration,  we  may  conceive  the  necessary  relation  which  exists  be- 
tween the  condition  of  the  sciences  in  general  and  that  of  the  arts  in  gen- 
eral, except  that  the  mutual  dependence  is  less  intense  in  proportion  as  it 
is  more  indirect.  The  same  is  the  case,  when,  instead  of  considering  the 
aggregate  of  the  social  phenomena  in  some  one  people,  we  examine  it  si- 
multaneously in  different  contemporaneous  nations;  between  which  the 
perpetual  reciprocity  of  influence,  especially  in  modern  times,  can  not  be 
contested,  though  the  consensus  must  in  this  case  be  ordinarily  of  a less 
decided  character,  and  must  decrease  gradually  with  the  affinity  of  the 
cases  and  the  multiplicity  of  the  points  of  contact,  so  as  at  last,  in  some 
cases,  to  disappear  almost  entirely;  as  for,  example,  between  Western  Eu- 
rope and  Eastern  Asia,  of  which  the  various  general  states  of  society  ap- 
pear to  have  been  hitherto  almost  independent  of  one  another. 

These  remarks  are  followed  by  illustrations  of  one  of  the  most  impor- 
tant, and  until  lately,  most  neglected,  of  the  general  principles  which,  in 
this  division  of  the  social  science, may  be  considered  as  established;  name- 
ly, the  necessary  correlation  between  the  form  of  government  existing  in 
any  society  and  the  contemporaneous  state  of  civilization:  a natural  law 
which  stamps  the  endless  discussions  and  innumerable  theories  respecting 
forms  of  government  in  the  abstract,  as  fruitless  and  worthless,  for  any 
other  purpose  than  as  a preparatory  treatment  of  materials  to  be  after- 
ward used  for  the  construction  of  a better  philosophy. 

As  already  remarked,  one  of  the  main  results  of  the  science  of  social 
statics  would  be  to  ascertain  the  requisites  of  stable  political  union.  There 
are  some  circumstances  which,  being  found  in  all  societies  without  excep- 
tion, and  in  the  greatest  degree  where  the  social  union  is  most  complete, 
may  be  considered  (when  psychological  and  ethological  laws  confirm  the 
indication)  as  conditions  of  the  existence  of  the  complex  phenomena  called 


HISTORICAL  METHOD. 


637 


a State.  For  example,  no  numerous  society  has  ever  been  held  together 
without  laws,  or  usages  equivalent  to  them;  without  tribunals,  and  an  or- 
ganized force  of  some  sort  to  execute  their  decisions.  There  have  always 
been  public  authorities  whom,  with  more  or  less  strictness  and  in  cases 
more  or  less  accurately  defined,  the  rest  of  the  community  obeyed,  or  ac- 
cording to  general  opinion  were  bound  to  obey.  By  following  out  this 
course  of  inquiry  we  shall  find  a number  of  requisites,  which  have  been 
present  in  every  society  that  has  maintained  a collective  existence,  and  on 
the  cessation  of  which  it  has  either  merged  in  some  other  society,  or  re- 
constructed itself  on  some  new  basis,  in  which  the  conditions  were  con- 
formed to.  Although  these  results,  obtained  by  comparing  different  forms 
and  states  of  society,  amount  in  themselves  only  to  empirical  laws;  some 
of  them,  when  once  suggested,  are  found  to  follow  with  so  much  proba- 
bility from  general  laws  of  human  nature,  that  the  consilience  of  the  two 
processes  raises  the  evidence  to  proof,  and  the  generalizations  to  the  rank 
of  scientific  truths. 

This  seems  to  be  affirm  able  (for  instance)  of  the  conclusions  arrived  at 
in  the  following  passage,  extracted,  with  some  alterations,  from  a criticism 
on  the  negative  philosophy  of  the  eighteenth  century,*  and  which  I quote, 
though  (as  in  some  former  instances)  from  myself,  because  I have  no  bet- 
ter way  of  illustrating  the  conception  I have  formed  of  the  kind  of  theo- 
rems of  which  sociological  statics  would  consist. 

“The  very  first  element  of  the  social  union,  obedience  to  a government 
of  some  sort,  has  not  been  found  so  easy  a thing  to  establish  in  the  world. 
Among  a timid  and  spiritless  race  like  the  inhabitants  of  the  vast  plains  of 
tropical  countries,  passive  obedience  may  be  of  natural  growth  ; though 
even  there  we  doubt  whether  it  has  ever  been  found  among  any  people  with 
whom  fatalism,  or  in  other  words,  submission  to  the  pressure  of  circum- 
stances as  a divine  decree,  did  not  prevail  as  a religious  doctrine.  But  the 
difficulty  of  inducing  a brave  and  warlike  race  to  submit  their  individual 
arbitrium  to  any  common  umpire,  has  always  been  felt  to  be  so  great,  that 
nothing  short  of  supernatural  power  has  been  deemed  adequate  to  over- 
come it;  and  such  tribes  have  always  assigned  to  the  first  institution  of 
civil  society  a divine  origin.  So  differently  did  those  judge  who  knew 
savage  men  by  actual  experience,  from  those  who  had  no  acquaintance 
with  them  except  in  the  civilized  state.  In  modern  Europe  itself,  after  the 
fall  of  the  Roman  empire,  to  subdue  the  feudal  anarchy  and  bring  the 
whole  people  of  any  European  nation  into  subjection  to  government 
(though  Christianity  in  the  most  concentrated  form  of  its  influence  was 
co-operating  in  the  work)  required  thrice  as  many  centuries  as  have  elapsed 
since  that  time. 

“Now  if  these  philosophers  had  known  human  nature  under  any  other 
type  than  that  of  their  own  age,  and  of  the  particular  classes  of  society 
among  whom  they  lived,  it  would  have  occurred  to  them,  that  wherever 
this  habitual  submission  to  law  and  government  has  been  firmly  and  du- 
rably established,  and  yet  the  vigor  and  manliness  of  character  which  re- 
sisted its  establishment  have  been  in  any  degree  preserved,  certain  requi- 
sites have  existed,  certain  conditions  have  been  fulfilled,  of  which  the  fol- 
lowing may  be  regarded  as  the  principal. 

“First:  there  has  existed,  for  all  who  were  accounted  citizens  — for 
all  who  were  not  slaves,  kept  down  by  brute  force — a system  of  education , 

* Since  reprinted  entire  in  Dissertations  and  Discussions,  as  the  concluding  paper  of  the  first 
volume. 


638 


LOGIC  OF  TILE  MORAL  SCIENCES. 


beginning  with  infancy  and  continued  through  life,  of  which  whatever  else 
it  might  include,  one  main  and  incessant  ingredient  was  restraining  disci- 
pline. To  train  the  human  being  in  the  habit,  and  thence  the  power,  of 
subordinating  his  personal  impulses  and  aims  to  what  were  considered  the 
ends  of  society ; of  adhering,  against  all  temptation,  to  the  course  of  con- 
duct which  those  ends  prescribed ; of  controlling  in  himself  all  feelings 
which  were  liable  to  militate  against  those  ends,  and  encouraging  all  such 
as  tended  toward  them ; this  was  the  purpose,  to  which  every  outward 
motive  that  the  authority  directing  the  system  could  command,  and  every 
inward  power  or  principle  which  its  knowledge  of  human  nature  enabled 
it  to  evoke,  were  endeavored  to  be  rendered  instrumental.  The  entire  civ- 
il and  military  policy  of  the  ancient  commonwealths  was  such  a system 
of  training;  in  modern  nations  its  place  has  been  attempted  to  be  supplied, 
principally,  by  religious  teaching.  And  whenever  and  in  proportion  as  the 
strictness  of  the  restraining  discipline  was  relaxed,  the  natural  tendency 
of  mankind  to  anarchy  re-asserted  itself;  the  state  became  disorganized 
from  within ; mutual  conflict  for  selfish  ends,  neutralized  the  energies 
which  were  required  to  keep  up  the  contest  against  natural  causes  of  evil; 
and  the  nation,  after  a longer  or  briefer  interval  of  progressive  decline,  be- 
came either  the  slave  of  a despotism,  or  the  prey  of  a foreign  invader. 

“ The  second  condition  of  permanent  political  society  has  been  found  to 
be,  the  existence,  in  some  form  or  other,  of  the  feeling  of  allegiance  or  loy- 
alty. This  feeling  may  vary  in  its  objects,  and  is  not  confined  to  any  par- 
ticular form  of  government;  but  whether  in  a democracy  or  in  a mon- 
archy, its  essence  is  always  the  same;  viz., that  there  be  in  the  constitution 
of  the  state  something  which  is  settled,  something  permanent,  and  not  to 
be  called  in  question ; something  which,  by  general  agreement,  has  a right 
to  be  where  it  is,  and  to  be  secure  against  disturbance,  whatever  else  may 
change.  This  feeling  may  attach  itself,  as  among  the  Jews  (and  in  most 
of  the  commonwealths  of  antiquity),  to  a common  God  or  gods,  the  pro- 
tectors and  guardians  of  their  state.  Or  it  may  attach  itself  to  certain  per- 
sons, who  are  deemed  to  be,  whether  by  divine  appointment,  by  long  pre- 
scription, or  by  the  general  recognition  of  their  superior  capacity  and 
worthiness,  the  rightful  guides  and  guardians  of  the  rest.  Or  it  may  con- 
nect itself  with  laws;  with  ancient  liberties  or  ordinances.  Or,  finally, 
(and  this  is  the  only  shape  in  which  the  feeling  is  likely  to  exist  hereafter), 
it  may  attach  itself  to  the  principles  of  individual  freedom  and  political  and 
social  equality,  as  realized  in  institutions  which  as  yet  exist  nowhere,  or  ex- 
ist only  in  a rudimentary  state.  But  in  all  political  societies  which  have 
had  a durable  existence,  there  has  been  some  fixed  point:  something  which 
people  agreed  in  holding  sacred ; which,  wherever  freedom  of  discussion 
was  a recognized  principle,  it  was  of  course  lawful  to  contest  in  theory,  but 
which  no  one  could  either  fear  or  hope  to  see  shaken  in  practice;  which, in 
short  (except  perhaps  during  some  temporary  crisis),  was  in  the  common 
estimation  placed  beyond  discussion.  And  the  necessity  of  this  may  easily 
be  made  evident.  A state  never  is,  nor  until  mankind  are  vastly  improved, 
can  hope  to  be,  for  any  long  time  exempt  from  internal  dissension ; for 
there  neither  is  nor  has  ever  been  any  state  of  society  in  which  collisions 
did  not  occur  between  the  immediate  interests  and  passions  of  powerful 
sections  of  the  people.  What,  then,  enables  nations  to  weather  these 
storms,  and  pass  through  turbulent  times  without  any  permanent  weaken- 
ing of  the  securities  for  peaceable  existence?  Precisely  this— that  how- 
ever important  the  interests  about  which  men  fell  out,  the  conflict  did  not 


HISTORICAL  METHOD. 


639 


affect  the  fundamental  principle  of  the  system  of  social  union  which  hap- 
pened to  exist ; nor  threaten  large  portions  of  the  community  with  the 
subversion  of  that  on  which  they  had  built  their  calculations,  and  with 
Avhich  their  hopes  and  aims  had  become  identified.  But  when  the  ques- 
tioning of  these  fundamental  principles  is  (not  the  occasional  disease,  or 
salutary  medicine,  but)  the  habitual  condition  of  the  body  politic,  and  when 
all  the  violent  animosities  are  called  forth,  which  spring  naturally  from  such 
a situation,  the  state  is  virtually  in  a position  of  civil  war;  and  can  never 
long  remain  free  from  it  in  act  and  fact. 

“ The  third  essential  condition  of  stability  in  political  society,  is  a strong 
and  active  principle  of  cohesion  among  the  members  of  the  same  commu- 
nity or  state.  We  need  scarcely  say  that  we  do  not  mean  nationality,  in 
the  vulgar  sense  of  the  term ; a senseless  antipathy  to  foreigners ; indiffer- 
ence to  the  general  welfare  of  the  human  race,  or  an  unjust  preference  of 
the  supposed  interests  of  our  own  country ; a cherishing  of  bad  peculiari- 
ties because  they  are  national,  or  a refusal  to  adopt  what  has  been  found 
good  by  other  countries.  We  mean  a principle  of  sympathy,  not  of  hostil- 
ity; of  union,  not  of  separation.  We  mean  a feeling  of  common  interest 
among  those  who  live  under  the  same  government,  and  are  contained  with- 
in the  same  natural  or  historical  boundaries.  We  mean,  that  one  part  of 
the  community  do  not  consider  themselves  as  foreigners  with  regard  to  an- 
other part ; that  they  set  a value  on  their  connection — feel  that  they  are 
one  people,  that  their  lot  is  cast  together,  that  evil  to  any  of  their  fellow- 
countrymen  is  evil  to  themselves,  and  do  not  desire  selfishly  to  free  them- 
selves from  their  share  of  any  common  inconvenience  by  severing  the  con- 
nection. How  strong  this  feeling  was  in  those  ancient  commonwealths 
which  attained  any  durable  greatness,  every  one  knows.  How  happily 
Rome,  in  spite  of  all  her  tyranny,  succeeded  in  establishing  the  feeling  of  a 
common  country  among  the  provinces  of  her  vast  and  divided  empire,  will 
appear  when  any  one  who  has  given  due  attention  to  the  subject  shall  take 
the  trouble  to  point  it  out.  In  modern  times  the  countries  which  have  had 
that  feeling  in  the  strongest  degree  have  been  the  most  powerful  countries  : 
England,  France,  and,  in  proportion  to  their  territory  and  resources,  Hol- 
land and  Switzerland ; while  England  in  her  connection  with  Ireland  is  one 
of  the  most  signal  examples  of  the  consequences  of  its  absence.  Every 
Italian  knows  why  Italy  is  under  a foreign  yoke;  every  German  knows 
what  maintains  despotism  in  the  Austrian  empire  ;*  the  evils  of  Spain  flow 
as  much  from  the  absence  of  nationality  among  the  Spaniards  themselves, 
as  from  the  presence  of  it  in  their  relations  with  foreigners:  while  the  com- 
pletest  illustration  of  all  is  afforded  by  the  republics  of  South  America, 
where  the  parts  of  one  and  the  same  state  adhere  so  slightly  together,  that 
no  sooner  does  any  province  think  itself  aggrieved  by  the  general  govern- 
ment than  it  proclaims  itself  a separate  nation.” 

§ 6.  While  the  derivative  laws  of  social  statics  are  ascertained  by  an- 
alyzing different  states  of  society,  and  comparing  them  with  one  another, 
without  regard  to  the  order  of  their  succession,  the  consideration  of  the 
successive  order  is,  on  the  contrary,  predominant  in  the  study  of  social 
dynamics,  of  which  the  aim  is  to  observe  and  explain  the  sequences  of  so- 
cial conditions.  This  branch  of  the  social  science  would  be  as  complete  as 
it  can  be  made,  if  every  one  of  the  leading  general  circumstances  of  each 


Written  and  first  published  in  1840. 


640 


LOGIC  OF  THE  MORAL  SCIENCES. 


generation  were  traced  to  its  causes  in  the  generation  immediately  preced- 
ing. But  the  consensus  is  so  complete  (especially  in  modern  history),  that 
in  the  filiation  of  one  generation  and  another,  it  is  the  whole  which  pro- 
duces the  whole,  rather  than  any  part  a part.  Little  progress,  therefore, 
can  be  made  in  establishing  the  filiation,  directly  from  laws  of  human  na- 
ture, without  having  first  ascertained  the  immediate  or  derivative  laws  ac- 
cording to  which  social  states  generate  one  another  as  society  advances ; 
the  axiomata  media  of  General  Sociology. 

The  empirical  laws  which  are  most  readily  obtained  by  generalization 
from  history  do  not  amount  to  this.  They  are  not  the  “middle  princi- 
ples” themselves,  but  only  evidence  toward  the  establishment  of  such  prin- 
ciples. They  consist  of  certain  general  tendencies  which  may  be  perceived 
in  society;  a progressive  increase  of  some  social  elements,  and  diminution 
of  others,  or  a gradual  change  in  the  general  character  of  certain  elements. 
It  is  easily  seen,  for  instance,  that  as  society  advances,  mental  tend  more 
and  more  to  prevail  over  bodily  qualities,  and  masses  over  individuals; 
that  the  occupation  of  all  that  portion  of  mankind  who  are  not  under  ex- 
ternal restraint  is  at  first  chiefly  military,  but  society  becomes  progressive- 
ly more  and  more  engrossed  with  productive  pursuits,  and  the  military 
spirit  gradually  gives  way  to  the  industrial;  to  which  many  similar  truths 
might  be  added.  And  with  generalizations  of  this  description,  ordinary 
inquirers,  even  of  the  historical  school  now  predominant  on  the  Continent, 
are  satisfied.  But  these  and  all  such  results  are  still  at  too  great  a dis- 
tance from  the  elementary  laws  of  human  nature  on  which  they  depend — 
too  many  links  intervene,  and  the  concurrence  of  causes  at  each  link  is  far 
too  complicated  — to  enable  these  propositions  to  be  presented  as  direct 
corollaries  from  those  elementary  principles.  They  have,  therefore,  in  the 
minds  of  most  inquirers,  remained  in  the  state  of  empirical  laws,  applica- 
ble only  within  the  bounds  of  actual  observation ; without  any  means  of 
determining  their  real  limits,  and  of  judging  whether  the  changes  which 
have  hitherto  been  in  progress  are  destined  to  continue  indefinitely,  or  to 
terminate,  or  even  to  be  reversed. 

§ 7.  In  order  to  obtain  better  empirical  laws,  we  must  not  rest  satisfied 
with  noting  the  progressive  changes  which  manifest  themselves  in  the  sep- 
arate elements  of  society,  and  in  which  nothing  is  indicated  but  the  rela- 
tion of  fragments  of  the  effect  to  corresponding  fragments  of  the  cause. 
It  is  necessary  to  combine  the  statical  view  of  social  phenomena  with 
the  dynamical,  considering  not  only  the  progressive  changes  of  the  differ- 
ent elements,  but  the  contemporaneous  condition  of  each;  and  thus  obtain 
empirically  the  law  of  correspondence  not  only  between  the  simultaneous 
states,  but  between  the  simultaneous  changes,  of  those  elements.  This 
law  of  correspondence  it  is,  which,  duly  verified  a 'priori , would  become 
the  real  scientific  derivative  law  of  the  development  of  humanity  and  hu- 
man affairs. 

' In  the  difficult  process  of  observation  and  comparison  which  is  here  re- 
quired, it  would  evidently  be  a great  assistance  if  it  should  happen  to  be 
the  fact,  that  some  one  element  in  the  complex  existence  of  social  man  is 
pre-eminent  over  all  others  as  the  prime  agent  of  the  social  movement. 
For  we  could  then  take  the  progress  of  that  one  element  as  the  central 
chain,  to  each  successive  link  of  which,  the  corresponding  links  of  all  the 
other  progressions  being  appended,  the  succession  of  the  facts  would  by 
this  alone  be  presented  in  a kind  of  spontaneous  order,  far  more  nearly  ap- 


HISTORICAL  METHOD. 


611 


proaching  to  the  real  order  of  their  filiation  than  could  be  obtained  by  any 
other  merely  empirical  process. 

Now,  the  evidence  of  history  and  that  of  human  nature  combine,  by  a 
striking  instance  of  consilience,  to  show  that  there  really  is  one  social  ele- 
ment which  is  thus  predominant,  and  almost  paramount,  among  the  agents 
of  the  social  progression.  This  is,  the  state  of  the  speculative  faculties  of 
mankind ; including  the  nature  of  the  beliefs  which  by  any  means  they 
have  arrived  at,  concerning  themselves  and  the  world  by  which  they  are 
surrounded. 

It  would  be  a great  error,  and  one  very  little  likely  to  be  committed,  to 
assert  that  speculation,  intellectual  activity,  the  pursuit  of  truth,  is  among 
the  more  powerful  propensities  of  human  nature,  or  holds  a predominating 
place  in  the  lives  of  any,  save  decidedly  exceptional,  individuals.  But,  not- 
withstanding the  relative  weakness  of  this  principle  among  other  sociolog- 
ical agents,  its  influence  is  the  main  determining  cause  of  the  social  prog- 
ress; all  the  other  dispositions  of  our  nature  which  contribute  to  that 
progress  being  dependent  on  it  for  the  means  of  accomplishing  their  share 
of  the  work.  Thus  (to  take  the  most  obvious  case  first),  the  impelling 
force  to  most  of  the  improvements  effected  in  the  arts  of  life,  is  the  desire 
of  increased  material  comfort;  but  as  we  can  only  act  upon  external  ob- 
jects in  proportion  to  our  knowledge  of  them,  the  state  of  knowledge  at 
any  time  is  the  limit  of  the  industrial  improvements  possible  at  that  time ; 
and  the  progress  of  industry  must  follow,  and  depend  on,  the  progress  of 
knowledge.  The  same  thing  may  be  shown  to  be  true,  though  it  is  not 
quite  so  obvious,  of  the  progress  of  the  fine  arts.  Further,  as  the  strong- 
est propensities  of  uncultivated  or  half-cultivated  human  nature  (being  the 
purely  selfish  ones,  and  those  of  a sympathetic  character  which  partake 
most  of  the  nature  of  selfishness)  evidently  tend  in  themselves  to  disunite 
mankind,  not  to  unite  them  — to  make  them  rivals,  not  confederates,  so- 
cial existence  is  only  possible  by  a disciplining  of  those  more  powerful 
propensities,  which  consists  in  subordinating  them  to  a common  system  of 
opinions.  The  degree  of  this  subordination  is  the  measure  of  the  com- 
pleteness of  the  social  union,  and  the  nature  of  the  common  opinions  de- 
termines its  kind.  But  in  order  that  mankind  should  conform  their  ac- 
tions to  any  set  of  opinions,  these  opinions  must  exist,  must  be  believed 
by  them.  And  thus,  the  state  of  the  speculative  faculties,  the  character  of 
the  propositions  assented  to  by  the  intellect,  essentially  determines  the 
moral  and  political  state  of  the  community,  as  we  have  already  seen  that 
it  determines  the  physical. 

These  conclusions,  deduced  from  the  laws  of  human  nature,  are  in  entire 
accordance  with  the  general  facts  of  history.  Every  considerable  change 
historically  known  to  us  in  the  condition  of  auy  portion  of  mankind,  when 
not  brought  about  by  external  force,  has  been  preceded  by  a change,  of 
proportional  extent,  in  the  state  of  their  knowledge,  or  in  their  prevalent 
beliefs.  As  between  any  given  state  of  speculation,  and  the  correlative 
state  of  every  thing  else,  it  was  almost  always  the  former  which  first  show- 
ed itself ; though  the  effects,  no  doubt,  reacted  potently  upon  the  cause. 
Every  considerable  advance  in  material  civilization  has  been  preceded  by 
an  advance  in  knowledge : and  when  any  great  social  change  has  come  to 
pass,  either  in  the  way  of  gradual  development  or  of  sudden  conflict,  it  has 
had  for  its  precursor  a great  change  in  the  opinions  and  modes  of  thinking 
of  society.  Polytheism,  Judaism,  Christianity,  Protestantism,  the  critical 
philosophy  of  modern  Europe,  and  its  positive  science — each  of  these  has 

41 


042 


LOGIC  OF  THE  MORAL  SCIENCES. 


been  a primary  agent  in  making  society  what  it  was  at  each  successive  pe- 
riod, while  society  was  but  secondarily  instrumental  in  making  them , each 
of  them  (so  far  as  causes  can  be  assigned  for  its  existence)  being  mainly 
an  emanation  not  from  the  practical  life  of  the  period,  but  from  the  pre- 
vious state  of  belief  and  thought.  The  weakness  of  the  speculative  pro- 
pensity in  mankind  generally  has  not,  therefore,  prevented  the  progress  of 
speculation  from  governing  that  of  society  at  large;  it  has  only,  and  too 
often,  prevented  progress  altogether,  where  the  intellectual  progression  has 
come  to  an  early  stand  for  want  of  sufficiently  favorable  circumstances. 

From  this  accumulated  evidence,  we  are  justified  in  concluding,  that  the 
order  of  human  progression  in  all  respects  will  mainly  depend  on  the  or- 
der of  progression  in  the  intellectual  convictions  of  mankind,  that  is,  on  the 
law  of  the  successive  transformations  of  human  opinions.  The  question 
remains,  whether  this  law  can  be  determined;  at  first  from  history  as  an 
empirical  law,  then  converted  into  a scientific  theorem  by  deducing  it  a 
priori  from  the  principles  of  human  nature.  As  the  progress  of  knowl- 
edge and  the  changes  in  the  opinions  of  mankind  are  very  slow,  and  mani- 
fest themselves  in  a well-defined  manner  only  at  long  intervals,  it  can  not 
be  expected  that  the  general  order  of  sequence  should  be  discoverable  from 
the  examination  of  less  than  a very  considerable  part  of  the  duration  of  the 
social  progress.  It  is  necessary  to  take  into  consideration  the  whole  of 
past  time,  from  the  first  recorded  condition  of  the  human  race,  to  the  mem- 
orable phenomena  of  the  last  and  present  generations. 

§ 8.  The  investigation  which  I have  thus  endeavored  to  characterize, 
has  been  systematically  attempted,  up  to  the  present  time,  by  M.  Comte 
alone.  His  work  is  hitherto  the  only  known  example  of  the  study  of  social 
phenomena  according  to  this  conception  of  the  Historical  Method.  With- 
out discussing  here  the  worth  of  his  conclusions,  and  especially  of  his  pre- 
dictions and  recommendations  with  respect  to  the  Future  of  society,  which 
appear  to  me  greatly  inferior  in  value  to  his  appreciation  of  the  Past,  I 
shall  confine  myself  to  mentioning  one  important  generalization,  which 
M.  Comte  regards  as  the  fundamental  law  of  the  progress  of  human  knowl- 
edge. Speculation  he  conceives  to  have,  on  every  subject  of  human  in- 
quiry, three  successive  stages ; in  the  first  of  which  it  tends  to  explain  the 
phenomena  by  supernatural  agencies,  in  the  second  by  metaphysical  ab- 
stractions, and  in  the  third  or  final  state  confines  itself  to  ascertaining  their 
laws  of  succession  and  similitude.  This  generalization  appears  to  me  to 
have  that  high  degree  of  scientific  evidence  which  is  derived  from  the  con- 
currence of  the  indications  of  history  with  the  probabilities  derived  from 
the  constitution  of  the  human  mind.  Nor  could  it  be  easily  conceived, 
from  the  mere  enunciation  of  such  a proposition,  what  a flood  of  light  it 
lets  in  upon  the  whole  course  of  history,  when  its  consequences  are  traced, 
by  connecting  with  each  of  the  three  states  of  human  intellect  which  it  dis- 
tinguishes, and  with  each  successive  modification  of  those  three  states,  the 
correlative  condition  of  other  social  phenomena.* 

* This  great  generalization  is  often  unfavorably  criticised  (as  by  Dr.Whewell,  for  instance) 
under  a misapprehension  of  its  real  import.  The  doctrine,  that  the  theological  explanation 
6f  phenomena  belongs  only  to  the  infancy  of  our  knowledge  of  them,  ought  not  to  be  con- 
strued as  if  it  was  equivalent  to  the  assertion,  that  mankind,  as  their  knowledge  advances, 
will  necessarily  cease  to  believe  in  any  kind  of  theology.  This  was  M.  Comte’s  opinion  ; but 
it  is  by  no  means  implied  in  his  fundamental  theorem.  All  that  is  implied  is,  that  in  an  ad- 
vanced state  of  human  knowledge,  no  other  Ruler  of  the  World  will  be  acknowledged  than 
one  who  rules  by  universal  laws,  and  does  not  at  all,  or  does  not  unless  in  very  peculiar  cases, 


HISTORICAL  METHOD. 


643 


But  whatever  decision  competent  judges  may  pronounce  on  the  results 
arrived  at  by  any  individual  inquirer,  the  method  now  characterized  is  that 
by  which  the  derivative  laws  of  social  order  and  of  social  progress  must 
be  sought.  By  its  aid  we  may  hereafter  succeed  not  only  in  looking  far 
forward  into  the  future  history  of  the  human  race,  but  in  determining  what 
artificial  means  may  be  used,  and  to  what  extent,  to  accelerate  the  natural 
progress  in  so  far  as  it  is  beneficial;  to  compensate  for  whatever  may  be 
its  inherent  inconveniences  or  disadvantages;  and  to  guard  against  the 
dangers  or  accidents  to  which  our  species  is  exposed  from  the  necessary 
incidents  of  its  progression.  Such  practical  instructions,  founded  on  the 
highest  branch  of  speculative  sociology,  will  form  the  noblest  and  most 
beneficial  portion  of  the  Political  Art. 

' — That  of  this  science  and  art  even  the  foundations  are  but  beginning  to 
be  laid,  is  sufficiently  evident.  But  the  superior  minds  are  fairly  turning 
themselves  toward  that  object.  It  has  become  the  aim  of  really  scientific 
thinkers  to  connect  by  theories  the  facts  of  universal  history  : it  is  acknowl- 
edged to  be  one  of  the  requisites  of  a general  system  of  social  doctrine, 
that  it  should  explain,  so  far  as  the  data  exist,  the  main  facts  of  history; 
and  a Philosophy  of  History  is  generally  admitted  to  be  at  once  the  verifi- 
cation, and  the  initial  form,  of  the  Philosophy  of  the  Progress  of  Society. 

If  the  endeavors  now  making  in  all  the  more  cultivated  nations,  and  be- 
ginning to  be  made  even  in  England  (usually  the  last  to  enter  into  the  gen- 
eral movement  of  the  European  mind)  for  the  construction  of  a Philosophy 
of  History,  shall  be  directed  and  controlled  by  those  views  of  the  nature  of 
sociological  evidence  which  I have  (very  briefly  and  imperfectly)  attempt- 
ed to  characterize;  they  can  not  fail  to  give  birth  to  a sociological  system] 
widely  removed  from  the  vague  and  conjectural  character  of  all  former  at- 
tempts, and  worthy  to  take  its  place,  at  last,  among  the  sciences.  When 
this  time  shall  come,  no  important  branch  of  human  affairs  will  be  any 
longer  abandoned  to  empiricism  and  unscientific  surmise:  the  circle  of  hu- 
man knowledge  will  be  complete,  and  it  can  only  thereafter  receive  further 
enlargement  by  perpetual  expansion  from  within. 

produce  events  by  special  interpositions.  Originally  all  natural  events  were  ascribed  to  such 
interpositions.  At  present  every  educated  person  rejects  this  explanation  in  regard  to  all 
classes  of  phenomena  of  which  the  laws  have  been  fully  ascertained;  though  some  have  not 
yet  reached  the  point  of  referring  all  phenomena  to  the  idea  of  Law,  but  believe  that  rain  and 
sunshine,  famine  and  pestilence,  victory  and  defeat,  death  and  life,  are  issues  which  the  Cre- 
ator does  not  leave  to  the  Operation  of  his  general  laws,  but  reserves  to  be  decided  by  express 
acts  of  volition.  M.  Comte’s  theory  is  the  negation  of  this  doctrine. 

Dr.  Whewell  equally  misunderstands  M.  Comte's  doctrine  respecting  the  second  or  meta- 
physical stage  of  speculation.  M.  Comte  did  not  mean  that  “discussions  concerning  ideas” 
are  limited  to  an  early  stage  of  inquiry,  and  cease  when  science  enters  into  the  positive  stage. 
(Philosophy  of  Discovery /,  pp.  226  et  seq.)  In  all  M.  Comte’s  speculations  as  much  stress  is 
laid  on  the  process  of  clearing  up  our  conceptions  as  on  the  ascertainment  of  facts.  When 
M.  Comte  speaks  of  the  metaphysical  stage  of  specidation,  he  means  the  stage  in  which  men 
speak  of  “Nature”  and  other  abstractions  as  if  they  were  active  forces,  producing  effects; 
when  Nature  is  said  to  do  this,  or  forbid  that,  when  Nature’s  horror  of  a vacuum,  Nature's 
non-admission  of  a break,  Nature’s  vis  medicatrix,  were  offered  as  explanations  of  phenome- 
na ; when  the  qualities  of  things  were  mistaken  for  real  entities  dwelling  in  the  things ; when 
the  phenomena  of  living  bodies  were  thought  to  be  accounted  for  by  being  referred  to  a “vi- 
tal force;”  when,  in  short,  the  abstract  names  of  phenomena  were  mistaken  for  the  causes  of 
their  existence.  In  this  sense  of  the  word  it  can  not  be  reasonably  denied  that  the  meta- 
physical explanation  of  phenomena,  equally  with  the  theological,  gives  way  before  the  ad- 
vance of  real  science. 

That  the  final,  or  positive  stage,  as  conceived  by  M.  Comte,  has  been  equally  misunderstood, 
and  that,  notwithstanding  some  expressions  open  to  just  criticism,  M.  Comte  never  dreamed 
of  denying  the  legitimacy  of  inquiry  into  all  causes  which  are  accessible  to  human  investiga- 
tion, I have  pointed  out  in  a former  place. 


644 


LOGIC  OF  THE  MORAL  SCIENCES. 


CHAPTER  XI. 

ADDITIONAL  ELUCIDATIONS  OF  THE  SCIENCE  OF  HISTORY. 

§ 1.  TnE  doctrine  which  the  preceding  chapters  were  intended  to  enforce 
and  elucidate — that  the  collective  series  of  social  phenomena,  in  other  words 
the  course  of  history,  is  subject  to  general  laws,  which  philosophy  may  pos- 
sibly detect— has  been  familiar  for  generations  to  the  scientific  thinkers 
of  the  Continent,  and  has  for  the  last  quarter  of  a century  passed  out  of 
their  peculiar  domain,  into  that  of  newspapers  and  ordinary  political  dis- 
cussion. In  our  own  country,  however,  at  the  time  of  the  first  publication 
of  this  Treatise,  it  was  almost  a novelty,  and  the  prevailing  habits  of  thought 
on  historical  subjects  were  the  very  reverse  of  a preparation  for  it.  Since 
then  a great  change  has  taken  place,  and  has  been  eminently  promoted  by 
the  important  work  of  Mr.  Buckle ; who,  with  characteristic  energy,  flung 
down  this  great  principle,  together  with  many  striking  exemplifications  of 
it,  into  the  arena  of  popular  discussion,  to  be  fought  over  by  a sort  of  com- 
batants, in  the  presence  of  a sort  of  spectators,  who  would  never  even  have 
been  aware  that  there  existed  such  a principle  if  they  had  been  left  to  learn 
its  existence  from  the  speculations  of  pure  science.  And  hence  has  arisen 
a considerable  amount  of  controversy,  tending  not  only  to  make  the  prin- 
ciple rapidly  familiar  to  the  majority  of  cultivated  minds,  but  also  to  clear 
it  from  the  confusions  and  misunderstandings  by  which  it  was  but  natural 
that  it  should  for  a time  be  clouded,  and  which  impair  the  worth  of  the 
doctrine  to  those  who  accept  it,  and  are  the  stumbling-block  of  many  who 
do  not. 

Among  the  impediments  to  the  general  acknowledgment,  by  thoughtful 
minds,  of  the  subjection  of  historical  facts  to  scientific  laws,  the  most  fun- 
damental continues  to  be  that  which  is  grounded  on  the  doctrine  of  Free 
Will,  or,  in  other  words,  on  the  denial  that  the  law  of  invariable  Causation 
holds  true  of  human  volitions ; for  if  it  does  not,  the  course  of  history,  being 
the  result  of  human  volitions,  can  not  be  a subject  of  scientific  laws,  since 
the  volitions  on  which  it  depends  can  neither  be  foreseen,  nor  reduced  to 
any  canon  of  regularity  even  after  they  have  occurred.  I have  discussed 
this  question,  as  far  as  seemed  suitable  to  the  occasion,  in  a former  chapter; 
and  I only  think  it  necessary  to  repeat,  that  the  doctrine  of  the  Causation 
of  human  actions,  improperly  called  the  doctrine  of  Necessity,  affirms  no 
mysterious  nexus,  or  overruling  fatality:  it  asserts  only  that  men’s  actions 
are  the  joint  result  of  the  general  laws  and  circumstances  of  human  na- 
ture, and  of  their  own  particular  characters ; those  characters  again  being 
the  consequence  of  the  natural  and  artificial  circumstances  that  constituted 
their  education,  among  which  circumstances  must  be  reckoned  their  own 
conscious  efforts.  Any  one  who  is  willing  to  take  (if  the  expression  may 
be  permitted)  the  trouble  of  thinking  himself  into  the  doctrine  as  thus 
stated,  will  find  it,  I believe,  not  only  a faithful  interpretation  of  the  uni- 
versal experience  of  human  conduct,  but  a correct  representation  of  the 
mode  in  which  he  himself,  in  every  particular  case,  spontaneously  interprets 
his  own  experience  of  that  conduct. 

But  if  this  principle  is  true  of  individual  man,  it  must  be  true  of  collect- 


SCIENCE  OF  HISTORY. 


645 


ive  man.  If  it  is  the  law  of  human  life,  the  law  must  be  realized  in  history. 
The  experience  of  human  affairs  when  looked  at  en  masse,  must  be  in  ac- 
cordance with  it  if  true,  or  repugnant  to  it  if  false.  The  support  which 
this  a posteriori  verification  affords  to  the  law,  is  the  part  of  the  case  which 
has  been  most  clearly  and  triumphantly  brought  out  by  Mr.  Buckle. 

The  facts  of  statistics,  since  they  have  been  made  a subject  of  careful  re- 
cordation and  study,  have  yielded  conclusions,  some  of  which  have  been  very 
startling  to  persons  not  accustomed  to  regard  moral  actions  as  subject  to  uni- 
form laws.  The  very  events  which  in  their  own  nature  appear  most  capri- 
cious and  uncertain,  and  which  in  any  individual  case  no  attainable  degree 
of  knowledge  would  enable  us  to  foresee,  occur,  when  considerable  numbers 
are  taken  into  the  account,  with  a degree  of  regularity  approaching  to  math- 
ematical. What  act  is  there  which  all  would  consider  as  more  completely 
dependent  on  individual  character,  and  on  the  exercise  of  individual  free 
will,  than  that  of  slaying  a fellow-creature?  Yet  in  any  large  country,  the 
number  of  murders,  in  proportion  to  the  population,  varies  (it  has  been 
found)  very  little  from  one  year  to  another,  and  in  its  variations  never  de- 
viates widely  from  a certain  average.  What  is  still  more  remarkable,  there 
is  a similar  approach  to  constancy  in  the  proportion  of  these  murders  an- 
nually committed  with  every  particular  kind  of  instrument.  There  is  a 
like  approximation  to  identity,  as  between  one  year  and  another,  in  the  com- 
parative number  of  legitimate  and  of  illegitimate  births.  The  same  thing 
is  found  true  of  suicides,  accidents,  and  all  other  social  phenomena  of  which 
the  registration  is  sufficiently  perfect;  one  of  the  most  curiously  illustrative 
examples  being  the  fact,  ascertained  by  the  registers  of  the  London  and 
Paris  post-offices,  that  the  number  of  letters  posted  which  the  writers  have 
forgotten  to  direct,  is  nearly  the  same,  in  proportion  to  the  whole  number 
of  letters  posted,  in  one  year  as  in  another.  “Year  after  year,”  says  Mr. 
Buckle,  “the  same  proportion  of  letter-writers  forget  this  simple  act;  so 
that  for  each  successive  period  we  can  actually  foretell  the  number  of  per- 
sons whose  memory  will  fail  them  in  regard  to  this  trifling,  and  as  it  might 
appear,  accidental  occurrence.”* 

This  singular  degree  of  regularity  en  masse,  combined  with  the  extreme 
of  irregularity  in  the  cases  composing  the  mass,  is  a felicitous  verification 
a posteriori  of  the  law  of  causation  in  its  application  to  human  conduct. 
Assuming  the  truth  of  that  law,  every  human  action,  every  murder,  for  in j 
stance,  is  the  concurrent  result  of  two  sets  of  causes.  On  the  one  part,  the 
general  circumstances  of  the  country  and  its  inhabitants;  the  moral,  educa- 
tionaT, 'economical,  and  other  influences  operating  on  the  whole  people,  and 
constituting  what  we  term  the  state  of  civilization.  On  the  other  part,  the 
great  variety  of  influences  special  to  the  individual : his  temperament,  and 
other  peculiarities  of  organization,  his  parentage,  habitual  associates,  temp- 
tations, and  so  forth.  If  we  now  take  the  whole  of  the  instances  which  oc- 
cur within  a sufficiently  large  field  to  exhaust  all  the  combinations  of  these 
special  influences,  or,  in  other  words,  to  eliminate  chance;  and  if  all  these 
instances  have  occurred  within  such  narrow  limits  of  time,  that  no  material 
change  can  have  taken  place  in  the  general  influences  constituting  the  state 
of  civilization  of  the  country;  we  maybe  certain,  that  if  human  actions  are 
governed  by  invariable  laws,  the  aggregate  result  will  be  something  like  a 
constant  quantity.  The  number  of  murders  committed  within  that  space 
and  time,  being  the  effect  partly  of  general  causes  which  have  not  varied, 


Buckle’s  History  of  Civilization,  i..  30. 


GIG 


LOGIC  OF  THE  MORAL  SCIENCES. 


and  partly  of  partial  causes  the  whole  round  of  whose  variations  lias  been 
included,  will  be,  practically  speaking,  invariable. 

Literally  and  mathematically  invariable  it  is  not,  and  could  not  be  expect- 
ed to  be : because  the  period  of  a year  is  too  short  to  include  all  the  possi- 
ble combinations  of  partial  causes,  while  it  is,  at  the  same  time,  sufficiently 
long  to  make  it  probable  that  in  some  years  at  least,  of  every  series,  there 
will  have  been  introduced  new  influences  of  a more  or  less  general  charac- 
ter; such  as  a more  vigorous  or  a more  relaxed  police;  some  temporary 
excitement  from  political  or  religious  causes  ; or  some  incident  generally 
notorious,  of  a nature  to  act  morbidly  on  the  imagination.  That  in  spite  of 
these  unavoidable  imperfections  in  the  data,  there  should  be  so  very  trifling 
a margin  of  variation  in  the  annual  results,  is  a brilliant  confirmation  of  the 
general  theory. 

§ 2.  The  same  considerations  which  thus  strikingly  corroborate  the  evi- 
dence of  the  doctrine,  that  historical  facts  are  the  invariable  effects  of 
causes,  tend  equally  to  clear  that  doctrine  from  various  misapprehensions, 
the  existence  of  which  has  been  put  in  evidence  by  the  recent  discussions. 
Some  persons,  for  instance,  seemingly  imagine  the  doctrine  to  imply,  not 
merely  that  the  total  number  of  murders  committed  in  a given  space  and 
time  is  entirely  the  effect  of  the  general  circumstances  of  society,  but  that 
every  particular  murder  is  so  too — that  the  individual  murderer  is,  so  to 
speak,  a mere  instrument  in  the  hands  of  general  causes  that  he  himself 
has  no  option,  or,  if  he  has,  and  chose  to  exercise  it,  some  one  else  would 
be  necessitated  to  take  his  place;  that  if  any  one  of  the  actual  murderers 
had  abstained  from  the  crime,  some  person  who  would  otherwise  have  re- 
mained innocent,  would  have  committed  an  extra  murder  to  make  up  the 
average.  Such  a corollary  would  certainly  convict  any  theory  which  nec- 
essarily led  to  it  of  absurdity.  It  is  obvious,  however,  that  each  particular 
murder  depends,  not  on  the  general  state  of  society  only,  but  on  that  com- 
bined with  causes  special  to  the  case,  which  arc  generally  much  more  pow- 
erful; and  if  these  special  causes,  which  have  greater  influence  than  the 
general  ones  in  causing  every  particular  murder,  have  no  influence  on  the 
number  of  murders  in  a given  period,  it  is  because  the  field  of  observation 
is  so  extensive  as  to  include  all  possible  combinations  of  the  special  causes 
- — all  varieties  of  individual  character  and  individual  temptation  compatible 
with  the  general  state  of  society.  The  collective  experiment,  as  it  may  be 
termed,  exactly  separates  the  effect  of  the  general  from  that  of  the  special 
causes,  and  shows  the  net  result  of  the  former;  but  it  declares  nothing  at. 
all  respecting  the  amount  of  influence  of  the  special  causes,  be  it  greater  or 
smaller,  since  the  scale  of  the  experiment  extends  to  the  number  of  cases 
within  which  the  effects  of  the  special  causes  balance  one  another,  and  dis- 
appear in  that  of  the  general  causes. 

I will  not  pretend  that  all  the  defenders  of  the  theory  have  always  kept 
their  language  free  from  this  same  confusion,  and  have  shown  no  tendency 
to  exalt  the  influence  of  general  causes  at  the  expense  of  special.  I am  of 
opinion,  on  the  contrary,  that  they  have  done  so  in  a very  great  degree, 
and  by  so  doing  have  encumbered  their  theory  with  difficulties,  and  laid  it 
open  to  objections,  which  do  not  necessarily  affect  it.  Some,  for  example 
(among  whom  is  Mr.  Buckle  himself),  have  inferred,  or  allowed  it  be 
supposed  that  they  inferred,  from  the  regularity  in  the  recurrence  of  events 
which  depend  on  moral  qualities,  that  the  moral  qualities  of  mankind  are 
little  capable  of  being  improved,  or  are  of  little  importance  in  the  general 


SCIENCE  OE  HISTORY. 


647 


progress  of  society,  compared  with  intellectual  or  economic  causes.  But 
to  draw  this  inference  is  to  forget  that  the  statistical  tables,  from  which 
the  invariable  averages  are  deduced,  were  compiled  from  facts  occurring 
within  narrow  geographical  limits  and  in  a small  number  of  successive 
years ; that  is,  from  a field  the  whole  of  which  was  under  the  operation  of 
the  same  general  causes,  and  during  too  short  a time  to  allow  of  much 
change  therein.  All  moral  causes  but  those  common  to  the  country  gen- 
erally, have  been  eliminated  by  the  great  number  of  instances  taken;  and 
those  which  are  common  to  the  whole  country  have  not  varied  considera- 
bly, in  the  short  space  of  time  comprised  in  the  observations.  If  we  admit 
the  supposition  that  they  have  varied ; if  we  compare  one  age  with  anoth- 
er, or  one  country  with  another,  or  even  one  part  of  a country  with  an- 
other, differing  in  position  and  character  as  to  the  moral  elements,  the 
crimes  committed  within  a year  give  no  longer  the  same,  but  a widely 
different  numerical  aggregate.  And  this  can  not  but  be  the  case  : for, 
inasmuch  as  every  single  crime  committed  by  an  individual  mainly  depends 
on  his  moral  qualities,  the  crimes  committed  by  the  entire  population  of 
the  country  must  depend  in  an  equal  degree  on  their  collective  moral  quali- 
ties. To  render  this  element  inoperative  upon  the  large  scale,  it  would 
be  necessary  to  suppose  that  the  general  moral  average  of  mankind  does 
not  vary  from  country  to  country  or  from  age  to  age ; which  is  not  true, 
and,  even  if  it  were  true,  could  not  possibly  be  proved  by  any  existing 
statistics.  I do  not  on  this  account  the  less  agree  in  the  opinion  of  Mr. 
Buckle,  that  the  intellectual  element  in  mankind,  including  in  that  expres- 
sion the  nature  of  their  beliefs,  the  amount  of  their  knowledge,  and  the 
development  of  their  intelligence,  is  the  predominant  circumstance  in  del 
termining  their  progress.  But  I am  of  this  opinion,  not  because  I regard 
their  moral  or  economical  condition  either  as  less  powerful  or  less  variable 
agencies,  but  because  these  are  in  a great  degree  the  consequences  of  the 
intellectual  condition,  and  are,  in  all  cases,  limited  by  it;  as  was  observed 
in  the  preceding  chapter.  The  intellectual  changes  are  the  most  conspicu- 
ous agents  in  history,  not  from  their  superior  force,  considered  in  them- 
selves, but  because  practically  they  work  with  the  united  power  belonging 
to  jfil  three.* 

§ 3.  There  is  another  distinction  often  neglected  in  the  discussion  of  this 
subject,  which  it  is  extremely  important  to  observe.  The  theory  of  the 

* I have  been  assured  by  an  intimate  friend  of  Mr.  Buckle  that  be  would  not  have  with- 
held his  assent  from  these  remarks,  and  that  he  never  intended  to  affirm  or  imply  that  man- 
kind are  not  progressive  in  their  moral  as  well  as  in  their  intellectual  qualities.  “ In  dealing 
with  his  problem,  he  availed  himself  of  the  artifice  resorted  to  by  the  Political  Economist, 
who  leaves  out  of  consideration  the  generous  and  benevolent  sentiments,  and  founds  his  sci- 
ence on  the  proposition  that  mankind  are  actuated  by  acquisitive  propensities  alone,”  not  be- 
cause such  is  the  fact,  but  because  it  is  necessary  to  begin  by  treating  the  principal  influence 
as  if  it  was  the  sole  one,  and  make  the  due  corrections  afterward.  “He  desired  to  make 
abstraction  of  the  intellect  as  the  determining  and  dynamical  element  of  the  progression,  elimi- 
nating the  more  dependent  set  of  conditions,  and  treating  the  more  active  one  as  if  it  were  an 
entirely  independent  variable.” 

The  same  friend  of  Mr.  Buckle  states  that  when  he  used  expressions  which  seemed  to  ex- 
aggerate the  influence  of  general  at  the  expense  of  special  causes,  and  especially  at  the  ex- 
pense of  the  influence  of  individual  minds,  Mr.  Buckle  really  intended  no  more  than  to  affirm 
emphatically  that  the  greatest  men  can  not  effect  great  changes  in  human  affairs  unless  the 
general  mind  has  been  in  some  considerable  degree  prepared  for  them  by  the  general  circum- 
stances of  the  age  ; a truth  which,  of  course,  no  one  thinks  of  denying.  And  there  certainly 
are  passages  in  Mr.  Buckle’s  writings  which  speak  of  the  influence  exercised  by  great  indi- 
vidual intellects  in  as  strong  terms  as  could  be  desired. 


G4S 


LOGIC  OF  THE  MORAL  SCIENCES. 


subjection  of  social  progress  to  invariable  laws,  is  often  held  in  conjunc- 
tion with  the  doctrine,  that  social  progress  can  not  be  materially  influenced 
by  the  exertions  of  individual  persons,  or  by  the  acts  of  governments. 
But  though  these  opinions  are  often  held  by  the  same  persons,  they  are 
two  very  different  opinions,  and  the  confusion  between  them  is  the  eter- 
nally recurring  error  of  confounding  Causation  with  Fatalism.  Because 
whatever  happens  will  be  the  effect  of  causes,  human  volitions  among  the 
rest,  it  does  not  follow  that  volitions,  even  those  of  peculiar  individuals, 
are  not  of  great  efficacy  as  causes.  If  any  one  in  a storm  at  sea,  because 
about  the  same  number  of  persons  in  every  year  perish  by  shipwreck, 
should  conclude  that  it  was  useless  for  him  to  attempt  to  save  his  own  life, 
we  should  call  him  a Fatalist;  and  should  remind  hint  that  the  efforts  of 
shipwrecked  persons  to  save  their  lives  are  so  far  from  being  immaterial, 
that  the  average  amount  of  those  efforts  is  one  of  the  causes  on  which  the 
ascertained  annual  number  of  deaths  by  shipwreck  depend.  However  uni- 
versal the  laws  of  social  development  may  be,  they  can  not  be  more  univer- 
sal or  more  rigorous  than  those  of  the  physical  agencies  of  nature;  yet 
human  will  can  convert  these  into  instruments  of  its  designs,  and  the  ex- 
tent to  which  it  does  so  makes  the  chief  difference  between  savages  and 
the  most  highly  civilized  people.  Human  and  social  facts,  from  their  more 
complicated  nature,  are  not  less,  but  more,  modifiable  than  mechanical  and 
chemical  facts ; human  agency,  therefore,  has  still  greater  power  over  them. 
And  accordingly,  those  who  maintain  that  the  evolution  of  society  depends 
exclusively,  or  almost  exclusively,  on  general  causes,  always  include  among 
these  the  collective  knowledge  and  intellectual  development  of  the  race. 
But  if  of  the  race,  why  not  also  of  some  powerful  monarch  or  thinker,  or 
of  the  ruling  portion  of  some  political  society,  acting  through  its  govern- 
ment? Though  the  varieties  of  character  among  ordinary  individuals  neu- 
tralize one  another  on  any  large  scale,  exceptional  individuals  in  important 
positions  do  not  in  any  given  age  neutralize  one  another;  there  was  not 
another  Themistocles,  or  Luther,  or  Julius  Caesar,  of  equal  powers  and 
contrary  dispositions,  who  exactly  balanced  the  given  Themistocles,  Luther, 
and  Caesar,  and  prevented  them  from  having  any  permanent  effect.  More- 
over, for  aught  that  appears,  the  volitions  of  exceptional  persons,  or  the 
opinions  and  purposes  of  the  individuals  who  at  some  particular  time  com- 
pose a government,  may  be  indispensable  links  in  the  chain  of  causation  by 
which  even  the  general  causes  produce  their  effects;  and  I believe  this  to 
be  the  only  tenable  form  of  the  theory. 

Lord  Macaulay,  in  a celebrated  passage  of  one  of  his  early  essays  (let 
me  add  that  it  was  one  which  he  did  not  himself  choose  to  reprint),  gives 
expression  to  the  doctrine  of  the  absolute  inoperativeness  of  great  men, 
more  unqualified,  I should  think,  than  has  been  given  to  it  by  any  writer 
of  equal  abilities.  He  compares  them  to  persons  who  merely  stand  on  a 
loftier  height,  and  thence  receive  the  sun’s  rays  a little  earlier,  than  the 
rest  of  the  human  race.  “The  sun  illuminates  the  hills  while  it  is  still  be- 
low the  horizon,  and  truth  is  discovered  by  the  highest  minds  a little  be- 
fore it  becomes  manifest  to  the  multitude.  This  is  the  extent  of  their  su- 
periority. They  are  the  first  to  catch  and  reflect  a light  which,  without 
their  assistance,  must  in  a short  time  be  visible  to  those  who  lie  far  be- 
neath them.”*  If  this  metaphor  is  to  be  carried  out,  it  follows  that  if 
there  had  been  no  Newton,  the  world  would  not  only  have  had  the  New 


Essay  on  Dryden,  in  Miscellaneous  Writings,  i.,  18G. 


SCIENCE  OE  HISTORY. 


649 


tonian  system,  but  would  have  had  it  equally  soon ; as  the  sun  would  have 
risen  just  as  early  to  spectators  in  the  plain  if  there  had  been  no  mountain 
at  hand  to  catch  still  earlier  rays.  And  so  it  would  be,  if  truths,  like  the 
sun,  rose  by  their  own  proper  motion,  without  human  effort;  but  not  oth- 
erwise. I believe  that  if  Newton  had  not  lived,  the  world  must  have  wait-1 
ed  for  the  Newtonian  philosophy  until  there  had  been  another  Newton, 
or  his  equivalent.  No  ordinary  man,  and  no  succession  of  ordinary  men, 
could  .have  achieved  it.  I will  not  go  the  length  of  saying  that  what  New- 
ton did  in  a single  life,  might  not  have  been  done  in  successive  steps  bv 
some  of  those  who  followed  him,  each  singly  inferior  to  him  in  genius. 
But  even  the  least  of  those  steps  required  a man  of  great  intellectual  supe- 
riority. Eminent  men  do  not  merely  see  the  coming  light  from  the  hill- 
top, they  mount  on  the  hill-top  and  evoke  it ; and  if  no  one  had  ever  as- 
cended thither,  the  light,  in  many  cases,  might  never  have  risen  upon  the 
plain  at  all.  Philosophy  and  religion  are  abundantly  amenable  to  general 
causes ; yet  few  will  doubt  that,  had  there  been  no  Socrates,  no  Plato,  and 
no  Aristotle,  there  would  have  been  no  philosophy  for  the  next  two  thou- 
sand years,  uor  in  all  probability  then;  and  that  if  there  had  been  no 
Christ,  and  no  St.  Paul,  there  would  have  been  no  Christianity. 

The  point  in  which,  above  all,  the  influence  of  remarkable  individuals  is 
decisive,  is  in  determining  the  celerity  of  the  movement.  In  most  states 
of  society  it  is  the  existence  of  great  men  which  decides  even  whether  there 
shall  be  any  progress.  It  is  conceivable  that  Greece,  or  that  Christian 
Europe,  might  have  been  progressive  in  certain  periods  of  their  history 
through  general  causes  only:  but  if  there  had  been  no  Mohammed,  would 
Arabia  have  produced  Avicenna  or  Averroes,  or  Caliphs  of  Bagdad  or  of 
Cordova?  In  determining,  however,  in  what  manner  and  order  the  prog- 
ress of  mankind  shall  take  place  if  it  take  place  at  all,  much  less  depends 
on  the  character  of  individuals.  There  is  a sort  of  necessity  established  in 
this  respect  by  the  general  laws  of  human  nature — by  the  constitution  of 
the  human  mind.  Certain  truths  can  not  be  discovered,  nor  inventions 
made,  unless  certain  others  have  been  made  first;  certain  social  improve- 
ments, from  the  nature  of  the  case,  can  only  follow,  and  not  precede,  others. 
The  order  of  human  progress,  therefore,  may  to  a certain  extent  have  defi- 
nite laws  assigned  to  it : while  as  to  its  celerity,  or  even  as  to  its  taking 
place  at  all,  no  generalization,  extending  to  the  human  species  generally,  can 
possibly  be  made ; but  only  some  very  precarious  approximate  generaliza- 
tions, confined  to  the  small  portion  of  mankind  in  whom  there  has  been 
any  thing  like  consecutive  progress  within  the  historical  period,  and  de- 
duced from  their  special  position,  or  collected  from  their  particular  history. 
Even  looking  to  the  manner  of  progress,  the  order  of  succession  of  social 
states,  there  is  need  of  great  flexibility  in  our  generalizations.  The  limits 
of  variation  in  the  possible  development  of  social,  as  of  animal  life,  are  a 
subject  of  Avhich  little  is  yet  understood,  and  are  one  of  the  great  problems 
in  social  science.  It  is,  at  all  events,  a fact,  that  different  portions  of  man- 
kind, under  the  influence  of  different  circumstances,  have  developed  them- 
selves in  a more  or  less  different  manner  and  into  different  forms ; and 
among  these  determining  circumstances,  the  individual  character  of  their 
great  speculative  thinkers  or  practical  organizers  may  well  have  been  one. 
Who  can  tell  how  profoundly  the  whole  subsequent  history  of  China  may 
have  been  influenced  by  the  individuality  of  Confucius  ? and  of  Sparta  (and 
hence  of  Greece  and  the  world)  by  that  of  Lycurgus? 

Concerning  the  nature  and  extent  of  what  a great  man  under  favorable 


050 


LOGIC  OF  THE  MORAL  SCIENCES. 


circumstances  can  do  for  mankind,  as  well  as  of  what  a government  can  do 
fur  a nation,  many  different  opinions  are  possible ; and  every  shade  of  opin- 
ion on  these  points  is  consistent  with  the  fullest  recognition  that  there  are 
invariable  laws  of  historical  phenomena.  Of  course  the  degree  of  influence 
which  has  to  be  assigned  to  these  more  special  agencies,  makes  a great  dif- 
ference in  the  precision  which  can  be  given  to  the  general  laws,  and  in  the 
confidence  with  which  predictions  can  be  grounded  on  them.  Whatever 
depends  on  the  peculiarities  of  individuals,  combined  with  the  accident  of 
the  positions  they  hold,  is  necessarily  incapable  of  being  foreseen.  Un- 
doubtedly these  casual  combinations  might  be  eliminated  like  any  others, 
by  taking  a sufficiently  large  cycle:  the  peculiarities  of  a great  historical 
character  make  their  influence  felt  in  history  sometimes  for  several  thou- 
sand years,  but  it  is  highly  probable  that  they  will  make  no  difference  at 
all  at  the  end  of  fifty  millions.  Since,  however,  we  can  not  obtain  an  aver- 
age of  the  vast  length  of  time  necessary  to  exhaust  all  the  possible  combi- 
nations of  great  men  and  circumstances,  as  much  of  the  law  of  evolution  of 
human  affairs  as  depends  upon  this  average,  is  and  remains  inaccessible  to 
us ; and  within  the  next  thousand  years,  which  are  of  considerably  more 
importance  to  us  than  the  whole  remainder  of  the  fifty  millions,  the  favor- 
able and  unfavorable  combinations  which  will  occur  will  be  to  us  purely 
accidental.  We  can  not  foresee  the  advent  of  great  men.  Those  who  in- 
troduce new  speculative  thoughts  or  great  practical  conceptions  into  the 
world,  can  not  have  their  epoch  fixed  beforehand.  What  science  can  do, 
is  this.  It  can  trace  through  past  history  the  general  causes  which  had 
brought  mankind  into  that  preliminary  state  which,  when  the  right  sort  of 
great  man  appeared,  rendered  them  accessible  to  his  influence.  If  this 
state  continues,  experience  renders  it  tolerably  certain  that  in  a longer  or 
shorter  period  the  great  man  will  be  produced ; provided  that  the  general 
circumstances  of  the  country  and  people  are  (which  very  often  they  are 
not)  compatible  with  his  existence;  of  which  point  also,  science  can  in 
some  measure  judge.  It  is  in  this  manner  that  the  results  of  progress,  ex- 
cept as  to  the  celerity  of  their  production,  can  be,  to  a certain  extent,  re- 
duced to  regularity  and  law.  And  the  belief  that  they  can  be  so,  is  equal- 
ly consistent  with  assigning  very  great,  or  very  little  efficacy,  to  the  influ- 
ence of  exceptional  men,  or  of  the  acts  of  governments.  And  the  same 
may  be  said  of  all  other  accidents  and  disturbing  causes. 

§ 4.  It  would  nevertheless  be  a great  error  to  assign  only  a trifling  im- 
portance to  the  agency  of  eminent  individuals,  or  of  governments.  It  must 
not  be  concluded  that  the  influence  of  either  is  small,  because  they  can  not 
bestow  what  the  general  circumstances  of  society,  and  the  course  of  its 
previous  history,  have  not  prepared  it  to  receive.  Neither  thinkers  nor 
governments  effect  all  that  they  intend,  but  in  compensation  they  often 
produce  important  results  which  they  did  not  in  the  least  foresee.  Great 
men,  and  great  actions,  are  seldom  wasted  ; they  send  forth  a thousand  un- 
seen influences,  more  effective  than  those  which  are  seen  ; and  though  nine 
cut  of  every  ten  tilings  done,  with  a good  purpose,  by  those  who  are  in 
advance  of  their  age,  produce  no  material  effect,  the  tenth  thing  produces 
effects  twenty  times  as  great  as  any  one  would  have  dreamed  of  predict- 
ing from  it.  Even  the  men  who  for  want  of  sufficiently  favorable  circum- 
stances left  no  impress  at  all  upon  their  own  age,  have  often  been  of  the 
greatest  value  to  posterity.  Who  could  appear  to  have  lived  more  entire- 
ly in  vain  than  some  of  the  early  heretics?  They  were  burned  or  mas- 


SCIENCE  OF  HISTORY. 


651 


sacred,  their  writings  extirpated,  their  memory  anathematized,  and  their 
very  names  and  existence  left  for  seven  or  eight  centuries  in  the  obscuri- 
ty of  musty  manuscripts — their  history  to  be  gathered,  perhaps,  only  from 
the  sentences  by  which  they  were  condemned.  Yet  the  memory  of  these 
men  — men  who  resisted  certain  pretensions  or  certain  dogmas  of  the 
Church  in  the  very  age  in  which  the  unanimous  assent  of  Christendom 
was  afterward  claimed  as  having  been  given  to  them,  and  asserted  as  the 
ground  of  their  authority — broke  the  chain  of  tradition,  established  a se- 
ries of  precedents  for  resistance,  inspired  later  Reformers  with  the  cour- 
age, and  armed  them  with  the  weapons,  which  they  needed  when  mankind 
were  better  prepared  to  follow  their  impulse.  To  this  example  from,  men, 
let  us  add  another  from  governments.  The  comparatively  enlightened 
rule  of  which  Spain  had  the  benefit  during  a considerable  part  of  the 
eighteenth  century,  did  not  correct  the  fundamental  defects  of  the  Spanish 
people;  and  in  consequence,  though  it  did  great  temporary  good,  so  much 
of  that  good  perished  with  it,  that  it  may  plausibly  be  affirmed  to  have 
had  no  permanent  effect.  The  case  has  been  cited  as  a proof  how  little 
governments  can  do  in  opposition  to  the  causes  which  have  determined 
the  general  character  of  the  nation.  It  does  show  how  much  there  is 
which  they  can  not  do;  but  not  that  they  can  do  nothing.  Compare  what 
Spain  was  at  the  beginning  of  that  half-century  of  liberal  government, 
with  what  she  had  become  at  its  close.  That  period  fairly  let  in  the  light 
of  European  thought  upon  the  more  educated  classes;  and  it  never  after- 
ward ceased  to  go  on  spreading.  Previous  to  that  time  the  change  was 
in  an  inverse  direction  ; culture,  light,  intellectual  and  even  material  activ- 
ity, were  becoming  extinguished.  Was  it  nothing  to  arrest  this  down- 
ward and  convert  it  into  an  upward  course?  How  much  that  Charles  the 
Third  and  Aranda  could  not  do,  has  been  the  ultimate  consequence  of 
what  they  did  ! To  that  half-century  Spain  owes  that  she  has  got  rid  of 
the  Inquisition,  that  she  has  got  rid  of  the  monks,  that  she  now  has  parlia- 
ments and  (save  in  exceptional  intervals)  a free  press,  and  the  feelings  of 
freedom  and  citizenship,  and  is  acquiring  railroads  and  all  the  other  con- 
stituents of  material  and  economical  progress.  In  the  Spain  which  pre- 
ceded that  era,  there  was  not  a single  element  at  work  which  could  have 
led  to  these  results  in  any  length  of  time,  if  the  country  had  continued  to 
be  governed  as  it  was  by  the  last  princes  of  the  Austrian  dynasty,  or  if 
the  Bourbon  rulers  had  been  from  the  first  what,  both  in  Spain  and  in  Na- 
ples, they  afterward  became. 

And  if  a government  can  do  much;  even  when  it  seems  to  have  done 
little,  in  causing  positive  improvement,  still  greater  are  the  issues  depend 
ent  on  it  in  the  way  of  warding  off  evils,  both  internal  and  external,  which 
else  would  stop  improvement  altogether.  A good  or  a bad  counselor,  in  a 
single  city  at  a particular  crisis,  has  affected  the  whole  subsequent  fate  of 
the  world.  It  is  as  certain  as  any  contingent  judgment  respecting  histor- 
ical events  can  be,  that  if  there  had  been  no  Themistocles  there  would 
have  been  no  victory  of  Salamis ; and  had  there  not,  where  would  have 
been  all  our  civilization  ? How  different,  again,  would  have  been  the  issue 
if  Epaminondas,  or  Timoleon,or  even  Iphicrates,  instead  of  Chares  and  Ly- 
sicles,  had  commanded  at  Chteroneia.  As  is  well  said  in  the  second  of  two 
Essays  on  the  Study  of  History,*  in  my  judgment  the  soundest  and  most, 
philosophical  productions  which  the  recent  controversies  on  this  subject 


In  the  Cornhill  Magazine  for  June  and  July,  1861. 


052 


LOGIC  OF  THE  MORAL  SCIENCES. 


have  called  forth,  historical  science  authorizes  not  absolute,  but  only  con- 
ditional predictions.  General  causes  count  for  much,  but  individuals  also 
“ produce  great  changes  in  history,  and  color  its  whole  complexion  long 

after  their  death No  one  can  doubt  that  the  Roman  republic  would 

have  subsided  into  a military  despotism  if  Julius  Caesar  had  never  lived” 
(thus  much  was  rendered  practically  certain  by  general  causes);  “but  is 
it  at  all  clear  that  in  that  case  Gaul  would  ever  have  formed  a province  of 
the  empire?  Might  not  Yarns  have  lost  his  three  legions  on  the  banks  of 
the  Rhone?  and  might  not  that  river  have  become  the  frontier  instead  of 
the  Rhine?  This  might  well  have  happened  if  Caesar  and  Crassus  had 
changed  provinces;  and  it  is  surely  impossible  to  say  that  in  such  an 
event  the  venue  (as  lawyers  say)  of  European  civilization  might  not  have 
been  changed.  The  Norman  Conquest  in  the  same  way  was  as  much  the 
act  of  a single  man,  as  the  writing  of  a newspaper  article;  and  knowing 
as  we  do  the  history  of  that  man  and  his  family,  we  can  retrospectively 
predict  with  all  but  infallible  certainty,  that  no  other  person”  (no  other  in 
that  age,  I presume,  is  meant)  “could  have  accomplished  the  enterprise. 
If  it  had  not  been  accomplished,  is  there  any  ground  to  suppose  that  either 
our  history  or  our  national  character  would  have  been  what  they  are?” 

As  is  most  truly  remarked  by  the  same  writer,  the  whole  stream  of  Gre- 
cian history,  as  cleared  up  by  Mr.  Grote,  is  one  series  of  examples  how  oft- 
en events  on  which  the  whole  destiny  of  subsequent  civilization  turned, 
were  dependent  on  the  personal  character  for  good  or  evil  of  some  one  in- 
dividual. It  must  be  said,  however,  that  Greece  furnishes  the  most  extreme 
example  of  this  nature  to  be  found  in  history,  and  is  a very  exaggerated 
specimen  of  the  general  tendency.  It  has  happened  only  that  once,  and 
will  probably  never  happen  again,  that  the  fortunes  of  mankind  depended 
upon  keeping  a certain  order  of  things  in  existence  in  a single  town,  or  a 
country  scarcely  larger  than  Yorkshire;  capable  of  being  ruined  or  saved 
by  a hundred  causes,  of  very  slight  magnitude  in  comparison  with  the  gen- 
eral tendencies  of  human  affairs.  Neither  ordinary  accidents,  nor  the  char- 
acters of  individuals,  can  ever  again  be  so  vitally  important  as  they  then 
were.  The  longer  our  species  lasts,  and  the  more  civilized  it  becomes,  the 
more,  as  Comte  remarks,  does  the  influence  of  past  generations  over  the 
present,  and  of  mankind  en  masse  over  every  individual  in  it,  predominate 
over  other  forces ; and  though  the  course  of  affairs  never  ceases  to  be  sus- 
ceptible of  alteration  both  by  accidents  and  by  personal  qualities,  the  in- 
creasing preponderance  of  the  collective  agency  of  the  species  over  all 
minor  causes,  is  constantly  bringing  the  general  evolution  of  the  race  into 
something  which  deviates  less  from  a certain  and  preappointed  track.  His- 
torical science,  therefore,  is  always  becoming  more  possible;  not  solely  be- 
cause it  is  better  studied,  but  because,  in  every  generation,  it  becomes  bet- 
ter adapted  for  study. 


CHAPTER  XII. 

OP  THE  LOGIC  OP  PRACTICE,  OR  ART;  INCLUDING  MORALITY  AND  POLICY. 

§ 1.  In  the  preceding  chapters  we  have  endeavored  to  characterize  the 
present  state  of  those  among  the  branches  of  knowledge  called  Moral,  which 
are  sciences  in  the  only  proper  sense  of  the  term,  that  is,  inquiries  into  the 
course  of  nature.  It  is  customary,  however,  to  include  under  the  term 


LOGIC  OF  PRACTICE,  OR  ART. 


653 


moral  knowledge,  and  even  (though  improperly)  under  that  of  moral  science, 
an  inquiry  the  results  of  which  do  not  express  themselves  in  the  indica- 
tive, hut  in  the  imperative  mood,  or  in  periphrases  equivalent  to  it;  what 
is  called  the  knowledge  of  duties ; practical  ethics,  or  morality. 

Now,  the  imperative  mood  is  the  characteiistic  of  art,  as  distinguished 
from  science.  Whatever  speaks  in  rules,  or  precepts,  not  in  assertions  re- 
specting matters  of  fact,  is  art;  and  ethics,  or  morality,  is  properly  a por- 
tion of  the  art  corresponding  to  the  sciences  of  human  nature  and  society.* 

The  Method,  therefore,  of  Ethics,  can  he  no  other  than  that  of  Art,  or 
Practice,  in  general;  and  the  portion  yet  uncompleted  of  the  task  which 
we  proposed  to  ourselves  in  the  concluding  Book,  is  to  characterize  the  gen- 
eral Method  of  Art,  as  distinguished  from  Science. 

§ 2.  In  all  branches  of  practical  business  there  are  cases  in  which  indi- 
viduals are  bound  to  conform  their  practice  to  a pre-established  rule,  while 
there  are  others  in  which  it  is  part  of  their  task  to  find  or  construct  the 
rule  by  which  they  are  to  govern  their  conduct.  The  first,  for  example,  is 
the  case  of  a judge,  under  a definite  written  code.  The  judge  is  not  called 
upon  to  determine  what  course  would  be  intrinsically  the  most  advisable 
in  the  particular  case  in  hand,  but  only  within  what  rule  of  law  it  falls  ; 
what  the  legislature  has  ordained  to  be  done  in  the  kind  of  case,  and  must 
therefore  be  presumed  to  have  intended  in  the  individual  case.  The  meth- 
od must  here  be  wholly  and  exclusively  one  of  ratiocination,  or  syllogism ; 
and  the  process  is  obviously,  what  in  our  analysis  of  the  syllogism  we 
showed  that  all  ratiocination  is,  namely  the  interpretation  of  a formula. 

In  order  that  our  illustration  of  the  opposite  case  may  be  taken  from  the 
same  class  of  subjects  as  the  former,  we  will  suppose,  in  contrast  with  the 
situation  of  the  judge,  the  position  of  the  legislator.  As  the  judge  has  laws 
for  his  guidance,  so  the  legislator  has  rules,  and  maxims  of  policy ; but  it 
would  be  a manifest  error  to  suppose  that  the  legislator  is  bound  by  these 
maxims  in  the  same  manner  as  the  judge  is  bound  by  the  laws,  and  that  all 
he  has  to  do  is  to  argue  down  from  them  to  the  particular  case,  as  the  judge 
does  from  the  laws.  The  legislator  is  bound  to  take  into  consideration  the 
reasons  or  grounds  of  the  maxim;  the  judge  has  nothing  to  do  with  those 
of  the  law, except  so  far  as  a consideration  of  them  may  throw  light  upon 
the  intention  of  the  law-maker,  where  his  words  have  left  it  doubtful.  To 
the  judge,  the  rule, once  positively  ascertained, is  final;  but  the  legislator, 
or  other  practitioner,  who  goes  by  rules  rather  than  by  their  reasons,  like 
the  old-fashioned  German  tacticians  who  were  vanquished  by  Napoleon, 
or  the  physician  who  preferred  that  his  patients  should  die  by  rule  rather 
than  recover  contrary  to  it,  is  l ightly  judged  to  be  a mere  pedant,  and  the 
slave  of  his  formulas. 

Now,  the  reasons  of  a maxim  of  policy,  or  of  any  other  rule  of  art,  can 
be  no  other  than  the  theorems  of  the  corresponding  science. 

The  relation  in  which  rules  of  art  stand  to  doctrines  of  science  may  be 
thus  characterized.  The  art  proposes  to  itself  an  end  to  be  attained,  de- 
fines the  end,  and  hands  it  over  to  the  science.  The  science  receives  it,  con- 
siders it  as  a phenomenon  or  effect  to  be  studied,  and  having  investigated 
its  causes  and  conditions,  sends  it  back  to  art  with  a theorem  of  the  com- 

* It  is  almost  superfluous  to  observe,  that  there  is  another  meaning  of  the  word  Art,  in 
which  it  may  be  said  to  denote  the  poetical  department  or  aspect  of  things  in  general,  in  con- 
tradistinction to  the  scientific.  In  the  text,  the  word  is  used  in  its  older,  and  I hope,  not  yet 
obsolete  sense. 


1)54 


LOGIC  OF  THE  MORAL  SCIENCES. 


bination  of  circumstances  by  which  it  could  be  produced.  Art  then  exam- 
ines these  combinations  of  circumstances,  arid  according  as  any  of  them  are 
or  are  not  in  human  power,  pronounces  the  end  attainable  or  not.  The  only 
one  of  the  premises,  therefore,  which  Art  supplies,  is  the  original  major 
premise,  which  asserts  that  the  attainment  of  the  given  end  is  desirable. 
Science  then  lends  to  Art  the  proposition  (obtained  by  a series  of  induc- 
tions or  of  deductions)  that  the  performance  of  certain  actions  will  attain 
the  end.  From  these  premises  Art  concludes  that  the  performance  of  these 
actions  is  desirable,  and  finding  it  also  practicable,  converts  the  theorem 
into  a rule  or  precept. 

§ 3.  It  deserves  particular  notice,  that  the  theorem  or  speculative  truth 
is  not  ripe  for  being  turned  into  a precept,  until  the  whole,  and  not  a part 
merely,  of  the  operation  which  belongs  to  science,  has  been  performed. 
Suppose  that  we  have  completed  the  scientific  process  only  up  to  a certain 
point ; have  discovered  that  a particular  cause  will  produce  the  desired  ef- 
fect, but  have  not  ascertained  all  the  negative  conditions  which  are  neces- 
sary, that  is,  all  the  circumstances  which,  if  present,  would  prevent  its  pro- 
duction. If,  in  this  imperfect  state  of  the  scientific  theory,  we  attempt  to 
frame  a rule  of  art,  we  perform  that  operation  prematurely.  Whenever  any 
counteracting  cause,  overlooked  by  the  theorem,  takes  place,  the  rule  will  be 
at  fault;  we  shall  employ  the  means  and  the  end  will  not  follow.  No  ar- 
guing from  or  about  the  rule  itself  will  then  help  us  through  the  difficulty; 
there  is  nothing  for  it  but  to  turn  back  and  finish  the  scientific  process 
which  should  have  preceded  the  formation  of  the  rule.  We  must  re-open 
the  investigation  to  inquire  into  the  remainder  of  the  conditions  on  which 
the  effect  depends  ; and  only  after  we  have  ascertained  the  whole  of  these 
are  we  prepared  to  transform  the  completed  law  of  the  effect  into  a pre- 
cept, in  which  those  circumstances  or  combinations  of  circumstances  which 
the  science  exhibits  as  conditions  are  prescribed  as  means. 

It  is  true  that,  for  the  sake  of  convenience,  rules  must  be  formed  from 
something  less  than  this  ideally  perfect  theory : in  the  first  place,  because 
the  theory  can  seldom  be  made  ideally  perfect;  and  next, because, if  all  the 
counteracting  contingencies,  whether  of  frequent  or  of  rare  occurrence, 
were  included,  the  rules  would  be  too  cumbrous  to  be  apprehended  and  re- 
membered by  ordinary  capacities,  on  the  common  occasions  of  life.  The 
rules  of  art  do  not  attempt  to  comprise  more  conditions  than  require  to  be 
attended  to  in  ordinary  cases;  and  are  therefore  always  imperfect.  In  the 
manual  arts,  where  the  requisite  conditions  are  not  numerous,  and  where 
those  which  the  rules  do  not  specify  are  generally  either  plain  to  common 
observation  or  speedily  learned  from  practice,  rules  may  often  be  safely  act- 
ed on  by  persons  who  know  nothing  more  than  the  rule.  But  in  the  com- 
plicated affairs  of  life,  and  still  more  in  those  of  states  and  societies,  rules 
can  not  be  relied  on,  without  constantly  referring  back  to  the  scientific  laws 
on  which  they  are  founded.  To  know  what  are  the  practical  contingen- 
cies which  require  a modification  of  the  rule,  or  which  are  altogether  ex- 
ceptions to  it,  is  to  know  what  combinations  of  circumstances  would  in- 
terfere with,  or  entirely  counteract,  the  consequences  of  those  laws;  and 
this  can  only  be  learned  by  a reference  to  the  theoretic  grounds  of  the  rule. 

By  a wise  practitioner,  therefore,  rules  of  conduct  will  only  be  consider- 
ed as  provisional.  Being  made  for  the  most  numerous  cases,  or  for  those 
of  most  ordinary  occurrence,  they  point  out  the  manner  in  which  it  will  be 
least  perilous  to  act,  where  time  or  means  do  not  exist  for  analyzing  the 


LOGIC  OF  PRACTICE,  OR  ART. 


655 


actual  circumstances  of  the  case,  or  where  we  can  not  trust  our  judgment 
in  estimating  them.  But  they  do  not  at  all  supersede  the  propriety  of  go- 
ing through,  when  circumstances  permit,  the  scientific  process  requisite 
for  framing  a rule  from  the  data  of  the  particular  case  before  us.  At  the 
same  time,  the  common  rule  may  very  properly  serve  as  an  admonition  that 
a certain  mode  of  action  has  been  found  by  ourselves  and  others  to  be  well 
adapted  to  the  cases  of  most  common  occurrence ; so  that  if  it  be  unsuita- 
ble to  the  case  in  hand,  the  reason  of  its  being  so  will  be  likely  to  arise 
from  some  unusual  circumstance. 

§ 4.  The  error  is  therefore  apparent  of  those  who  would  deduce  the  line 
of  conduct  proper  to  particular  cases  from  supposed  universal  practical 
maxims,  overlooking  the  necessity  of  constantly  referring  back  to  the  prin- 
ciples of  the  speculative  science,  in  order  to  be  sure  of  attaining  even  the 
specific  end  which  the  rules  have  in  view.  How  much  greater  still,  then, 
must  the  error  be,  of  setting  up  such  unbending  principles,  not  merely  as 
universal  rules  for  attaining  a given  end,  but  as  rules  of  conduct  generally, 
without  regard  to  the  possibility,  not  only  that  some  modifying  cause  may 
prevent  the  attainment  of  the  given  end  by  the  means  which  the  rule  pre- 
scribes, but  that  success  itself  may  contlict  with  some  other  end,  which  may 
possibly  chance  to  be  more  desirable. 

This  is  the  habitual  error  of  many  of  the  political  speculators  whom  I 
have  characterized  as  the  geometrical  school;  especially  in  France,  where 
ratiocination  from  rules  of  practice  forms  the  staple  commodity  of  journal-; 
ism  and  political  oratory — a misapprehension  of  the  functions  of  Deduction 
which  has  brought  much  discredit,  in  the  estimation  of  other  countries, 
upon  the  spirit  of  generalization  so  honorably  characteristic  of  the  French 
mind.  The  commonplaces  of  politics  in  France  are  large  and  sweeping 
practical  maxims,  from  which,  as  ultimate  premises,  men  reason  downward 
to  particular  applications;  and  this  they  call  being  logical  and  consistent. 
For  instance,  they  are  perpetually  arguing  that  such  and  such  a measure 
ought  to  be  adopted,  because  it  is  a consequence  of  the  principle  on  which 
the  form  of  government  is  founded;  of  the  principle  of  legitimacy,  or  the 
principle  of  the  sovereignty  of  the  people.  To  which  it  may  be  answered, 
that  if  these  be  really  practical  principles,  they  must  rest  on  speculative 
grounds ; the  sovereignty  of  the  people,  for  example,  must  be  a right  foun- 
dation for  government,  because  a government  thus  constituted  tends  to  pro- 
duce certain  beneficial  effects.  Inasmuch,  however,  as  no  government  pro- 
duces  all  possible  beneficial  effects,  but  all  are  attended  with  more  or  few- 
er inconveniences,  and  since  these  can  not  usually  be  combated  by  means 
drawn  from  the  very  causes  which  produce  them,  it  would  be  often  a much 
stronger  recommendation  of  some  practical  arrangement,  that  it  does  not 
follow  from  what  is  called  the  general  principle  of  the  government,  than 
that  it  does.  Under  a government  of  legitimacy,  the  presumption  is  far 
rather  in  favor  of  institutions  of  popular  origin ; and  in  a democracy,  in 
favor  of  arrangements  tending  to  check  the  impetus  of  popular  will.  The 
line  of  augmentation  so  commonly  mistaken  in  France  for  political  philoso- 
phy, tends  to  the  practical  conclusion  that  we  should  exert  our  utmost  ef- 
forts to  aggravate,  instead  of  alleviating,  whatever  are  the  characteristic 
imperfections  of  the  system  of  institutions  which  we  prefer,  or  under  which 
we  happen  to  live. 


5.  The  grounds,  then,  of  every  rule  of  art,  are  to  be  found  in  the  the- 


G56 


LOGIC  OF  THE  MORAL  SCIENCES. 


oreras  of  science.  An  art,  or  a body  of  art,  consists  of  the  rules,  together 
with  as  much  of  the  speculative  propositions  as  comprises  the  justification 
of  those  rules.  The  complete  art  of  any  matter  includes  a selection  of 
such  a portion  from  the  science  as  is  necessary  to  show  on  what  condi- 
tions the  effects,  which  the  art  aims  at  producing,  depend.  And  Art  in 
general,  consists  of  the  truths  of  Science,  arranged  in  the  most  convenient 
order  for  practice,  instead  of  the  order  which  is  the  most  convenient  for 
thought.  Science  groups  and  arranges  its  truths,  so  as  to  enable  us  to 
take  in  at  one  view  as  much  as  possible  of  the  general  order  of  the  uni- 
verse. Art,  though  it  must  assume  the  same  general  laws,  follows  them 
only  into  such  of  their  detailed  consequences  as  have  led  to  the  formation 
of  rules  of  conduct;  and  brings  together  from  parts  of  the  field  of  science 
most  remote  from  one  another,  the  truths  relating  to  the  production  of  the 
different  and  heterogeneous  conditions  necessary  to  each  effect  which  the 
exigencies  of  practical  life  require  to  be  produced.* 

Science,  therefore,  following  one  cause  to  its  various  effects,  while  art 
traces  one  effect  to  its  multiplied  and  diversified  causes  and  conditions, 
there  is  need  of  a set  of  intermediate  scientific  truths,  derived  from  the 
higher  generalities  of  science,  and  destined  to  serve  as  the  generalia  or 
first  principles  of  the  various  arts.  The  scientific  operation  of  framing 
these  intermediate  principles,  M.  Comte  characterizes  as  one  of  those  re- 
sults of  philosophy  which  are  reserved  for  futurity.  The  only  complete 
example  which  he  points  out  as  actually  realized,  and  which  can  be  held 
up  as  a type  to  be  imitated  in  more  important  matters,  is  the  general  the- 
ory of  the  art  of  Descriptive  Geometry,  as  conceived  by  M.  Monge.  It  is 
not,  however,  difficult  to  understand  what  the  nature  of  these  intermediate 
principles  must  generally  be.  After  framing  the  most  comprehensive  pos- 
sible conception  of  the  end  to  be  aimed  at,  that  is,  of  the  effect  to  be  pro- 
duced, and  determining  in  the  same  comprehensive  manner  the  set  of  con- 
ditions on  which  that  effect  depends,  there  remains  to  be  taken,  a general 
survey  of  the  resources  which  can  be  commanded  for  realizing  this  set  of 
conditions;  and  when  the  result  of  this  survey  has  been  embodied  in  the 
fewest  and  most  extensive  propositions  possible,  those  propositions  will 
express  the  general  relation  between  the  available  means  and  the  end,  and 
will  constitute  the  general  scientific  theory  of  the  art,  from  which  its 
practical  methods  will  follow  as  corollaries. 

§ G.  But  though  the  reasonings  which  connect  the  end  or  purpose  of  ev- 
ery art  with  its  means  belong  to  the  domain  of  Science,  the  definition  of 
the  end  itself  belongs  exclusively  to  Art,  and  forms  its  peculiar  province. 
Every  art  has  one  first  principle,  or  general  major  premise,  not  borrowed 
from  science;  that  which  enunciates  the  object  aimed  at,  and  affirms  it  to 
be  a desirable  object.  The  builder’s  art  assumes  that  it  is  desirable  to 
have  buildings;  architecture,  as  one  of  the  fine  arts,  that  it  is  desirable 
to  have  them  beautiful  or  imposing.  The  hygienic  and  medical  arts  as- 
sume, the  one  that  the  preservation  of  health,  the  other  that  the  cure  of 
disease,  are  fitting  and  desirable  ends.  These  are  not  propositions  of  sci- 
ence. Propositions  of  science  assert  a matter  of  fact : an  existence,  a co- 
existence, a succession,  or  a resemblance.  The  propositions  now  spoken 
of  do  not  assert  that  any  thing  is,  but  enjoin  or  recommend  that  something 
should  be.  They  are  a class  by  themselves.  A proposition  of  which  the 

* Professor  Bain  and  others  call  the  selection  from  the  truths  of  science  made  for  the  pur- 
poses of  an  art,  a Practical  Science,  and  confine  the  name  Art  to  the  actual  rules. 


LOGIC  OE  PRACTICE,  OR  ART. 


657 


predicate  is  expressed  by  the  words  ought  ov  should  be,  is  generically  dif- 
ferent from  one  which  is  expressed  by  is,  or  im.ll  be.  It  is  true,  that  in  the 
largest  sense  of  the  words,  even  these  propositions  assert  something  as  a 
matter  of  fact.  The  fact  affirmed  in  them  is,  that  the  conduct  recommend- 
ed excites  in  the  speaker’s  mind  the  feeling  of  approbation.  This,  how- 
ever, does  not  go  to  the  bottom  of  the  matter ; for  the  speaker’s  approba- 
tion is  no  sufficient  reason  why  other  people  should  approve ; nor  ought  it 
to  be  a conclusive  reason  even  with  himself.  For  the  purposes  of  practice, 
every  one  must  be  required  to  justify  his  approbation;  and  for  this  there 
is  need  of  general  premises,  determining  what  are  the  proper  objects  of  ap- 
probation, and  what  the  proper  order  of  precedence  among  those  objects. 

These  general  premises,  together  with  the  principal  conclusions  which  may 
be  deduced  from  them,  form  (or  rather  might  form)  a body  of  doctrine, ! 
which  is  properly  the  Art  of  Life,  in  its  three  departments,  Morality,  Pru- 
dence or  Policy,  and  ^Esthetics' the  Right,  the  Expedient,  and  the  Beau- 
tiful or  Noble,  in  human  conduct  and  works.  To  this  art  (which,  in  the 
main,  is  unfortunately  still  to  be  created),  all  other  arts  are  subordinate ; 
since  its  principles  are  those  which  must  determine  whether  the  special  aim 
of  any  particular  art  is  worthy  and  desirable,  and  what  is  its  place  in  the 
scale  of  desirable  things.  Every  art  is  thus  a joint  result  of  laws  of  nature 
disclosed  by  science,  and  of  the  general  principles  of  what  has  been  called 
Teleology,  or  the  Doctrine  of  Ends  ;*  which,  borrowing  the  language  of  the 
German  metaphysicians,  may  also  be  termed,  not  improperly,  the  principles 
of  Practical  Reason. 

A scientific  observer  or  reasoner,  merely  as  such,  is  not  an  adviser  for 
practice.  His  part  is  only  to  show  that  certain  consequences  follow  from 
certain  causes,  and  that  to  obtain  certain  ends,  certain  means  are  the  most  ef- 
fectual. Whether  the  ends  themselves  are  such  as  ought  to  be  pursued,  and 
if  so,  in  what  cases  and  to  how  great  a length,  it  is  no  part  of  his  business 
as  a cultivator  of  science  to  decide,  and  science  alone  will  never  qualify  him 
for  the  decision.  In  purely  physical  science,  there  is  not  much  temptation 
to  assume  this  ulterior  office ; but  those  who  treat  of  human  nature  and  so. 
ciety  invariably  claim  it : they  always  undertake  to  say,  not  merely  what 
is,  but  what  ought  to  be.  To  entitle  them  to  do  this,  a complete  doctrine 
of  Teleology  is  indispensable.  Al  scientific  theory,  however  perfect,  of  the 
subject-matter,  considered  merely  as  part  of  the  order  of  nature,  can  in  no 
degree  serve  as  a substitute.  In  this  respect  the  various  subordinate  arts 
afford  a misleading  analogy.  In  them  there  is  seldom  any  visible  necessity 
for  justifying  the  end,  since  in  general  its  desirableness  is  denied  by  nobody, 
and  it  is  only  when  the  question  of  precedence  is  to  be  decided  between 
that  end  and  some  other,  that  the  general  principles  of  Teleology  have  to 
be  called  in ; but  a writer  on  Morals  and  Politics  requires  those  principles 
at  every  step.  The  most  elaborate  and  well -digested  exposition  of  the 
laws  of  succession  and  co-existence  among  mental  or  social  phenomena,  and 
of  their  relation  to  one  another  as  causes  and  effects,  will  be  of  no  avail 
toward  the  art  of  Life  or  of  Society,  if  the  ends  to  be  aimed  at  by  that  art 
are  left  to  the  vague  suggestions  of  the  intellectus  sibi  permissus,  or  are 
taken  for  granted  without  analysis  or  questioning. 

§ 7.  There  is,  then,  a pliilosophia  prirna  peculiar  to  Art,  as  there  is  one 
which  belongs  to  Science.  There  are  not  only  first  principles  of  Knowl- 

* The  word  Teleology  is  also,  but  inconveniently  and  improperly,  employed  by  some  writers 
as  a name  for  the  attempt  to  explain  the  phenomena  of  the  universe  from  final  causes. 

42 


LOGIC  OF  THE  MORAL  SCIENCES. 


033 

edge,  but  first  principles  of  Conduct.  There  must  be  some  standard  by 
which  to  determine  the  goodness  or  badness,  absolute  and  comparative,  of 
ends,  or  objects  of  desire.  And  whatever  that  standard  is,  there  can  be  but 
one  ; for  if  there  were  several  ultimate  principles  of  conduct,  the  same  con- 
duct might  be  approved  by  one  of  those  principles  and  condemned  by  an- 
other; and  there  would  be  needed  some  more  general  principle,  as  umpire 
between  them. 

Accordingly,  writers  on  Moral  Philosophy  have  mostly  felt  the  necessity 
not  only  of  referring  all  rules  of  conduct,  and  all  judgments  of  praise  and 
blame,  to  principles,  but  of  referring  them  to  some  one  principle;  some 
rule,  or  standard,  with  which  all  other  rules  of  conduct  were  required  to  be 
consistent,  and  from  which  by  ultimate  consequence  they  could  all  be  de- 
duced. Those  who  have  dispensed  with  the  assumption  of  such  a universal 
standard,  have  only  been  enabled  to  do  so  by  supposing  that  a moral  sense, 
or  instinct,  inherent  in  our  constitution,  informs  us,  both  what  principles  of 
conduct  we  are  bound  to  observe,  and  also  in  what  order  these  should  be 
subordinated  to  one  another. 

The  theory  of  the  foundations  of  morality  is  a subject  which  it  would  be 
out  of  place,  in  a work  like  this,  to  discuss  at  large,  and  which  could  not  to 
any  useful  purpose  be  treated  incidentally.  I shall  content  myself,  therefore, 
with  saying,  that  the  doctrine  of  intuitive  moral  principles,  even  if  true, 
would  provide  only  for  that  portion  of  the  field  of  conduct  which  is  prop- 
erly called  moral.  For  the  remainder  of  the  practice  of  life  some  general 
principle,  or  standard,  must  still  be  sought;  and  if  that  principle  be  rightly 
chosen,  it  will  be  found,  I apprehend,  to  serve  quite  as  well  for  the  ultimate 
principle  of  Morality,  as  for  that  of  Prudence,  Policy,  or  Taste. 

Without  attempting  in  this  place  to  justify  my  opinion,  or  even  to  define 
the  kind  of  justification  which  it  admits  of,  I merely  declare  my  conviction, 
that  the  general  principle  to  which  all  rules  of  practice  ought  to  conform, 
and  the  test  by  which  they  should  be  tried,  is  that  of  conduciveness  t.o  the 
happiness  of  mankind,  or  rather,  of  all  sentient  beings ; in  other  words,  that 
the  promotion  of  happiness  is  the  ultimate  principle  of  Teleology.* 

I do  not  mean  to  assert  that  the  promotion  of  happiness  should  be  itself 
the  end  of  all  actions,  or  even  of  all  rules  of  action.  It  is  the  justification, 
and  ought  to  be  the  controller,  of  all  ends,  but  it  is  not  itself  the  sole  end. 
There  are  many  virtuous  actions,  auu  even  virtuous  modes  of  action  (though 
the  cases  are,  I think,  less  frequent  than  is  often  supposed),  by  which  hap- 
piness in  the  particular  instance  is  sacrificed,  more  pain  being  produced 
than  pleasure.  But  conduct  of  which  this  can  be  truly  asserted,  admits  of 
justification  only  because  it  can  be  shown  that,  on  the  whole,  more  happiness 
will  exist  in  the  world,  if  feelings  are  cultivated  which  will  make  people,  in 
certain  cases, regardless  of  happiness.  I fully  admit  that  this  is  true;  that 
the  cultivation  of  an  ideal  nobleness  of  will  and  conduct  should  be  to  indi- 
vidual human  beings  an  end,  to  which  the  specific  pursuit  either  of  their 
own  happiness  or  of  that  of  others  (except  so  far  as  included  in  that  idea) 
should,  in  any  case  of  confiict,  give  way.  But  I hold  that  the  very  ques- 
tion, what  constitutes  this  elevation  of  character,  is  itself  to  be  decided  by 
a reference  to  happiness  as  the  standard.  The  character  itself  should  be, 
to  the  individual,  a paramount  end,  simply  because  the  existence  of  this 
ideal  nobleness  of  character,  or  of  a near  approach  to  it,  in  any  abundance, 
would  go  farther  than  all  things  else  toward  making  human  life  happy, 

* For  an  express  discussion  and  vindication  of  this  principle,  see  the  little  volume  entitled 
“ Utilitarianism.” 


LOGIC  OF  PRACTICE,  OR  ART. 


659 


both  in  the  comparatively  humble  sense  of  pleasure  and  freedom  from 
pain,  and  in  the  higher  meaning,  of  rendering  life,  not  what  it  now  is  almost 
universally,  puerile  and  insignificant,  but  such  as  human  beings  with  high- 
ly developed  faculties  can  care  to  have. 

§ 8.  With  these  remarks  we  must  close  this  summary  view  of  the  appli- 
cation of  the  general  logic  of  scientific  inquiry  to  the  moral  and  social  de- 
partments of  science.  Notwithstanding  the  extreme  generality  of  the 
principles  of  method  which  I have  laid  down  (a  generality  which,  I trust, 
is  not,  in  this  instance,  synonymous  with  vagueness),  I have  indulged  the 
hope  that  to  some  of  those  on  whom  the  task  will  devolve  of  bringing  those 
most  important  of  all  sciences  into  a more  satisfactory  state,  these  observa- 
tions may  be  useful,  both  in  removing  erroneous,  and  in  clearing  up  the 
true,  conceptions  of  the  means  by  which,  on  subjects  of  so  high  a degree  of 
complication,  truth  can  be  attained.  Should  this  hope  be  realized,  what  is 
probably  destined  to  be  the  great  intellectual  achievement  of  the  next  two 
or  three  generations  of  European  thinkers  will  have  been  in  some  degree 
forwarded. 


THE  E2TOo 


